What were Patrick Henry's concerns in his speech before the Virginia Ratifying Convention?

In the simplest terms, Patrick Henry thought it was crazy for the United States to put themselves under the rule of a consolidated government. What had the Revolutionary War been fought over if not freedom from unfair tax policies and the oppressive British rule under the tyrant King George? Henry took issue with the idea of electing a president for fear of America appointing a despot of its own.
As an Anti-Federalist, Henry opposed big government and favored states' rights. At the time of Henry's speech, many Americans' strongest allegiance was to their state and not to America, which was still in its infancy. Henry was a five-term governor of Virginia, and as such, he was very concerned about the economic future of Virginia and the entire South. Henry simply did not trust the North to keep the South's best interests in mind, and he felt like he had been burned before. For example, it was Henry's belief that Congress failed to send enough troops to the Ohio River Valley to protect Virginia settlers there. He was also a staunch opponent of the Jay-Gardoqui Treaty, which would have sold the navigation rights to the Mississippi River to Spain for 25 long years.
Henry was a fierce protector of personal freedoms, as well. He wanted the Constitution to include a bill of rights that would safeguard individual rights. Liberty, Henry believed, should be America's highest and most shielded priority. He wanted the Constitution to set limits on the government's power and avoid placing the future of many in the hands of few. In particular, Henry wanted to strip the government of its power to establish and collect taxes. He and his fellow Anti-Federalists feared that if the government was allowed to tax and spend at will, they would quickly spiral out of control, racking up dangerous levels of debt.
Ultimately, Henry was defeated. Virginia approved the Constitution by a vote of 89-79, but Henry never wavered in his belief that the Constitution undermined the very spirit of the American Revolution.
http://press-pubs.uchicago.edu/founders/documents/v1ch8s38.html

Trace Elie Wiesel's faith. Does he ever regain it?

It is debatable whether Eliezer completely loses his faith in Night. However, there can be no doubt that his beliefs undergo substantial change throughout as a result of his experiences. Initially, Eliezer's faith is instinctive, unthinking, and an integral part of his cultural heritage. When a fellow prisoner asks him why he always cries when he prays, Eliezer is unable to give a satisfactory explanation. The same thing occurs when the man asks him the follow-up question "Why do you pray?":

Why did I pray? Strange question. Why did I live? Why did I breathe? "I don't know," I told him, even more troubled and ill at ease. "I don't know."

We sense that Eliezer has never really reflected on his faith before. However, the horrors of life in Auschwitz have changed all that. They challenge his faith; they force him to question everything he has ever believed in. Under the daily torments of life in the camp, Eliezer's understanding of what God is changes significantly. At first, he does not outright reject God's existence. Instead, he refuses to believe that he is a just, merciful God. He cannot reconcile such a God with the sheer evil and moral degradation he is forced to witness each day:

Blessed be God’s name? Why, but why would I bless Him? Every fiber in me rebelled. Because He caused thousands of children to burn in His mass graves? Because He kept six crematoria working day and night, including Sabbath and the Holy Days? Because in His great might, He had created Auschwitz, Birkenau, Buna, and so many other factories of death? How could I say to Him: Blessed be Thou, Almighty, Master of the Universe, who chose us among all nations to be tortured day and night, to watch as our fathers, our mothers, our brothers end up in the furnaces? Praised be Thy Holy Name, for having chosen us to be slaughtered on Thine altar?

It is only during the hanging of the young boy, the Kapo's assistant, that Eliezer's faith finally appears to vanish altogether. The young boy seems so fresh-faced and so innocent. His slow, painful death at the end of a rope represents a new low—even by the standards of Nazi brutality. As the prisoners are forced to watch the sordid spectacle, a voice cries out "Where is God now?" In his mind, Eliezer now believes that God has effectively died with the young boy.
Yet later on, Eliezer appears to have some belief in the existence of God once more, albeit in a somewhat ambiguous sense. However, this time he is no longer in the position of a suppliant; he is an accuser, castigating God for what he sees as his indifference toward the suffering of his chosen people:

I knew that my sins grieved the Almighty and so I pleaded for forgiveness. In those days, I fully believed that the salvation of the world depended on every one of my deeds, on every one of my prayers. But now, I no longer pleaded for anything. I was no longer able to lament. On the contrary, I felt very strong. I was the accuser, God the accused.

Whether or not this represents Eliezer's final position on the matter, we cannot know for sure. However, there seems little doubt that he derives new strength from his apostasy. Elie feels that, even if God does exist, he is no longer worthy of Eliezer's prayers; he is worthy only of ceaseless condemnation.

In Charles Dickens' novel Great Expectations, how are money and the sense of belonging portrayed in society from an approach of New Historicism?

New Historicism attempts to understand what a text tells us about currents of thought at the time it was written. From this approach, Great Expectations can be seen as a commentary on the rise of new types of wealthy English people and their attempt to emulate the manners and education of gentlemen and gentlewomen.
When Pip mysteriously comes into his fortune, he is working as a blacksmith's apprentice in Kent. After receiving his money, he travels to London and attempts to turn himself into a gentleman by dedicating himself to studying the classics, learning how to eat properly, and largely abandoning himself to idleness and sports such as rowing. However, while he becomes more learned, he never really feels like a gentleman, and when his money runs out, he returns to Kent and to feeling more comfortable alongside Joe, the kind but unlearned man who raised him. Using the approach of New Historicism, the reader can understand that Dickens is critiquing the ability of the new industrial classes from outside London to transform themselves into gentlemen. The reader can infer that the new classes were seen as ungentlemanly and that people at the time thought that money only gave the newly rich a veneer but did not truly turn them into people who belonged in the nobility.

Single Variable Calculus, Chapter 8, 8.1, Section 8.1, Problem 28

Evaluate $\displaystyle \int^2_1 \frac{(mx)^2}{x^3} dx$ by using Integration by parts.
If we let $u = mx$, then $e^u = x$ and $\displaystyle du = \frac{1}{dx} dx$ we must also make the upper and lower limits in terms of $u$, so...

$
\begin{equation}
\begin{aligned}
\text{so } \int^2_1 \frac{(\ln x)^2}{x^3} dx &= \int^{\ln(2)}_{\ln(1)} \frac{u^2}{(e^u)^3} x du = \int^{\ln 2}_0 \frac{u^2}{(eu)^3} (e^u) du\\
\\
&= \int^{\ln 2}_0 \frac{u^2}{e^{2u}} du
\end{aligned}
\end{equation}
$


To evaluate $\displaystyle \int^{\ln 2}_0 \frac{u^2}{e^{2u}} du$ we must use integration by parts. Then,
if we let $u_1 = u^2$ and $dv_1 = e^{-2u} du$
$du_1 = 2u du$ and $\displaystyle v_1 = \int e^{-2u} du = -\frac{1}{2} e^{-2u}$

So,

$
\begin{equation}
\begin{aligned}
\int^{\ln 2}_0 \frac{u^2}{e^{2u}} du = u_1 v_1 - \int v_1 du_1 &= - \frac{u^2}{2} e^{-2u} - \int -\frac{1}{2} e^{-2u} (2u du)\\
\\
&= -\frac{u^2}{2} e^{-2u} + \int ue^{-2u} du
\end{aligned}
\end{equation}
$

To evaluate $\displaystyle \int ue^{-2u} du$, we must use integration by parts once more, so...
If we let $u_2 = i$ and $dv_2 e^{-2u} du$, then
$du_2 = du$ and $\displaystyle v_2 = \int e^{-2u} du = -\frac{1}{2}e^{-2u}$

So,

$
\begin{equation}
\begin{aligned}
\int ue^{-2u} du = u_2 v_2 - \int v_2 du_2 &= -\frac{u}{2} e^{-2u} - \int \left( -\frac{1}{2}e^{-2u} \right) (du)\\
\\
&= -\frac{u}{2} e^{-2u} + \frac{1}{2} \int e^{-2u} du\\
\\
&= -\frac{u}{2} e^{-2u} + \frac{1}{2} \left( -\frac{1}{2} e^{-2u}\right)\\
\\
&= -\frac{u}{2} e^{-2u} - \frac{1}{4} e^{-2u}
\end{aligned}
\end{equation}
$


Going back to the first equation,

$
\begin{equation}
\begin{aligned}
\int^{\ln 2}_0 \frac{u^2}{e^{2u}} &= -\frac{u^2}{2} e^{-2u} + \left[ -\frac{u}{2} e^{-2u} - \frac{1}{4} e^{-2u} \right]\\
\\
&= -\frac{u^2}{2} e^{-2u} -\frac{u}{2}e^{-2u} - \frac{1}{4} e^{-2u}\\
\\
&= -\frac{e^{-2u}}{2} \left( -u^2 - u - \frac{1}{2} \right)
\end{aligned}
\end{equation}
$


Evaluating from 0 to $\ln 2$

$
\begin{equation}
\begin{aligned}
&= \left[ \frac{e^{-2 \ln 2}}{2} \left( -(\ln2)^2 - \ln 2 - \frac{1}{2} \right) \right] - \left[ \frac{e^{-2(0)}}{2} \left( 0^2 - 0 - \frac{1}{2} \right) \right]\\
\\
&= \frac{3}{16} - \frac{1}{8} \left[ (\ln 2)^2 + \ln 2 \right]
\end{aligned}
\end{equation}
$

Is the Industrial Revolution the real villain in Hard Times?

The Industrial Revolution certainly provides an appropriate backdrop for the exercise of serial villainy. Most of the characters in Hard Times have, to some extent, been corrupted by the rapid development of industrial capitalism—morally, spiritually, and economically. In the villainous character of Mr. Bounderby we have the epitome of the dark side of the Industrial Revolution with its rampant greed, exploitation, and crass materialism. Bounderby lives in the lap of luxury while his impoverished workforce slaves away to keep him in a position to which he's become accustomed.
And it's not just coldhearted plutocrats who are the product of the Industrial Revolution. The system also throws up unpleasant characters like the dastardly Slackbridge, a cynical demagogue who turns the workers against Stephen Blackpool because Stephen refuses to join his labor union.
Yet despite his harsh portrayal of entrepreneurs, business per se is not a problem for Dickens; rather, it's the particularly rapacious and exploitative variety of industrial capitalism to which he objects. Mr. Sleary, proprietor of a traveling circus, is presented in a sympathetic light. Making money and bringing much-needed joy and merriment to people's otherwise drab lives are by no means mutually exclusive activities, Dickens appears to be saying in this portrayal. This in turn makes the villainous behavior of the self-appointed captains of industry all the more repugnant. For the Bounderbys and Gradgrinds of this world, this is nothing more than humbug and mawkish sentimentality. In their world of the factory and the countinghouse, cold hard facts and utility must prevail. Their villainy is the villainy of the system to which they remain so utterly devoted.

Why might Parris refer to Reverend Hale as Mr. Hale?

Reverend Samuel Parris is not well-liked in the community of Salem, despite his position as their spiritual leader. Consequently, he is insecure. His insecurity drives him to try to exert more power and authority to compensate. Although he is responsible for inviting Reverend Hale to Salem to get to the bottom of what is plaguing the girls, his insecurity deepens when Hale arrives and takes charge of what should really be Parris's responsibilities. It is reasonable to think that Parris mistakenly thought that he would look like a wise leader for bringing in an expert consultant, but instead, he looks like a panicked and fearful weakling quickly relegated to the the sidelines. Reverend Hale has a reputation for being a witchcraft expert, and Parris quickly comes to view him as a rival. In calling him "Mr." instead of "Reverend," Parris is trying to downplay his rival's strength.

Is "A Day's Wait" a good title?

The short story "A Day's Wait" by Ernest Hemingway tells of a nine-year-old boy who becomes ill with a fever. His father, the narrator, sends him to bed and calls for the doctor. The doctor informs the father in the boy's presence that he has a temperature of 102 degrees. Downstairs out of the boy's earshot, the doctor says the boy will be fine and prescribes medicine. When the father tries to read to his son, the boy seems worried and distracted and refuses to sleep.
After the father returns from hunting, the boy confesses that he is waiting to die. In France where he attended school he was told that people with temperatures above 44 would die, and his is 102. The father explains that the means of measurement are different and that the boy is in no danger. After the explanation, the boy is able to sleep, but the next day he is emotionally sensitive.
The titles of stories are very important, as they are the first things readers notice when they are considering reading a piece of literature. Authors choose titles for several reasons. For instance, some titles reflect the theme of a story, the name of the main character, or the protagonist's occupation. Other titles might use a quote from a famous poem or song.
"A Day's Wait" has a seemingly very simple title. When you first hear it, you might think of waiting for a train or a bus, waiting for a special person to arrive, or waiting for an important event. However, the title takes on great significance when you realize that the boy has not merely been waiting for an important situation or circumstance. Fully convinced that his sickness is beyond cure, the boy has been waiting to die. All day he has been waiting for his very existence to be snuffed out. When you look at the title from this perspective, it has special meaning, so yes, it is a good title.

Ernest Hemingway chose the titles of his short stories with considerable care. They tend to be either allusive and descriptive ("Hills Like White Elephants," "The Short Happy Life of Francis Macomber," "A Clean, Well-Lighted Place") or very short and simple ("Indian Camp," "The Killers," "Cat in the Rain"). The latter style predominates and one has the sense that Hemingway preferred his titles as simple and direct as possible unless there was a very strong indication within the story of what the title ought to be.
"A Day's Wait" falls very firmly into the short and simple category: three monosyllables with approximately the same vowel sounds (exactly the same if you decided, admittedly rather artificially, to pronounce the initial "A" as "ay" rather than "uh"). Moreover, "Day's" sounds the same as "daze," a state of bewilderment and stupefaction which affects both father and son, while "Wait" is a homonym for the "weight" both have on their shoulders.
This aside, the title "A Day's Wait" perfectly suits Hemingway's iron control of his prose style. The boy is waiting for death and spends the day after the revelation of his mistake crying at things of no importance. The author, however, will not permit such hand-wringing in his prose style, which remains, like the title, laconic and unemotional.

"A Day's Wait" is an appropriate title for the story because the passage of a certain day makes all the difference in the psyche of the boy Schatz. 
Hemingway's "A Day's Wait" is what is called a slice of life story—a narrative that opens a brief window into real life and examines the philosophical implications of these moments. The narrative of "A Day's Wait" revolves around a boy's fever of 102 degrees Fahrenheit that the child misinterprets as 102 degrees Celsius because he has gone to school in France.
When his father leaves Schatz alone to rest, he does not realize that his son thinks he will soon die: Poor Schatz lies awake in his room, waiting throughout the day in the belief that he will not be alive the next day.

He lay still in the bed and seemed very detached from what was going on. . . [he] refused to let any one come into the room.

When Schatz's father returns, he takes his son's temperature, and Schatz asks him what the thermometer has read. "Something like a hundred," the father lies. "It was a hundred and two," Schatz counters. Then, the father notices that Schatz has been "holding tight onto himself about something."
When the father gets Schatz to reveal what he has been thinking, he realizes that Schatz "had been waiting to die all day, ever since nine o'clock in the morning." Sadly, Schatz's "day's wait" has been unnecessarily stressful because his fever is not dangerous. His father explains the difference between Celsius and Fahrenheit, and although Schatz is relieved and "the hold over himself relaxed, too," the boy is no longer the same, and he cries easily.

Why do some people tend to vote more than others? And what influences their choice of candidate?

According to the Pew Research Center (see the link below), people who vote intermittently are less likely to be married than those who vote regularly. They are also more likely to feel distrustful towards others, and they express less (not more) anger at the government. Intermittent voters, who don't always vote in elections, are less likely to know much about the candidates, and they report feeling bored about what goes on in politics. These voters are the most likely group to swing between candidates, and they tend to be less educated and less affluent than regular voters. People who don't vote at all or who are not even registered to vote, according to the Pew Research Center, don't believe that voting will make a difference and don't feel guilty about not voting. 
Who people vote for is influenced by several factors, including the voter's background. For example, African-Americans tend to vote for Democrats, and more women than men voted for Hillary Clinton. When John Kennedy, who was Catholic, ran for President, a majority of Catholic voters cast their votes for him. In addition, people's party identifications influence who they vote for, as people who are registered as Democrats tend to vote Democratic, while those registered as Republicans vote Republican. In addition, a voter's ideology affects their voting, as those who are more liberal tend to vote for more liberal candidates, while those who are more conservative seek out conservative candidate. Finally, people evaluate a candidate's personal characteristics, and their perceptions of the candidates' honesty and other personality factors influence their voting.  
https://www.icpsr.umich.edu/icpsrweb/instructors/setups/voting.jsp

https://www.people-press.org/2006/10/18/who-votes-who-doesnt-and-why/

What time period is "Sonny's Blues" set in?

Sonny's Blues is set in Harlem in the 1950s. Both the location and the historical setting are extremely important in relation to the themes explored by the book. The 1950s was a decade of enormous social change for African Americans. The nascent civil rights movement had scored a major victory in overturning segregation in the landmark Supreme Court ruling of Brown v. Board of Education in 1954. At the same time, growing numbers of African Americans migrated north to escape widespread prejudice in the South and to seek out employment opportunities. The populations of Northern and Midwestern cities grew rapidly as a consequence.
In the 1950s Harlem was the epicenter of a vibrant African American culture, especially in relation to various kinds of music. The importance of music in Harlem culture is reflected in Sonny's becoming a jazz pianist. But the 1950s setting also allows Baldwin to explore wide facets of the African American experience. As well as the richness and vibrancy of Harlem's cultural scene, we're also introduced to the seamier side of life—the drugs, the prejudice, the poverty, the lack of opportunity, the atomized nature of big city life.
In the character of the unnamed author, Sonny's brother, we're further provided with a glimpse into the lives of the growing black middle class. Sonny's brother is a math teacher with a stable family and a good standard of living. The contrast between his life and that of his drug addict criminal brother adds depth to the portrayal of a significant era in the history of African Americans.

According to Hurston, through what methods should African Americans attain their freedom and recognition? What role does black art, cultural expression, and creativity play?

"How It Feels to Be Colored Me," published in 1928, is a personal essay based both on Hurston's upbringing in Eatonville, Florida and part of her adulthood in New York City.
She addresses "methods of [attaining] freedom and recognition," as you mention, when writing about the "sobbing" school of Negrohood, a group from which she distinguishes herself. Hurston was referencing fellow writers in the Harlem Renaissance who focused on the more tragic elements of black identity. For Hurston, the flaw of this "school" lay in what she perceives as its pessimism, its persistent sense of injustice, and its backward stance toward life:

I do not belong to the sobbing school of Negrohood who hold that nature somehow has given them a lowdown dirty deal and whose feelings are all hurt about it. . . . No, I do not weep at the world—I am too busy sharpening my oyster knife.

The answer to attaining freedom was to perceive oneself as free. The world need not be a thing at which to "weep"; according to Hurston, it is a treat that, with some effort and even a bit of struggle, one could open and enjoy.
The fact that she is "the granddaughter of slaves" is no cause for "depression." For her, slavery was the price that she "paid for civilization" and access to the world. Conversely, she argues that her "white neighbor" has a more difficult time in life, for "no brown specter pulls up a chair beside me. . . . The game of keeping what one has is never so exciting as the game of getting." For her, it is an exciting time to be black. The whole world existed with "[everything] to be won and nothing to be lost." On the other hand, the "white neighbor" feared that black gain necessitated his loss.
Hurston had "no separate feeling about being an American citizen and colored"—and thus rejected W.E.B. Du Bois's notion of "double-consciousness." Instead, she indirectly references Walt Whitman's "Song of Myself" by describing herself as "merely a fragment of the Great Soul that surges within the boundaries." This sense of being a part of the universal collective gives her the sense of freedom to be herself ("When I set my hat at a certain angle and saunter down Seventh Avenue . . . feeling as snooty as the lions in front of the Forty-Second Street Library, for instance"). This sense of being "full of herself"—that is, aware and proud of all of her elements—leaves her astonished when someone discriminates against her: " How can any deny themselves the pleasure of my company? It's beyond me." That company includes not only her cultural and feminine expression, but also her extraordinary individual self, which, to Hurston, matters far more than anyone else's ideas of who she is.

Each of these stories culminates in a murder (the novel The White Tiger and the movie Theeb). How justified was each murder, respectively, and how does this murder and its justification serve as an embodiment of the core theme of each story?

Let's first consider the plot of each of these stories:
The movie Theeb, written and directed by Naji Abu Nowar, follows the story of the titular Theeb--an orphan who is the third son of a Bedouin sheik--as he attempts to survive in the Wadi Rum desert in 1916. In the film, Theeb and his older brother, Hussein, help guide a British officer, Edward, and an Arab man, Marji, to a Roman well that borders the Ottoman railway. However, shortly after discovering that the well is contaminated with dead bodies, Edward and Marji are shot by a gang of raiders. Although Hussein and Theeb manage to make an initial escape, Hussein is soon thereafter murdered by one of the men, and Theeb falls into a well. Theeb manages to climb out and eventually stumbles upon an unconscious man stationed on a camel. This man is Hassan, an injured mercenary. In their equally weakened states, Hassan and Theeb assist each other in escaping the desert terrain. They manage to make their way to an Ottoman railway station, discovering in the process many dead Arab revolutionaries who had depended on Edward's survival (as we learn that he was in possession of a detonator which was meant to blow up the railway). Hassan winds up selling Edward's belongings, which triggers a realization in Theeb: Hassan has betrayed his Arab brethren in supports of the Turks. Thus, Theeb shoots Hassan, killing him as revenge for this deceit and for the death of Hussein. 
Aravind Adiga's novel The White Tiger follows the story of Balram Halwai, the son of a rickshaw puller, who explains his escape from servitude through letters to the Chinese Premier, Wen Jiabao. Balram leaves behind his village of Laxmangarh to work in a teashop in Dhanbad, where he learns how to drive and gains knowledge about India's government by eavesdropping on his customers. He begins working as a driver for Ashok (a son of the city's landlord) and abandons his affiliations with his family, eventually making the move with Ashok and Pinky Madam (Ashok's wife) to New Delhi. After Pinky Madam runs over and kills a child while drunkenly driving Balram's vehicle one night, Balram is pressured to take responsibility for the death. Balram instead decides to murder Ashok in order to escape the "Rooster Coop." This sets off a chain of other violence, with Balram later paying off the family of a bike messenger killed by one of Balram's new business's drivers and with Balrom certain that his family has been murdered by Ashok's relatives as revenge. 
Your question of how "justified" each respective murder was is a difficult one. I don't know that we can necessarily say murder is ever justified--whether fictional or not--but perhaps we can consider the motives and emotions that supported these characters' actions.
I would argue that Theeb's decision to murder Hassan is a much more sympathetic (and, thus, "justified") one than Balram's decision to murder Ashok. Theeb is just a child who has been rendered totally alone in the world by the death of his brother; the murder is arguably an act of passion and awakening as Theeb transitions from adolescence into adulthood. This murder of Hassan was one that also represented an important political agenda/theme--the tensions in the Middle East during World War One and the Great Arab Revolt against the Ottoman Empire.  
Balram, on the other hand, had much more agency in his situation, and his decision to murder Ashok is one motivated out of self-interest rather than as revenge for some injustice. Balram's egotistical obsession with his own "freedom" at the cost of the lives of others is problematic. While his individualistic spirit and personal quest for autonomy may be inspiring thematically as he rises out of the "darkness" of the lower caste, it is ultimately achieved at a high price. One could understand why he did what he did, but it is also a more difficult decision for readers to swallow. 

Find evidence to prove that Macbeth feels guilty for the murder of Macduff's family.

What is really striking about the killing of Macduff's family is that Macbeth seems to feel very little guilt about it. When Macbeth kills Duncan, for instance, he is immediately overcome with guilt. He has hallucinations and wishes that Duncan would wake up from his eternal sleep. In contrast, when Macbeth sends his men to kill Macduff's wife and child, he does not experience any similar thoughts or feelings.
In fact, it is only in act 5, scene 8 that Macbeth expresses any feelings of guilt. Standing face to face with Macduff, he says:

My soul is too much charged
With blood of thine already.

In other words, Macbeth is saying that his soul is tainted by the murder of Macduff's family. It is clear that Macbeth feels some shame and guilt here because he tells Macduff to go away. He has no desire to further taint his soul with the blood of Macduff. 

How does the narrator say that nature speaks to those who visit in their happier hours?

The answer to this question can be found in lines 3-5 of this poem. The first two lines of the poem introduce readers to a man that really enjoys nature. He enjoys it so much that he is able to hold "communion" with nature.  

To him who in the love of Nature holds   
Communion with her visible forms,

Notice that "Nature" is capitalized. This alerts readers to the idea that nature might be more than a thing. The narrator might be telling readers that nature is a person. That suspicion is confirmed at the end of line 2 when the narrator says that "she" (Nature) speaks to him during his times of communion with her.  


To him who in the love of Nature holds   
Communion with her visible forms, she speaks   
A various language



The narrator then goes on to explain how Nature speaks to him. He explains that Nature responds differently to him depending on his mood. The first mood he explains is what the question is asking about. In his happier, "gayer" moods, nature speaks to him with a smile and gladness. She is also beautiful and eloquent. 


for his gayer hours   
She has a voice of gladness, and a smile   
And eloquence of beauty,



Basically, when he is happy, nature is happy. He then goes on to say that when he is sad, Nature responds with sympathy and helps him feel better.  


and she glides   
Into his darker musings, with a mild   
And healing sympathy, that steals away   
Their sharpness, ere he is aware. 



 

In Maniac Magee by Jerry Spinelli, why does the protagonist tell people his name is Jeffrey when everyone calls him Maniac?

Jeffrey's name is all he has left from his parents.
Jeffrey does not think of himself as a legend because he wants to be a normal kid with a normal address. The way Jeffrey’s nickname starts is that he is a stranger in town.  It is actually kind of sad.  No one knows who he is, and that is part of why they call him Maniac.  

Nobody knows who said it first, but somebody must have: "Kid's gotta be a maniac."…
And that was it. Nobody (except Amanda Beale) had any other name for him, so pretty soon, when they wanted to talk about the new kid, that's what they called him: Maniac. (Ch. 8) 

Jeffrey has a name, but what he doesn’t have is a family.  He wants an address.  He wants people to know who he is.  He wants to belong.  This is why he moves in with the Beales when they offer to let him stay, and why he goes down to look at the street number.  It doesn’t matter to Jeffrey that he is white and they are black.  He wants to be Jeffrey.  Amanda introduces him by name, though she does have to ask him his last name. 
Jeffrey does get tired of being called Maniac, even by people that he knows. 

And pretty soon everybody was saying it … and, finally, in the kitchen one day … Mrs. Beale said it: "You that Maniac?"
He told her what he told everyone. "I'm Jeffrey. You know me." Because he was afraid of losing his name, and with it the only thing he had left from his mother and father. (Ch. 14) 

Jeffrey’s name is important to him because it is all that is left of his family.  His parents died, and he ran away from his aunt and uncle because they were dysfunctional.  They were not ready to be a family.  

what was jonathan harker doing when he first discovered the count in the wooden box

In one entry in Harker's diary prior to his discovery of the Count in his box, it occurs to him that he has "not yet seen the Count in daylight." This leads him to wonder whether he actually sleeps at night, and Harker decides he must seek out where the Count sleeps and try to get into his room.
In the next entry, Harker recounts how he "made the effort" and escaped back to his own room unscathed. Taking off his boots, he climbed out of his own bedroom window and in through the Count's but found the room entry. Venturing through a "heavy door" in the corner of the room, he then descended down a dark passage, out of which came "the odour of old earth newly turned." Proceeding still further into the vaults, Harker found a pile of "great boxes" on a pile of "newly dug earth." In one of these lay the Count, "either dead or asleep," with his eyes open and yet not having the appearance of death.

Verify the identity. tan x plus pi divided by two = -cot x

Hello! Probably you mean "tangent of (x plus pi / 2)", not "(tangent of x) plus pi / 2", i.e. tan(x + pi / 2) = - cot (pi / 2).
It is correct. The simplest way to verify it is to recall that tan u = (sin u) / (cos u) and apply the known identities about the sine and cosine of a sum,
sin(u + v) = sin u cos v + cos u sin v and cos(u + v) = cos u cos v - sin u sin v.
Form these identities we obtain
tan(x + pi / 2) = (sin(x + pi / 2)) /(cos(x + pi / 2)) =(sin x cos(pi / 2) + cos x sin(pi / 2)) /(cosx cos(pi / 2) - sin x sin(pi / 2)).
Recall that sin( pi/2) = 1 and cos( pi/2) = 0, and the equality becomes
tan(x + pi / 2) = (cos x ) /( - sin x ),  which is indeed equal to -cot x.
 
Actually, one can directly use the identities sin(x+pi/2)=cos x and cos(x+pi/2)=-sin x.
 

Single Variable Calculus, Chapter 7, 7.4-1, Section 7.4-1, Problem 56

Determine $\displaystyle \frac{d^9}{dx^9} \left( x^8 \ln x \right)$

$
\begin{equation}
\begin{aligned}
\frac{d}{dx} \left( x^8 \ln x \right) &= x^8 \frac{d}{dx} (\ln x) + (\ln x) \frac{d}{dx} (x^8)\\
\\
\frac{d}{dx} \left( x^8 \ln x \right) &= x^8 \cdot \frac{1}{x} + \ln x \cdot 8 x^7\\
\\
\frac{d}{dx} \left( x^8 \ln x \right) &= x^7 + 8x^7 \ln x
\end{aligned}
\end{equation}
$


$
\begin{equation}
\begin{aligned}
\frac{d^2}{dx^2} \left( x^8 \ln x \right) &= \frac{d}{dx} (x^7) + \left[ 8x^7 \frac{d}{dx}(\ln x)+ (\ln x) 8 \frac{d}{dx} (x^7) \right]\\
\\
\frac{d^2}{dx^2} \left( x^8 \ln x \right) &= 7x^6 + 8x^7 \cdot \frac{1}{x} + \ln x \cdot 56 x^6\\
\\
\frac{d^2}{dx^2} \left( x^8 \ln x \right) &= 7x^6 + 8x^6 + 56x^6 \ln x\\
\\
\frac{d^2}{dx^2} \left( x^8 \ln x \right) &= 15x^6 + 56x^6 \ln x
\end{aligned}
\end{equation}
$


$
\begin{equation}
\begin{aligned}
\frac{d^3}{dx^3} \left( x^8 \ln x \right) &= 15 \frac{d}{dx} (x^6) + \left[ 56x^6 \frac{d}{dx} (\ln x) + (\ln x) 56 \frac{d}{dx}(x^6) \right]\\
\\
\frac{d^3}{dx^3} \left( x^8 \ln x \right) &= 15(6x^5) + 56x^6 \cdot \frac{1}{x} + \ln x \cdot 56(6x^5)\\
\\
\frac{d^3}{dx^3} \left( x^8 \ln x \right) &= 90x^5 + 56x^5 + 336x^5 \ln x\\
\\
\frac{d^3}{dx^3} \left( x^8 \ln x \right) &= 146x^5 + 336x^5 \ln x
\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}
\frac{d^4}{dx^4} \left( x^8 \ln x \right) &= 146 \frac{d}{dx} (x^5) + \left[ 336x^5 \frac{d}{dx} (\ln x) + (\ln x) 336 \frac{d}{dx}(x^5) \right]\\
\\
\frac{d^4}{dx^4} \left( x^8 \ln x \right) &= 146 (5x^4) + 336x^5 \cdot \frac{1}{x} + \ln x \cdot 336(5x^4)\\
\\
\frac{d^4}{dx^4} \left( x^8 \ln x \right) &= 730x^4 + 336x^4 + 1680 x^4 \ln x\\
\\
\frac{d^4}{dx^4} \left( x^8 \ln x \right) &= 1066 x^4 + 1680x^4 \ln x
\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}
\frac{d^5}{dx^5} \left( x^8 \ln x \right) &= 1066 \frac{d}{dx} (x^5) + \left[ 1680x^4 \frac{d}{dx} (\ln x) + (\ln x) 1680 \frac{d}{dx}(x^4) \right]\\
\\
\frac{d^5}{dx^5} \left( x^8 \ln x \right) &= 1066 (4x^3) + 1680x^4 \cdot \frac{1}{x} + \ln x \cdot 1680(4x^3)\\
\\
\frac{d^5}{dx^5} \left( x^8 \ln x \right) &= 4264x^3 + 1680x^3 + 6720 x^3 \ln x\\
\\
\frac{d^5}{dx^5} \left( x^8 \ln x \right) &= 5944 x^3 + 6720x^3 \ln x
\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}
\frac{d^6}{dx^6} \left( x^8 \ln x \right) &= 5944 \frac{d}{dx} (x^3) + \left[ 6720x^3 \frac{d}{dx} (\ln x) + (\ln x) 6720 \frac{d}{dx}(x^3) \right]\\
\\
\frac{d^6}{dx^6} \left( x^8 \ln x \right) &= 5944 (3x^2) + 6720 x^3 \cdot \frac{1}{x} + \ln x \cdot 6720(3x^2)\\
\\
\frac{d^6}{dx^6} \left( x^8 \ln x \right) &= 17832 x^2 + 6720 x^2 + 20160 x^2 \ln x\\
\\
\frac{d^6}{dx^6} \left( x^8 \ln x \right) &= 24552 x^2 + 20160 x^2 \ln x
\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}
\frac{d^7}{dx^7} \left( x^8 \ln x \right) &= 24552 \frac{d}{dx} (x^2) + \left[ 20160 x^2 \frac{d}{dx} (\ln x) + (\ln x) 20160 \frac{d}{dx}(x^2) \right]\\
\\
\frac{d^7}{dx^7} \left( x^8 \ln x \right) &= 24552 (2x) + 20160 x^2 \cdot \frac{1}{x} + \ln x \cdot 20160(2x)\\
\\
\frac{d^7}{dx^7} \left( x^8 \ln x \right) &= 49104 x + 20160 x + 40320 x\ln x\\
\\
\frac{d^7}{dx^7} \left( x^8 \ln x \right) &= 69264 x + 40320 x \ln x
\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}
\frac{d^8}{dx^8} \left( x^8 \ln x \right) &= 69264 \frac{d}{dx} (x) + \left[ 40320 x \frac{d}{dx} (\ln x) + (\ln x) 40320 \frac{d}{dx}(x) \right]\\
\\
\frac{d^8}{dx^8} \left( x^8 \ln x \right) &= 69264 + 40320 x \cdot \frac{1}{x} + 40320 \ln x\\
\\
\frac{d^8}{dx^8} \left( x^8 \ln x \right) &= 69264 + 40320 + 40320 \ln x\\
\\
\frac{d^8}{dx^8} \left( x^8 \ln x \right) &= 109584 + 40320 \ln x
\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}
\frac{d^9}{dx^9} \left( x^8 \ln x \right) &= \frac{d}{dx} (109584) + 40320 \frac{d}{dx}(\ln x)\\
\\
\frac{d^9}{dx^9} \left( x^8 \ln x \right) &= 0 + 40320 \cdot \frac{1}{x}
\\
\frac{d^9}{dx^9} \left( x^8 \ln x \right) &= \frac{40320}{x}
\end{aligned}
\end{equation}
$

In poem "David" by Earle Birney, what does Bobbie learn from his experience?

Bobbie learns that it is impossible to predict the consequences of one small act of carelessness.
In the poem, Bobbie goes mountain-climbing with his friend, David. The two friends climb a mountain in the Ramparts Range, Sundance Peak, Mount Inglismaldie, the Fortress, and the Finger in the Sawback Range. They also climb Mount Gleam, but it is a fictitious mountain. It is while climbing the Finger that David loses his balance and falls fifty feet. The accident occurs when David reaches out to steady Bobbie; in trying to save his friend from certain death, David loses his own foothold.
Later, we learn that the accident happened because Bobbie neglected to test his foothold as he climbed the Finger. Thus, he blames himself bitterly for David's suffering. For his part, David refuses to let Bobbie torture himself. He tries to get Bobbie to see that an unintentional mistake does not make someone a villain.
David bleeds profusely from the fall; from the poem, we can deduce that David has been paralyzed by his accident. Both Bobbie and David know that David will not leave the mountains alive; in the end, David asks his friend to do the unthinkable. He begs Bobbie to push him over the ledge so that he can end his suffering. Although Bobbie is horrified at the implications of his friend's request, he respects David's desire to be freed from his tormenting pain.
His merciful deed done, Bobbie tells us that he lost his youthful innocence forever on the day he pushed his friend to his death. Bobbie learns that unintentional mistakes can result in gruesome consequences that precipitate horrific moral choices.
https://rpo.library.utoronto.ca/poems/david

What does Mr. Martin buy at the cigar store in "The Catbird Seat"? Why is this unusual?

James Thurber's story "The Catbird Seat" opens with the following sentence:

Mr. Martin bought the pack of Camels on Monday night in the most crowded cigar store on Broadway.

This purchase was extremely unusual for Mr. Martin, the protagonist and viewpoint character, because he was known to be a nonsmoker. He plans to use one of the cigarettes to plant a false clue in Ulgine Barrows' apartment after he murders her. She smoked Lucky Strike cigarettes. Camels and Luckies were the two leading brands at the time the story was published in 1942. Both brands were heavily advertised on the radio, in magazines, on billboards, and on posters all over "point-of-purchase" settings. Television had not been introduced to American consumers at that time because World War II was still in progress and monopolized manufacturing production.

It was his idea to puff a few puffs on a Camel (after the rubbing-out), stub it out in the ashtray holding her lipstick-stained Luckies, and thus drag a small red herring across the trail.

No one noticed Martin when he bought the Camels. He was not the sort of man whom anyone would notice, especially on the main street of America's premier city. After he changes his mind about killing Ulgine Barrows and decides instead to pretend to be a deranged heroin addict who plans to kill their mutual employer Mr. Fitweiler with a bomb, she effectively eliminates herself from Martin's life by staging a big scene in Fitweiler's office the next morning.

"If you weren't such a drab, ordinary little man," she said, "I'd think you'd planned it all. Sticking your tongue out, saying you were sitting in the catbird seat, because you thought no one would believe me when I told it! My God, it's really too perfect!" She glared at Mr. Fitweiler. "Can't you see how he has tricked us, you old fool? Can't you see his little game?"

Mr. Martin planned to commit the perfect crime by murdering the woman and leaving a partly smoked Camel to create the impression that the smoker of that cigarette had been the killer. Instead, he changes his mind and creates a more perfect plot to get rid of Ulgine Barrows without killing her. Mr. Fitweiler is convinced that Mrs. Barrows is insane and has her forcibly removed from his office. Her career as Fitweiler's irresponsible "special adviser" is over.

In Bartleby, the Scrivener, what is Nippers like? Compared to Turkey, when is he a good worker? What does Bartleby's life edict ("I would prefer not to") mean?

Nippers and Turkey together form a kind of "clock" that marks the passage of the work day. Turkey is an older man who is an admirable worker in the morning, but, once dinner is done at 12, becomes more and more red-faced and passionate about his copying work -- to the point of making many mistakes:

The difficulty was, he was apt to be altogether too energetic. There was a strange, inflamed, flurried, flighty recklessness of activity about him. He would be incautious in dipping his pen into his inkstand. All his blots upon my documents, were dropped there after twelve o’clock, meridian.

The suggestion is that Turkey is red-faced in the afternoons because he has been drinking. The "red-ink" Nippers says he spends all his money on is probably liquor.
Nippers, on the other hand, is younger, more ambitious, yet prone to indigestion. Nippers, unlike Turkey, isn't a drinker, but his impatience with being a mere scrivener, coupled with his morning indigestion, makes him extremely irritable in the mornings:

Though concerning the self-indulgent habits of Turkey I had my own private surmises, yet touching Nippers I was well persuaded that whatever might be his faults in other respects, he was, at least, a temperate young man. But indeed, nature herself seemed to have been his vintner, and at his birth charged him so thoroughly with an irritable, brandy-like disposition, that all subsequent potations were needless. When I consider how, amid the stillness of my chambers, Nippers would sometimes impatiently rise from his seat, and stooping over his table, seize the whole desk, and move it, and jerk it, with a grim, grinding motion on the floor, as if the table were a perverse voluntary agent, intent on thwarting and vexing him; I plainly perceive that for Nippers, brandy and water were altogether superfluous.

Turkey does his best work in the mornings; Nippers calms down in the afternoons. Between the two of them, the lawyer is able to get a full day's work. It is, as he says, "a good natural arrangement under the circumstances."
Bartleby, of course, is a different story. Whereas Turkey and Nippers obey a sort of natural law, each having their own time for working, Bartleby works (or doesn't) whenever he wishes. His mantra of "I would prefer not to" can be understood in many ways. It is, of course, an outright refusal to work; but it can also be understood as a determination to take life on his own terms, come what may. It may be that ultimately what Bartleby "prefers not" to do is to be trapped in the mundane existence of people like Turkey and Nippers.

In "Contents of the Dead Man's Pocket," why does Tom go out on the ledge?

Tom Benecke risks his life by going out onto the ledge of his eleventh floor apartment because he desires business advancement above all else.
In his ambition for a promotion at work, Tom spends his free time and weekends on his new idea for "a grocery-store display method." One evening, rather than accompany his wife to a movie she had wanted to see, Tom decides to stay home and continue working on his project in the hope that it will lead to a promotion. If he finishes it before he returns to work on Monday, he can take it to his boss, who might read it over the weekend before seeing any other projects. 
Unfortunately, Mrs. Benecke's opening of the apartment door causes the warm air from the hall to enter the apartment. This rush of air passes through the room and lifts up Tom's yellow sheet from the desk. While Tom watches in dismay, the worksheet drops to the window ledge and slides out onto the ledge of the building. Desperately, Tom tries to reach it with his arms extended out the open window, but the yellow sheet is too far from him. Staring at the yellow paper for a long minute, Tom waits for it to move and fall to the street so that he can hurry to retrieve it. Unfortunately, the paper stubbornly sits on the ledge:

It was hard for him to understand that he actually had to abandon it--it was ridiculous--and he began to curse. Of all the papers on his desk, why did it have to be this one in particular!

This single yellow sheet contains the efforts of many lunch hours, four long Saturdays, "snatched half hours" at work, and many evenings at home. It would take months to redo this project. As Tom reflects upon all the hours he has spent toiling on this project, he realizes he cannot let the yellow sheet just lie there. To him, it represents a chance to become "a name in the minds of the company officials." Therefore, he decides to retrieve it by going out onto the ledge.

In the short story “Contents of the Dead Man’s Pocket” by Jack Finney, Tom Benecke goes out on the ledge of his apartment building to retrieve a piece of paper. It is not just any piece of paper; it is ledger containing the results of many months of personal market research Tom accumulated in hope of presenting new, innovative ideas to his bosses. He must decide whether the risk of retrieving the piece of paper is worth the reward.
The author alludes to a play on words by having Tom “go out on a ledge.” When one does that, they are generally putting themselves in a dangerous or difficult situation with the hope of receiving accolades or rewards for presenting an idea that goes against the mainstream. In this case, Tom goes out on the ledge of a building that is eleven stories above a busy New York City street.
As you read the story, you determine whether the risk was worth the reward for Tom’s escapades on that ledge.

Who is Emmanuel Goldstein?

Emmanuel Goldstein is considered Big Brother’s most prominent enemy, who is a figurehead for the opposition and is used as a scapegoat by the Party. According to the Party, Goldstein is the leader of an underground anti-government organization known as the Brotherhood and wrote a book that explains how the authoritarian regime retains its power and control. The Party uses Emmanuel Goldstein to cultivate a hysterical atmosphere and displays his image during the daily Two Minutes Hate period. Emmanuel Goldstein is an enigmatic figure, whose whereabouts remain unknown and is dedicated to the demise of the Party and Big Brother. Fittingly, the Party blames its mistakes and miscalculations on Emmanuel Goldstein and portrays him as the ultimate villain.
Whether or not Goldstein actually exists remains unclear, but the Party does use his image and identity to strike fear into the hearts of Party members. Winston Smith, who is a political dissident, is attracted to Goldstein’s anti-government rhetoric and actually attempts to join the Brotherhood. Overall, Emmanuel Goldstein is the figurehead of the Party’s opposition and is depicted as Big Brother’s most prominent enemy.

Emmanuel Goldstein is a supposed opposition figure to Big Brother and the leading enemy of the state. O'Brien tells Winston and Julia that he is also head of a subversive underground organization called The Brotherhood, which is determined to overthrow the Party. Goldstein is said to be a great intellectual and to have written a number of books that set out, in great detail, how the Party may be defeated.
No one is absolutely certain that Emmanuel Goldstein even exists. As for The Brotherhood, it is almost certainly wholly fictitious as O'Brien is not, as he claims, an enemy of the Party, but a high-ranking cadre who is going to destroy Winston and Julia. The likelihood is that Goldstein does not really exist; he is a creation of the Party, a hate figure used as a convenient scapegoat for the the regime's failures. Inventing an oppositional figure also allows the Party to flush out potential subversives who may be inspired by his liberating message. Though deeply cynical, this is a successful counter-revolutionary strategy, one that lures Winston and Julia into a deadly trap.

Single Variable Calculus, Chapter 3, 3.6, Section 3.6, Problem 40

By using implicit differentiation, show that the tangent to the ellipse $\displaystyle \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ at the point $(x_0, y_0)$ is $\displaystyle \frac{x_0 x}{a^2} + \frac{y_0 y}{b^2} = 1$

Taking the derivative of the ellipse implicitly we get


$
\begin{equation}
\begin{aligned}

\frac{1}{a^2} (2x) + \frac{1}{b^2} \left( 2y \frac{dy}{dx} \right) =& 0
\\
\\
\frac{dy}{dx} =& \frac{xb^2}{ya^2}

\end{aligned}
\end{equation}
$



Using Point Slope Form @ $(x_0, y_0)$


$
\begin{equation}
\begin{aligned}

y - y_0 =& m(x - x_0)
\\
\\
y - y_0 =& \frac{xb^2}{ya^2} (x - x_0)

\end{aligned}
\end{equation}
$


Multiplying $\displaystyle \frac{y}{b^2}$ on both sides of the equation we have..


$
\begin{equation}
\begin{aligned}

\frac{y}{b^2} (y - y_0) =& \frac{x}{a^2} (x - x_0)
\\
\\
\frac{y^2}{b^2} - \frac{yy_0}{b^2} =& \frac{x^2}{a^2} - \frac{xx_0}{a^2}
\\
\\
\frac{xx_0}{a^2} - \frac{yy_0}{b^2} =& \frac{x^2}{a^2} - \frac{y^2}{b^2}

\end{aligned}
\end{equation}
$


From the given equation, we know that $\displaystyle \left( \frac{x^2}{a^2} - \frac{y^2}{b^2} \right) = 1$ so..

$\displaystyle \frac{xx_0}{a^2} - \frac{yy_0}{b^2} = 1$\

Hence, the equation of the tangent line at point $(x_0, y_0)$

Why does the Declaration of Independence use the word “unalienable” to describe the rights listed in the preamble?

"Unalienable rights" or "inalienable rights" is another way to describe "natural rights." This is a reflection of the Founding Fathers' ideology. They believed that all human beings are given a certain set of rights by God. They are natural in that they belong to us not by virtue of our being American, French, British, or any other nationality, but simply because we are human. Because these rights are God-given and natural, they cannot legitimately be interfered with by any human institution, such as government. In other words, they are "inalienable."
Jefferson included "life, liberty, and the pursuit of happiness" as among our inalienable rights. If we examine each one of them carefully, we can see that they are all necessary components of what most people would regard as essential to our humanity. We cannot truly flourish as human beings if our right to life is in any way violated. Nor can we can do so if we are restricted from using our innate liberty to pursue our own projects and goals in life, "the pursuit of happiness" in the Declaration's famous words.
The biggest threat to our inalienable rights is the unchecked power of government. Government, unlike our inalienable rights, is artificial. It exists to serve and protect our natural rights. The Founding Fathers set about constructing political institutions that would fulfill this purpose. This warranted the establishment of a limited government with a system of checks and balances in order to prevent any one branch of government from getting too powerful and potentially abusing its power to threaten our inalienable rights.

Is there evidence of sexism in For Whom the Bell Tolls?

A common theme in the work of Ernest Hemingway is gender dynamics, femininity, and masculinity. In his epic For Whom the Bell Tolls, these themes are pervasive. The novel takes place during the Spanish Civil War and follows a group of rebellious guerilla fighters that include both men and women.
When the novel's protagonist, Robert Jordan, begins a sexual relationship with Maria, a young woman who had her head shaved after being raped by a gang of fascists, she is frequently objectified by Jordan as a sexual object. When she is unable or unwilling to perform sexual acts with him, he becomes frustrated and wholly disappointed. While he pretends to be satisfied with lying near her and conversing, his disappointment is evident, thus suggesting his categorizing her as a sexual being.
Pilar, the heroic and headstrong female leader/maternal figure of the rebellious guerrilla group, often is criticized by Maria and the men for possessing traits they consider masculine. "Why do you speak in such a brutal manner," Maria says to her in one passage (140). In another passage, Pilar says to a male member of the group, Primitivo, "Thou must act like a man," (299). This reinforces the gender roles set about and questioned by Hemingway. In these roles, women are not meant to be brutal, while men are not meant to be delicate. The men speak crudely to Pilar, "thou hast the tongue of the great whore!" (383).
Even though Hemingway certainly seems aware of the sexist overtones of For Whom the Bell Tolls, it becomes difficult to classify the novel itself as sexist, particularly because of the questioning of these dynamics. Pilar is often criticized for not being feminine, yet she continues in her crude ways, often bullying some of the men. Maria is sexualized by Robert Jordan, but after they have sex, these dynamics are questioned. She finds power in her sexuality, and she finds enjoyment in it. Robert attempts to speak to her, but she replies, "speak not" (379). The stereotype of emotionally vulnerable, talkative women is placed here upon Robert Jordan, who attempts to converse with the silent and distant Maria.
While For Whom the Bell Tolls may contain elements of sexism, Hemingway veers from making the novel itself a sexist work. Confident and surely ahead of his time, Hemingway praises the untraditional female character of Pilar, giving her great power over the men. Maria, too, is given power, though in her sexuality, over Robert Jordan.

sum_(n=1)^oo 1/n^(1/2) Use the Integral Test to determine the convergence or divergence of the p-series.

The Integral test is applicable if f is positive and decreasing function on the infinite interval [k, oo) where kgt= 1 and a_n=f(x) . Then the series sum_(n=1)^oo a_n converges if and only if the improper integral int_1^oo f(x) dx converges. If the integral diverges then the series also diverges.
For the given series sum_(n=1)^oo 1/n^(1/2) , then a_n = 1/n^(1/2) then applying a_n=f(x) , we consider:
f(x) = 1/x^(1/2) .  
As shown on the graph of f(x) , the function is positive on the interval [1,oo) . As x at the denominator side gets larger, the function value decreases.

 
Therefore, we may determine the convergence of the improper integral as:
int_1^oo 1/x^(1/2) = lim_(t-gtoo)int_1^t 1/x^(1/2) dx
Apply Law of exponent: 1/x^m = x^(-m) .
lim_(t-gtoo)int_1^t 1/x^(1/2) dx =lim_(t-gtoo)int_1^t x^(-1/2) dx
Apply Power rule for integration: int x^n dx = x^(n+1)/(n+1) .
lim_(t-gtoo)int_1^t x^(-1/2) dx=lim_(t-gtoo)[ x^(-1/2+1)/(-1/2+1)]|_1^t
                               =lim_(t-gtoo)[ x^(1/2)/(1/2)]|_1^t
                                =lim_(t-gtoo)[ x^(1/2)*(2/1)]|_1^t
                                =lim_(t-gtoo)[ 2x^(1/2)]|_1^t
                             or  lim_(t-gtoo)[ 2sqrt(x)]|_1^t
Apply definite integral formula: F(x)|_a^b = F(b)-F(a) .
lim_(t-gtoo)[ 2sqrt(x)]|_1^t=lim_(t-gtoo)[2sqrt(t) -2sqrt(1)]
                            =lim_(t-gtoo)[2sqrt(t) -2*1]
                           =lim_(t-gtoo)[2sqrt(t) -2]
                          = oo
Note: lim_(t-gtoo)( -2) =-2 and lim_(t-gtoo)2sqrt(t) = oo then oo-2~~oo .
The lim_(t-gtoo)[ 2sqrt(x)]|_1^t = oo implies that the integral diverges.
Conclusion: The integralint_1^oo 1/x^(1/2) diverges, therefore the series sum_(n=1)^oo 1/n^(1/2) must also diverge.

For "My Papa's Waltz" by Theodore Roethke, write an analysis of the poem's use of imagery and/or symbolism.

This poem by Theodore Roethke can be interpreted on two levels. Read literally, it is a poem about a "waltz," or "romp," between a young boy and his father, which the boy finds "not easy." Symbolically, however, the waltz may represent something bigger than itself, with the elements which make the waltz "not easy" for the boy giving us indications of how the boy and his father interact in their wider relationship.
The very first line of the poem serves to support this thesis: the "whiskey on your breath / Could make a small boy dizzy." We know already, then, that the father, intoxicated, has initiated this "waltz" between himself and his son, in which the boy "hung on like death." The dance is not easy for him, nor do we get the sense that there has been a mutual decision to dance. We could interpret this, then, as a suggestion that the father's relationship with whiskey, in the boy's mind, influenced some elements of their relationship, and that the boy perhaps felt that he was forced to simply hang on while his father made decisions about that relationship and its direction.
The imagery in the poem very much enhances the symbolism of the waltz-as-relationship. The two of them "romped," a word which has undertones of something rougher than a dance, "until the pans slid from the shelf." A "romp" is generally defined as rough, energetic play, usually between children. In this instance, it may be that the father does not know his own strength, or that he is so much stronger than his son that the effect of his energetic approach is that "the pans slid from the shelf." The landscape around the two is changed, broken down, by the father's behavior, although there is no suggestion that this is deliberate. The mother's expression, however—which "could not unfrown itself"—suggests disapproval from her: she has observed, perhaps, how the father's behavior affects their son, but does not feel able to interrupt.
The final two stanzas give a hint of something else in the relationship between father and son. The father's hand, which "held my wrist / Was battered on one knuckle." Meanwhile, the sensory image of the father's buckle which "scraped" the boy's ear "at every step you missed" raises the specter of what else the father might use the buckle for. Every time the father missteps, the son suffers a minor pain, but he does not complain. The fact that these are missteps, rather than deliberate, again suggests that the boy does not blame his father entirely; it is carelessness, rather than malice, causing the discomfort. But the interconnection between these missteps and the belt buckle has undertones of corporal punishment: the boy is keenly aware of his proximity to the buckle, as if he has encountered it intimately before.
This man, with his "battered" hands, who "beat time on" his son's head, is not depicted as a villain, but he is strong, capable of missing steps, and overly rough with his child. The "whiskey on his breath" is foregrounded as the first image in the poem, indicating that it is important in the son's memory of his father. If the waltz in the poem symbolizes the relationship with father and son, we can observe that the son feels powerless in it: the waltz is controlled by his whiskey-drinking, mistake-prone father, and the son suffers consequences for his father's mistakes but does not feel able to protest—perhaps because he knows that, at heart, the father genuinely means no malice.

xdy = (x + y + 2)dx , y(1) = 10 Find the particular solution of the differential equation that satisfies the initial condition

Given xdy = (x + y + 2)dx
=> xdy/dx = (x + y + 2)
=> y'=1+y/x+2/x
=> y'-y/x = 1+2/x
=> y'-y/x =(x+2)/x
when the first order linear ordinary differential equation has the form of
y'+p(x)y=q(x)
then the general solution is ,
y(x)=((int e^(int p(x) dx) *q(x)) dx +c)/e^(int p(x) dx)
so,
y'-y/x =(x+2)/x--------(1)
y'+p(x)y=q(x)---------(2)
on comparing both we get,
p(x) = -1/x and q(x)=(x+2)/x
so on solving with the above general solution we get:
y(x)=((int e^(int p(x) dx) *q(x)) dx +c)/e^(int p(x) dx)
=((int e^(int (-1/x) dx) *((x+2)/x)) dx +c)/e^(int (-1/x) dx)
first we shall solve
e^(int (-1/x) dx)=e^(ln(1/x)) = (1/x)     
so
proceeding further, we get
y(x) =((int e^(int (-1/x) dx) *((x+2)/x)) dx +c)/e^(int (-1/x) dx)
=((int (1/x) *((x+2)/x)) dx +c)/(1/x)
=(int (1/x) *((1+(2)/x)) dx +c)/(1/x)
= x(ln(x)-2/x +c)
so now let us find the particular solution of differential equation at y(1)=10
y(1) = 1(ln(1)-2/1 +c)
=> 10 = 0-2+c
c=12
y(x) =x(ln(x)-2/x +12) is the solution

(x+y)dx - xdy = 0 Solve the first-order differential equation by any appropriate method

Given (x+y)dx - xdy= 0
=> (x+y) - xdy/dx= 0
=> x+y-xy'=0
=> x+y=xy'
=> 1+y/x=y'
=> y' -y/x=1
when the first order linear ordinary differential equation has the form of
y'+p(x)y=q(x)
then the general solution is ,
y(x)=((int e^(int p(x) dx) *q(x)) dx +c)/e^(int p(x) dx)
so,
y' -y/x=1--------(1)
y'+p(x)y=q(x)---------(2)
on comparing both we get,
p(x) = -1/x and q(x)=1
so on solving with the above general solution we get:
y(x)=((int e^(int p(x) dx) *q(x)) dx +c)/e^(int p(x) dx
=(int e^(int (-1/x) dx) *(1) dx +c)/e^(int (-1/x) dx)
first we shall solve
e^(int (-1/x) dx)=e^(-ln(x))=1/x     
so
proceeding further, we get
y(x) =(int e^(int (-1/x) dx) *(1) dx +c)/e^(int -1/x dx)
 =(int (1/x) *(1) dx +c)/(1/x)
=(ln(x) +c)/(1/x ) = x(ln(x)+c)
So , y(x) = x(ln(x)+c)

What was the price of a newspaper in the 1920s?

The day after the Wall Street Crash in 1929, The New York Times cost the princely sum of two cents. Meanwhile, out West in Wisconsin, The Milwaukee Leader, a publication with a much smaller circulation, cost a penny more.
Overall, the cover price of newspapers didn't change all that much over the course of the decade. The demand for news and the supply of paper remained relatively stable throughout this period, ensuring that there were no significant fluctuations in the price of newsprint. Fierce competition also kept prices down as most American cities had several newspapers, each with a morning and an evening edition. Increased automation and developments in printing technology kept production costs low which inevitably had a knock-on effect on cover prices. As papers were also the main source of news for most Americans, they could count on a regular supply of advertising revenue to keep going, something that in this digital age is no longer the case.

The answer to this depends, of course, upon which country we're discussing and which year from this decade we're talking about, as it's always possible that prices may have changed over a ten year period. As such, we'll need to check 1920 and 1929 to see these trends. There is a very helpful website providing historic prices, hosted by Morris County Library in New Jersey. This website allows you to find the prices of most standard everyday items in any year of your choice.
According to Morris County Library, a newspaper in 1920, undefined as to the type of newspaper, cost 2 cents. Morris County Library also finds that newspapers in 1929 were still 2 cents. The record for 1925 specifies that this paper was the NJ Daily Record.

Calculus: Early Transcendentals, Chapter 7, 7.2, Section 7.2, Problem 9

Let us call our integral I.
I=int_0^pi cos^4 2t dt=int_0^pi(cos^2 2t)^2dt
Use formula for cosine of double angle: cos^2 theta=(1+cos2theta)/2
int_0^pi((1+cos4t)/2)^2dt=1/4int_0^pi(1+2cos4t+cos^2 4t)dt=
1/4int_0^pi dt+1/2int_0^pi cos4tdt+1/4int_0^picos^2 4tdt
Let us denote the above three integrals by I_1,I_2 and I_3 respectively i.e.
I=1/4I_1+1/2I_2+1/4I_3
I_1=t|_0^pi=pi
To solve I_2 we make substitution u=4t=>(du)/4=dt with new limits of integration u_1=4cdot0=0 and u_2=4cdotpi=4pi.
I_2=1/4int_0^(4pi)cos u du=1/4sin u|_0^(4pi)=0
To calculate I_3 we use formula for cosine of double angle once again.
I_3=int_0^pi(1+cos8t)/2 dt
Make substitution u=8t=>(du)/8=dt with new limits of integration u_1=8cdot0=0 and u_2=8cdotpi=8pi
1/16int_0^(8pi)(1+cos u)du=1/16(u+sin u)|_0^(8pi)=1/16(8pi+0-0-0)=pi/2
Now that we have calculated the three integrals we can return to calculate I.
I=1/4cdot pi+1/2cdot0+1/4cdotpi/2=pi/4+pi/8=(3pi)/8

How can I do a character analysis for We Need To Talk About Kevin by Lionel Shriver?

We Need to Talk about Kevin is a disturbing novel with many disturbing characters.  A character analysis most definitely should focus on one of the three main characters--Kevin, his mother Eva, or his father Franklin.  Any of these three would make a fascinating character, or even psychological, study.  
Kevin is introduced as a hopeless psychopath.  From the time he is an infant, he is different and unsettling.  He won't nurse, he destroys his mother's projects, he refuses to talk.  Even his nanny, who has much experience with children, finds him uncontrollable.  As the novel progresses, we see Kevin's psychopathic tendencies worsen.  He is cruel to other children at school, but he is especially vicious to his little sister Cecilia when he convinces her to wash her eye out with Draino.  Despite others' attempt to befriend him--his English teacher, who tries to bring out Kevin's potential in writing; his father, who believes in him and defends him; and even his mother who sees Kevin for what he is and tries to manage him--Kevin cannot be helped and is the perpetrator of a cruel, senseless mass murder at school.  Any character analysis of Kevin would have to involve his detachment from his mother, his contempt of his father, and his rejection of all those who try to help him and are deceived by him.  Shriver seems to show us that some people are born this way and how easy it is for others to misjudge them because it's difficult to believe that a son, student, friend, or child can be evil.  If you were to focus on Kevin, you might look at his relationship with his mother and how that develops throughout the novel, his relationship with his father, and how his actions become more and more savage, devious, and manipulative.  His victims seem to be those who seem to see him as normal or good.  The focus should be not really on why Kevin acts as he does--there may be no real explanation for why some people are how they are--but on the way others treat Kevin or refuse to see the truth.   

1. What is your reaction to Junot Díaz’s “How to Date a Browngirl, Blackgirl, Whitegirl, or Halfie”? Did you enjoy reading this story? Why, or why not? 2. Describe the narrator, Yunior. Does he seem realistic to you? Does he fit with Cleeve’s concept of a character that “springs alive”? If so, what makes this character seem especially real to you? 3. What are some of the major and minor themes that this story presents? 4. Meyer describes irony as “a device that reveals a reality different from what appears to be true” (226). Can this story be described as ironic? What in the style and tone of this story reveal that “what we see” in Yunior is not really “what we get” (ibid.).

What you think of this story is up to you. Did you find yourself relating to Yunior, or did you find him too cynical? Many readers enjoy the story's sense of realism; Yunior seems like a real guy who has ulterior motives and tries to sweet talk girls into giving him sexual favors. For example, he says, "It must have been hard" when trying to romance "halfies" whose parents met in the Movement. It's clear that a lot of what he says isn't sincere, but the reader feels sorry for him nonetheless because he has to hide a lot about himself. For example, he has to hide the "government cheese" (a term for food provided by the government to poor people) from his date, no matter what the color of her skin. These types of insecurities make Yunior seem real and make the story enjoyable to read.
The themes in this story include the need to lie to others, symbolized by Yunior's attempt to hide the government cheese. He feels that he has to change himself for the person he is dating and that he can't present his true self. Another theme is the self-hatred Yunior feels as a Latino. He says of his white date's skin and hair, "you love them more than you love your own." He is drawn to white girls over other girls, perhaps because he feels a sense of racial inferiority. In this sense, Yunior is an ironic character. He at first seems arrogant and ready to deceive girls to make them want to sleep with him. Underneath this bravado, however, the reader realizes that Yunior is in fact vulnerable and insecure. 
 

Is there bias in 1491 by Charles C. Mann?

While bias is inherent in all works by humans—even raw data can be manipulated to favor a conclusion—1491 appears to be pushing a very specific hypothesis and agenda. Rather than a presentation of facts and subsequent analysis of the potential factors to determine which among them is the most likely, Mann operates in a manner designed to convince the reader of a conclusion rather than push them toward a more balanced and nuanced view. His claim that the natives possessed superior fire power is highly misleading. He makes very broad statements that are simply unverifiable and dismisses the established consensus on the rather serious charge of racism and ethnocentrism. If I were to propose a bias for Mann, I would say he was more concerned with being groundbreaking and consensus-defying than being accurate and scientific in methodology. 

Now, it wasn’t all interesting information and preconception busting fun times though. There’s a portion of the book, a probably forty or fifty page chunk in the middle, that is mostly centred completely around academic warfare (who was pushing different agendas and points of view, and why) that I found reaaaaaaaaaaaally hard to get through. I understand why it was there, I do (the author is attempting to explain the fact that this information is still not being taught in highschools, though it’s been a pretty prevalent point of view among academics for like fifty years), but if there’s anything I find less interesting than old stuffy intellectuals getting into a dick measuring contest over academic prestige, I haven’t come across it yet. Still, there was some genuinely neat information still peppered throughout that section, and it wasn’t enough of a slog to really effect my recommendation.

The book 1491, by Charles Mann has forced historians to take another look at long held assumptions about what took place during the European colonization of the New World over 500 years ago.  For centuries it had been held that the Native American population that inhabited the Americas was inferior in almost every aspect of life.  Mann challenges these assumptions by claiming that the Native American population was advanced well beyond what historians have claimed.
There is no doubt that Mann is persuasive in his argument that Native American civilization was advanced.  Cities such as the Aztec capital of Tenochtitlan were certainly on par, if not superior, to European cities such as London.  His claims that the environment of the Americas was intentionally manipulated by natives in places such as the Amazon, while controversial, are presented in a fair manner.
To completely abolish bias however, is an almost impossible endeavor.  At times Mann seems as if he is trying to convince the reader to believe his theories instead of actually proving them.  No where is this more apparent than his claim that Europeans did not have superior firepower to the Native Americans.  It feels like a bit of stretch to come to this conclusion based on evidence to the contrary.
There are areas where the reader has to take a leap of faith to believe Mann.  He has reached the conclusion that Native American populations were thriving the year prior to the arrival of Columbus and paints with a broad brush to convince the reader he is correct. It is no easy task to create a history that is in complete opposition to long held beliefs. Mann, like most men, is no doubt biased to a degree is his assertions presented in the book 1491.

In a 2002 article in the Atlantic Monthly, Charles Mann alludes to his bias in his book 1491.
In that book, Mann makes a fascinating argument. While the early European settlers of the New World, such as the Pilgrims, thought they were entering a pristine or untouched wilderness, Mann argues that in both North and South America, Native Americans had been cultivating and managing the environment for a very long time. The Europeans simply did not understand this because Native land management did not look like the way they cultivated their land—or the Europeans did not want to understand this, because it was more convenient to treat the land as wilderness. Mann points out the large fires the Indians set to clear land as an example of managing the environment. He also argues that the Indians were more advanced than the Europeans in understanding agriculture, which is why the Europeans made Native crops, such as the potato, staples in their own cultures.
Because of this research, Mann is biased against letting land simply return to wilderness, which he says has led to an outcry in some environmental circles. Mann writes, however, that the land must be managed:

Guided by the pristine myth, mainstream environmentalists want to preserve as much of the world’s land as possible in a putatively intact state. But “intact,” if the new research is correct, means “run by human beings for human purposes.” Environmentalists dislike this, because it seems to mean that anything goes. In a sense they are correct. Native Americans managed the continent as they saw fit. Modern nations must do the same.

Charles C. Mann's book 1491 is considered groundbreaking because he looks at American history from an indigenous point of view.  The book states that indigenous societies were older than already thought and that they were every bit as strong and diverse as contemporary societies in Africa and Europe. Many academics have praised Mann's work as adding to the historical conversation about Native American tribes, as most of the work done in this field has been based on the natives' relationship to the European.  
Mann's work does have some bias, however.  He discounts most of the work done over the last two hundred years by previous native historians as being biased towards Europeans and, in many cases, racist.  While this is a valid point in many cases, it would be a mistake to throw out all of the work done in this field over the last hundred years.  Also, Mann is not an anthropologist by trade, so his arguments would carry more weight if he included some work done by leading anthropologists.  Mann's 1491 is most valuable in that this is one of the first mainstream history books that looks at Native American achievements pre-Columbus; hopefully other books will find a way to combine earlier historical studies with Mann's.  

Why does Calpurnia act and speak differently when she is around her friends?

In Chapter 12, Calpurnia takes the children to First Purchase African M.E. for Sunday service. Throughout the service, Jem and Scout notice that Calpurnia is speaking differently than she does at home. After Cal explains that she taught Zeebo to read using Blackstone's Commentaries, Jem asks her why she talks informally like the rest of the colored folks at the church when she obviously knows correct English. Scout immediately becomes aware of Calpurnia's "modest double life" and asks her the same question. Calpurnia responds by saying, "Well, in the first place I'm black---" (Lee 77). She proceeds to tell the children that it would be out of place for her to speak like white folks around black people. Cal says that if she spoke properly around her community members, they would think she was "puttin' on airs to beat Moses." When Scout mentions that Cal knows better than to talk incorrectly, Cal says that it's not necessary to tell all you know, and that it's not ladylike because people don't like being around somebody who knows more than they do. Cal chooses to speak informally to fit in with her community members and not come off as being pretentious. 

What importance does Miss Prism have in The Importance of Being Earnest by Oscar Wilde?

Despite her inauspicious beginning as Cecily's ironically unintelligent tutor, Miss Prism ends up being a hugely important character in the play, because she turns out to be the woman who erroneously deposited Mr. Jack Worthing in a cloakroom at Victoria Station, the Brighton Line, when he was an infant. Jack never knew who his parents were because he had been found in a handbag given to Mr. Thomas Cardew in place of his own. Mr. Cardew kept and raised the baby until his own death. Later in the play, when Aunt Augusta visits Jack's home to retrieve her daughter, Gwendolyn, she hears someone speak Miss Prism's name, and she remembers Miss Prism as the servant of her sister's family, the nanny who disappeared with the infant one day and never returned. This prompts Miss Prism to tell the story of what happened to the baby, the baby who turns out to be Jack, and when Jack produces the very handbag that used to belong to Miss Prism, it confirms his identity as that baby, meaning he is Algernon's brother, Aunt Augusta's nephew, and Gwendolyn's cousin.  As he has now acquired parents and pedigree, he is granted permission, by Aunt Augusta, to marry Gwendolyn, which was his goal from the beginning of the play. The revelation of Miss Prism's identity and history makes both Jack and Gwendolyn's and Algernon and Cecily's weddings possible.

How has Marlowe transformed Edward II, a chronicle play, into a tragedy?

Marlowe was no respecter of the status quo, and his plays reflect this. Modern scholars also believe he was gay, which likely drew him to the history of the unhappy Edward II, also presumed to be gay and presented as so in the play.
Edward's story becomes a tragedy in Marlowe's hands, instead of merely a chronicle of history, because the playwright sees Edward as not only someone who is foolhardy, rash, and totally unfit to be king, but as someone who is placed by fate in a position he's unqualified to fill. The tragedy is made more poignant by Edward's inability to see that his own actions have brought his fate upon him. He mourns his favorites:

O Gaveston, ’tis for thee that I am wrong’d,For me, both thou and both the Spencers died!And for your sakes a thousand wrongs I’ll take.The Spencers’ ghosts, wherever they remain,Wish well to mine; then tush, for them I’ll die.

But he never acknowledges the wrongs his mismanagement of the state have done.
In that sense, Marlowe created a very modern image, a flawed, yet articulate and passionate person, crushed by both his own behavior and that of the ambitious, ruthless people around him.

Why does Mrs. Who speak using quotations?

In the novel, A Wrinkle in Time, the three women, Mrs. Which, Mrs. Whatsit, and Mrs. Who, are all stars who, after fighting the darkness in space, have come to Earth to help Meg, Calvin, and Charles Wallace defeat the darkness and save Meg and Charles Wallace's father. They have disguised themselves as elderly human women, but because they are really stars they have a hard time fitting in and getting their disguises right. Mrs. Whatsit is the youngest and therefore has the easiest time adapting, but Mrs. Who and Mrs. Which struggle a bit more. Mrs. Who, in particular, struggles to make herself understood and so relies on quotations to get her meaning across. She also does it in part to help keep everyone's spirits up.

We find out in the novel that Mrs. Who, Mrs. Whatsit, and Mrs. Which are stars who have come to earth in human form. They pose as old ladies, and part of the humor in the novel is that they don't quite get their disguises exactly right, coming off as odd and eccentric. For instance, their names are not quite normal: how many people have as surnames Who or Which?
Mrs. Whatsit explains why Mrs. Who speaks in quotes after Charles Wallace says to Mrs. Who in annoyance that he wishes she would stop doing so. Mrs. Whatsit says to him:

But she finds it so difficult to verbalize, Charles dear. It helps her if she can quote instead of working out words of her own.

Mrs. Who then chimes in that she does it, in part, to be funny, saying that we all need to keep our sense of humor in serious times.

Calculus: Early Transcendentals, Chapter 1, Review Exercises, Section Review Exercises, Problem 28

Graph the three functions $y = x^a, y = a^x,$ and $y = \log_a x$ on the same screen
for two or three values of $a > 1$. For large values of $x$, which of these function has
the largest values and which has the smallest values?







We can see from the graphs that the graph of $y = a^x$ is more steep than the other. So,
for large values of $x$, the fraction $y = a^x$ has the largest values. On the other hand, for small values
of $x$, the fraction $y = \log ax$ has the smallest values.

Write f(x)=|x| as a piecewise function. Find the domain and range of f(x).

Hello!
Actually, the function |x| (absolute value of x ) is defined as a piece-wise function:
|x| = {(x if xgt=0),(-x if xlt0):}
There are two "pieces" on which this function is defined using elementary functions, (-oo, 0) and [0, +oo).
The domain of a function is the set of numbers where it is defined. As we see, absolute value function is defined everywhere, so its domain is the entire set of real numbers RR (also we can write it as (-oo, +oo) ).
The range of a function is the set of all its values. Our function, |x|, is obviously always non-negative, so negative numbers are not in its range. Any non-negative number y is, in turn, in its range, because |y| = y. Thus the range of absolute value function is [0, +oo).
 

Calculus of a Single Variable, Chapter 8, 8.4, Section 8.4, Problem 62

To find the arc length of a curve, we follow the formula:
S = int_a^b sqrt(1+((dy)/(dx))^2) if y=f(x) , alt=xlt=b or [a,b] .
For the given problem: y =x^2/2 on interval [0,4] , we have boundary values: a= 0 and b=4 .
Apply Power Rule for differentiation: d/(dx) x^n = n * x^(n-1) * dx .
(dy)/(dx) = d/(dx) (x^2/2)
= 1/2d/(dx) (x^2)
= 1/2 * [ 2 *x^(2-1) * 1 ]
=1/2 * [ 2x]
= (2x)/2
= x
Plug-n a=0 , b = 4 , and (dy)/(dx)= x on the formula S = int_a^b sqrt(1+((dy)/(dx))^2) , we get:
S = int_0^4 sqrt(1+x^2) dx
From indefinite integral table, the problem resembles the formula for integral with roots:
int sqrt(u^2+-a^2) dx=1/2usqrt(a^2+-u^2)+-1/2a^2ln|u+sqrt(u^2+-a^2)| .
Take note we have "+ " sign inside the radical part then we follow formula as:
int sqrt(u^2+a^2)dx=1/2*usqrt(a^2+u^2)+1/2*a^2ln|u+sqrt(u^2+a^2)| .
Applying the formula, we get
S = int_0^4 sqrt(1+(x)^2)
=[1/2*xsqrt(1^2+x^2)+1/2*1^2ln|x+sqrt(x^2+1^2)|]|_0^4
=[1/2*xsqrt(1+x^2)+1/2*ln|x+sqrt(x^2+1)|]|_0^4
=[(xsqrt(1+x^2))/2+(ln|x+sqrt(x^2+1)|)/2]|_0^4
Apply definite integration formula: F(x)|_a^b= F(b)-F(a) .
S =[(4sqrt(1+4^2))/2+(ln|4+sqrt(4^2+1)|)/2]-[(0sqrt(1+0^2))/2+(ln|0+sqrt(0^2+1)|)/2]
=[(4sqrt(1+16))/2+(ln|4+sqrt(16+1)|)/2]-[(0sqrt(1+0))/2+(ln|0+sqrt(0+1)|)/2]
=[(4sqrt(17))/2+(ln|4+sqrt(17)|)/2]-[0/2+(ln|0+sqrt(1)|)/2]
=[ 2sqrt(17)+(ln|4+sqrt(17)|)/2]-[0+(ln|1|)/2]
=[ 2sqrt(17)+(ln|4+sqrt(17)|)/2]-[0+0/2]
=[ 2sqrt(17)+(ln|4+sqrt(17)|)/2]-[0]
=2sqrt(17)+(ln|4+sqrt(17)|)/2 or 9.29 (approximated value)

Precalculus, Chapter 6, 6.3, Section 6.3, Problem 49

The magnitude of a vector v=v_x*i + v_y*j is given by the following formula, such that:
|v| = sqrt(v_x^2+v_y^2)
The problem provides the information that |v| = 10:
10 = sqrt(v_x^2+v_y^2)
You may evaluate the direction angle of the vector v, such that:
tan alpha = (v_y)/(v_x)
The problem provides the information that the direction angle of the vector v coincides to the direction angle of the vector u = <-3,4> .
tan alpha = -4/3
(v_y)/(v_x) = -4/3 => v_y = (-4/3 )*(v_x)
Replacing (-4/3 )*(v_x) for v_y yields:
10 = sqrt(v_x^2+(16/9)*(v_x^2))
10 = +-(5/3)*(v_x)
2 = +-(1/3)*(v_x) => v_x = +-6 => v_y = +-8
Hence, evaluating the vector v yields v = 6i - 8j or v = -6i + 8j.

What are some of the popular data encryption software that uses military grade encryption?

Most encryption software available today use military grade encryption. The term military grade is used for marketing purposes to infer that the software has strong encryption capabilities. Any encryption software worth using today should be based on the Advanced Encryption Standard (AES). The algorithm working under AES uses the same key to encrypt and decrypt data. The algorithm was approved by the National Security Agency (NSA) for top secret data, earning its military grade status.Some of the popular encryption software running the military grade algorithm include the following:

BitLocker, which comes prepackaged with the modern Windows operating system. The encryption system has the ability to encrypt entire drives on a PC.

Folder Lock is also another popular encryption system running on the Advanced Encryption Standard. The software also comes with file shredding capabilities.

7ZIP is a popular encryption software that runs on the AES protocol and encrypts files and folders that a user wants to transfer over the internet.
https://heimdalsecurity.com/blog/free-encryption-software-tools/

https://www.toptenreviews.com/best-encryption-software

Single Variable Calculus, Chapter 3, 3.8, Section 3.8, Problem 6

At what rate is the volume increasing when the diameter is 80min?

Given: $\displaystyle \frac{dr}{dt} = 4mm/s$

Required: $\displaystyle \frac{dv}{dt}$ when $d = 80mm$

Solution: Let $V =\frac{4}{3} \pi r^3$ be the volume of the sphere

where $r$ = radius, diameter = 2 (radius); $\displaystyle r = \frac{d}{2} = \frac{80}{2} = 40$

It is also stated in the problem that $r$ is a constant so,


$
\begin{equation}
\begin{aligned}

\frac{dv}{dt} =& \frac{dv}{dr} \left( \frac{dr}{dt} \right) = \frac{4}{3} (3) \pi r^2 \left( \frac{dr}{dt} \right)
\\
\\
\frac{dv}{dt} =& 4 \pi r^2 \left( \frac{dr}{dt} \right)
\\
\\
\frac{dv}{dt} =& 4 \pi (40)^2(4)

\end{aligned}
\end{equation}
$


$\fbox{$\large \frac{dv}{dt} = 25600 \pi mm^3/s $}$

Intermediate Algebra, Chapter 3, 3.5, Section 3.5, Problem 54

Identify whether the relation $\displaystyle y = \frac{7}{x-2}$ defines $y$ as the function of $x$ and give the domain.

Given any value of $x$ in the domain, we find $y$ by substituting $2$ from $x$ and then dividing the result into $7$.
This process produces exactly one value of $y$ for each value in the domain, so the given equation defines a function.
The domain includes all real numbers except those which value the denominator . We find these numbers by setting the
denominator equal to and solving for $x$. In this case,

$
\begin{equation}
\begin{aligned}
x - 2 &= 0 && \text{Add 2}\\
\\
x &= 2
\end{aligned}
\end{equation}
$

The domain includes all real numbers except $2$, written $(-\infty, 2) \bigcup (2, \infty)$

We see word-play on the word "fair" in the short exchange between Hermia and Helena in Act I Scene I of A Midsummer Night’s Dream.Try your hand at some word-play. You can just go at it on the page if you would like. Or, think of a scene, situation, or circumstance. Then, think of a few words you might associate with that scene, situation, or circumstance and see if you can’t situate some of the scene’s circumstances in a circumstance or situation that’s not been seen before.

As I understand this, you are being asked to create a pun on a word that can have two meanings, and then add a scene to A Midsummer Night's Dream, or perhaps create just any scene, using that punning word.
Three words jump to mind that might be applied to A Midsummer Night's Dream. The first would be to pun on see/sea since the play illustrates that love is blind. Titania and her entourage, including Bottom with his ass's head, could fly to the seashore. One of Titania's fairies could then have fun with the wordplay of Titania seeing the sea, but not seeing who she fallen in love with, i.e., Bottom. Perhaps Bottom could be swimming and the fairy could comment that in seeing the sea Titania sees not what is in the sea.
Another punning word that could apply to the play could be spectacles. Perhaps we could imagine Helena (or any character) donning spectacles, as in eyeglasses, but still not be able to perceive the spectacles, as in events, unfolding before her because she is blinded by love.
We could also think of glass as both a mirror (looking glass) that a character blinded by love could look into but not see through and the clear, see-through glass of a window. The could work well with the idea of love being narcissistic or reflecting back to people, like a looking glass, what they want to see, rather than being a clear pane through which they see reality.
I hope this helps in getting you started with thinking of words that have more than one meaning in which the meanings can be played off each other.

Intermediate Algebra, Chapter 4, 4.2, Section 4.2, Problem 28

Solve the system of equations $
\begin{equation}
\begin{aligned}

5x - 2z =& 8 \\
4y + 3z =& -9 \\
\frac{1}{2}x + \frac{2}{3}y =& -1

\end{aligned}
\end{equation}
$.


$
\begin{equation}
\begin{aligned}

15x \phantom{+8y} - 6z =& 24
&& 3 \times \text{ Equation 1}
\\
\phantom{15x + } 8y + 6z =& -18
&& 2 \times \text{ Equation 2}
\\
\hline

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

15x + 8y \phantom{+ 6z} =& 6
&& \text{Add}

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

15x + 8y =& 6
&& \text{Equation 4}
\\
\frac{1}{2}x + \frac{2}{3}y =& -1
&& \text{Equation 3}


\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

15x + 8y =& 6
&& \text{Equation 4}
\\
-6x - 8y =& 12
&& 12 \times \text{ Equation 3}
\\
\hline

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

9x \phantom{-8y} =& 18
&& \text{Add}
\\
x =& 2
&& \text{Divide each side by $9$}

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

5(2) - 2z =& 8
&& \text{Substitute } x = 2 \text{ in Equation 1}
\\
10 - 2z =& 8
&& \text{Multiply}
\\
-2z =& -2
&& \text{Subtract each side by $10$}
\\
z =& 1
&& \text{Divide each side by $-2$}

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

4y + 3(1) =& -9
&& \text{Substitute } z = 1 \text{ in Equation 2}
\\
4y + 3 =& -9
&& \text{Multiply}
\\
4y =& -12
&& \text{Subtract each side by $3$}
\\
y =& -3
&& \text{Divide each side by $-3$}

\end{aligned}
\end{equation}
$



The ordered triple is $\displaystyle \left( 2, -3, 1 \right)$.

Why does Foner say that the New Deal “transformed the role of the federal government”?

Prior to the Great Depression, the prevailing consensus was that the Federal government had a very limited role to play in running the economy. According to the doctrine of laissez-faire, the Federal government should simply establish the legal and regulatory structure in which businesses operate and allow the free market to determine the production and allocation of goods.
In the aftermath of the Wall Street crash and the ensuing Depression, this reigning economic orthodoxy was challenged. Many now believed that lack of effective government regulation of the economy was partly to blame for the economic catastrophe that had descended upon the country. But according to such critics, tighter regulation wasn't enough; the government had to get directly involved in running the economy.
It was this attitude that finally prevailed with the election of Roosevelt in 1932. Under his New Deal, the role of the Federal government, not just in relation to the economy, expanded rapidly in a manner that until recently would have been unthinkable. The new consensus held that it was perfectly legitimate for the government to create jobs through massive public works projects such as the Works Progress Administration, or WPA.
The New Deal also established a Federal system of Social Security, which still exists to this day. For the first time, the principle was established that the Federal government should establish some kind of safety net for seniors, who previously had to rely on their own savings, help from their families, or private philanthropy.
Americans have always had an inherent suspicion of over-mighty government, seeing it as a threat to their hard-won liberties. The Revolution against the British was fought on just such grounds. Yet thanks to the New Deal, a growing number of people in the United States began to accept that government control in some areas was not just a necessary evil, but actually a positive good, conducive to giving people freedom from the indignities of poverty, unemployment, and want. The New Deal had vastly expanded both the size and scope of the Federal government, and though future administrations would attempt to cut back on what they saw as "big government," there was to be no going back to the days of laissez-faire.

Calculus of a Single Variable, Chapter 7, 7.1, Section 7.1, Problem 15

x=4-y^2 , x=y-2
(a) first let us find the area of the region with respect to x
so ,
the lines are
x=4-y^2
=> y^2=4-x
y=sqrt(4-x) -------------(1)
and
x=y-2
=> y=x+2---------(2)
let us find the curves where they intersect
so ,
sqrt(4-x) =x+2
4-x=(x+2)^2
4-x=x^2+4x+4
=>x^2+5x=0
=> x(x+5)=0
=>x=0 or x=-5
and the let let us get the points where they intersect with respect to y
4-y^2=y-2
6=y+y^2
=> y^2+y-6=0
=>y^2+3y-2y-6=0
=>y(y+3)-2(y+3)=0
=>(y-2)(y+3)=0
so y=2 or y= -3

so the points of intersection of the curves are (0,2) & (-5,-3)
but the curve x=4-y^2 is beyond x=0 and intersects the x-axis (setting y=0) at x=4.

So the area of the region with respect to x -axis needs to have two integrals.
Area=int_-5^0[(x+2)-(-(sqrt(4-x)))] dx +
int_0^4[(sqrt(4-x)-(-(sqrt(4-x)))] dx

=int_-5^0 [(x+2)+((sqrt(4-x)))] dx +int_0^4 [(sqrt(4-x)+((sqrt(4-x)))] dx
=[x^2/2+2x-2/3(4-x)^(3/2)]_-5^0 +[-2/3(4-x)^(3/2)-2/3(4-x)^(3/2)]_0^4
=[(-2/3)(4)^(3/2)]-[25/2-10-(2/3)(9)^(3/2)]+[0]-[(-4/3)(4)^(3/2)]
=-16/3+31/2 +0+32/3
=61/6+32/3 =125/6
so the Area is 125/6

(b) area of the region with respect to y is
Area = int _-3 ^2 [(y-2)-(4-y^2)] dy
= [y^2/2 -2y -4y+y^3/3]_-3 ^2
= [4/2 -4 -8 +8/3]-[9/2 +6+12-27/3]
=-22/3 -27/2
=-125/6
= -20.833

But since the area cannot be negative then the area is 20.833 or 125/6

Intermediate Algebra, Chapter 2, 2.7, Section 2.7, Problem 28

Solve the inequality $|3r - 1| \geq 8$, and graph the solution set.

The absolute value inequality is rewritten as

$3r - 1 \geq 8$ or $3r - 1 \leq -8$,

because $3r - 1$ must represent a number that is more than $8$ units from on either side of the number line. We can solve the compound inequality.


$
\begin{equation}
\begin{aligned}

3r - 1 \geq & 8 \qquad \text{or} &&& 3r - 1 \leq & -8
&&
\\
3r \geq & 9 \qquad \text{or} &&& 3r \leq & -7
&& \text{Add } 1
\\
r \geq & 3 \qquad \text{or} &&& r \leq & \frac{-7}{3}
&& \text{Divide by } -3

\end{aligned}
\end{equation}
$


The solution set is $\displaystyle \left( - \infty, \frac{-7}{3} \right] \bigcup [3, \infty)$.

In what ways might RFID technology be used to serve customers better? What problems might arise? Do you think the technology might be valuable when implanted in animals or people?

With current storage technology, a very small tag could contain an enormous amount of data and transmit it rapidly. Megabytes or even gigabytes would easily be feasible, even though we normally don't use RFID for that much data.
Used on products, we could include all sorts of information about the product, things that wouldn't fit on the label, including safety records, labor standards, environmental impact, and information about the supply chain. This would dramatically increase transparency and make it much easier for consumers who care about being socially responsible to make informed decisions. Businesses have little incentive to provide this information on their own, but they could be required to do so by regulation or incentivized by tax and subsidy systems.
In the opposite direction, RFID tags could provide businesses with even more detailed information about consumer purchasing patterns, enabling businesses to use computer algorithms to project future purchasing and target advertising. Because businesses have a powerful incentive to do this, this process is already underway. It likely increases economic efficiency, but it also raises serious privacy concerns, because a person's purchasing habits can tell a great deal about them, and could reveal potentially embarrassing or damaging information.
RFID implants are already used to great effect in animals: pets can be implanted with RFID chips to ensure they can always be identified in case they are lost. This dramatically improves the odds of a lost pet finding its way home.
As for humans, I think there will be a lot more resistance on ethical grounds, but if security and privacy concerns are properly addressed it could catch on. Instead of carrying a wallet full of cash and cards, you might only need an RFID implant to verify your identity and make purchases directly from your chosen accounts. The main concern I have is security; currently, RFID has a very poor track record of encryption (I've linked a famous case where fare cards in the Netherlands were hacked), and unless this improves people should not trust such implants. If encryption improved, this could actually be more secure than cash and cards, as an implant is impossible to steal without physically injuring the person who is implanted.
https://science.howstuffworks.com/innovation/everyday-innovations/pet-microchip.htm

https://www.computerworld.com/article/2537817/how-they-hacked-it--the-mifare-rfid-crack-explained.html

https://www.forbes.com/sites/kashmirhill/2012/02/16/how-target-figured-out-a-teen-girl-was-pregnant-before-her-father-did/

How is civilization portrayed as barbaric in Huck Finn?

Civilization is portrayed as barbaric in Huckleberry Finn because it condones slavery. Huck feels full of guilt because he is helping Jim to escape. His Southern society has taught him that slaves are property rather than human beings. The friendship he develops with Jim traveling on the Mississippi teaches him, however, that Jim is a human being. Huck can't help but remember all the times Jim has been loyal to him and sacrificed for him. So Huck wages a war of conscience. 
In the upside-down moral universe in which has been brought up, Huck has been taught that everything he is doing for Jim is a sin. He "knows" he should write a letter revealing Jim's whereabouts. Yet he decides that, even if it means he is going to go to hell, he can't. We as readers perceive that Huck's moral self-torture is wrong. Huck is, in fact, doing the right thing in helping Jim.
It's also worth also noting that Huck and Jim encounter people who could be considered barbaric. For example, the King and the Duke put money ahead of other people's welfare. They are quite willing to defraud orphans. Twain exposes a world in which too often people put things ahead of people, instead of the opposite.   

What are some of the most compelling issues concerning the Christian faith that the skeptic will be forced to consider as a consequence of reading Mere Christianity, by C.S. Lewis?

It's first important to note that Lewis, basing the book on radio talks aimed at a mass audience, doesn't stray from  standard Christian theology. "Mere" Christianity is orthodox Christianity. As such it challenges skeptics in essential ways. At its core, what might be most compelling to the skeptic is not Lewis's theology but his method: he is using logical, rational argumentation to show that, in his opinion, Christianity makes sense and is compatible with a rationally ordered universe. He is not saying one merely has to accept Christian doctrine because "the Bible says so." Even when he says he accepts certain Christian doctrine on "authority," he offers a chain of logical reasons for doing so. Relentlessly throughout the book, he offers reasoning the skeptic can think about and argue with. Among other claims, Lewis asserts the following:
That moral law exists as fully as physical law as part of the fabric of universal reality and that it proves that God exists. Lewis says that we humans have a universal sense of right and wrong and a yearning to see justice enacted that can only have been implanted by a deity. Our "natural" sense of moral right and wrong thus proves God's existence.
That Jesus Christ really was the son of God and not merely a charlatan or madman "lunatic." Once again, Lewis lays out a logical, three-part argument for this and offers rational reasons for choosing the first option. 
That Christians are imperfect but that fact doesn't negate the faith: "a Christian is not a man[sic] who never does wrong ..."
That God did come to earth (become incarnate) as a human being to atone for human sin and that this worked. Lewis likens atonement to nutrition. We don't know exactly how either one works and there are rival theories but we all agree "if you are tired and hungry, a meal will do you good."
That humans cannot fully grasp the logic or the magnitude of the divine gift of atonement, but can accept it. This is an arguably post-modern argument that our logical constructs are kluges with limitations that ultimately collapse under the weight of their own contradictions--but Lewis argues, the truth is still out there and we can accept it gratefully, if not with full comprehension.
That human traits such as pride and love are spiritually undergirded: pride is the great sin ("the utmost vice") dividing humans and love ("a state not of feelings but of the will"; the determination to act charitably) the great secret holding the universe together. A skeptic might find it compelling to think about how simple, concrete behaviors could have an outsize impact on the cosmos.
In the end, Lewis's Christian claims about the reality of God, sin, and atonement might not persuade the skeptic, but his logical argumentation provides a framework that offers food for thought.