How much emphasis is placed on social class, and what role does it play in helping you understand human motivation and aspiration?

Social class, race, and gender are all addressed in Malcolm Gladwell's Blink. Gladwell makes the claim that we tend to make snap judgments in a few seconds based on "thin slices" of information. Rather than taking time to learn about people and evaluate them based on a wide range of metrics, we tend to categorize them almost immediately, based on appearance, membership in particular groups (age, race, class), or subliminal cues such as body language. For Gladwell, this process tends to reinforce stereotypes. For example, a real estate agent might see someone dressed in a way typical of a certain economic class and use that information to curate a selection of properties to show that person. Gladwell argues that much of this behavior is not so much conscious discrimination as a hardwired need to make quick and efficient decisions, but he also suggests that we can consciously work to counteract such biases.
Our own stereotyped thinking can also lead us to use information clustered around such thin slices to limit our aspirations. We might make the judgment that our families are "professional" and thus we should not consider careers in skilled trades such as plumbing or carpentry, even if we really prefer working with our hands to sitting in an office, or we might apply to a local community college rather than an Ivy League school despite stellar grades, because we associate certain universities with certain class markers.  

What factors were most significant in shaping a character’s attitude toward marriage in Jane Austen's Pride and Prejudice?

Fortune and status play a major role in shaping many characters' attitudes toward marriage in this text.  Consider Lady Catherine de Bourgh's high status and the way it affects her view of marriage: she longs to keep both her daughter's and nephew's fortune and status intact, and so she hopes they will marry one another.  Mrs. Bennet's lower status and fortune make her desperate to marry her daughters off, even to strangers, and to marry them off well (a.k.a. to men of fortune and status).  In any case, for many characters, including Caroline Bingley, the desire to retain or acquire fortune and status is the major factor in making a marriage match.
A character's sex (and the restrictions or opportunities provided by society for that sex) often plays a role in shaping their views of marriage as well.  For example, Mr. Collins wants to marry because he believes it will make him happy and is appropriate for a man of his profession.  However, his eventual wife, Charlotte, doesn't marry for happiness, but for security.  Her options, as a woman of 27, are extremely limited, and she fears becoming a burden on her family (something a man, who can make his own fortune, would be much less likely to fear).  Likewise, Mr. Bennet seems as though he couldn't care less about his daughters' marriage prospects, while the very same topic seems to occupy almost every one of Mrs. Bennet's waking thoughts.

Why is John F Kennedy considered one of the greatest Presidents? what did he do for the US well as the world - please give examples . ( high school level )

Kennedy's accomplishments were rather limited, but this is mainly due to his term being cut short by an assassination.  Kennedy was open to dialogue on civil rights, though he proceeded quite cautiously in order to avoid upsetting Southern Democrats in Congress.  Kennedy's rhetoric in his first inaugural address--"ask not what your country can do for you; ask what you can do for your country," has inspired generations.  Kennedy's establishment of the Peace Corps is a lasting legacy of his administration, and the organization has helped millions in the developing world.  Kennedy also urged Americans to put a man on the moon before 1970; while he would not live to see it, the lunar landing in 1969 was part of his legacy.  
Kennedy's greatest foreign policy achievement was the Cuban Missile Crisis in which he was able to defuse a possible nuclear conflict with the Soviet Union over nuclear bases in Cuba.  He opened direct negotiations with the Kremlin and removed missile bases from Turkey which threatened the Soviet Union.  This proved to be a minor but important thaw in American-Soviet relations in the early 1960s.  

when buttercup thinks westley is dead, she agrees to marry Humperdinck. since buttercup never would have dreamed of wedding another while westley was still alive, isn't it horribly unfair of him to call her ''unfaithful''

This is an opinion question. Some readers are going to think that Buttercup was unfaithful, while others will agree that calling her unfaithful is indeed unfair. Looking at chapter 4, I would agree that calling Buttercup unfaithful isn't fair. To Buttercup's credit, she doesn't want to marry the Prince. She's simply not in love with him, and he essentially forces her to marry him. He's the Prince, she's a commoner of the area, and she's required to obey him. Buttercup actually refuses his command a couple of times, and she even accepts that her end fate is death for refusing the Prince.

"I am your Prince and you will marry me," Humperdinck said.
Buttercup whispered, "I am your servant and I refuse."
"I am your Prince and you cannot refuse."
"I am your loyal servant and I just did."
"Refusal means death."
"Kill me then."
"I am your Prince and I'm not that bad—how could you rather be dead than married to me?"
"Because," Buttercup said, "marriage involves love, and that is not a pastime at which I excel. I tried once, and it went badly, and I am sworn never to love another."

The Prince then does something incredibly honest. He tells Buttercup that he isn't marrying her for love, and he doesn't need her to love him; he needs somebody to provide him an heir. So he gives Buttercup a choice. She can be rich, powerful, and alive as Queen, or she can be dead. Faced with that choice, Buttercup chooses to marry Humperdinck.

"So you can either marry me and be the richest and most powerful woman in a thousand miles and give turkeys away at Christmas and provide me a son, or you can die in terrible pain in the very near future. Make up your own mind."
"I'll never love you."
"I wouldn't want it if I had it."
"Then by all means let us marry."

I don't believe that she is being emotionally unfaithful to Westley or his memory. She doesn't hide the fact that she loved another and won't love anybody else.

Calculus and Its Applications, Chapter 1, 1.6, Section 1.6, Problem 26

Differentiate $F(x) = (-3x^2 +4x)( 7 \sqrt{x} + 1)$
By multiplying first before differentiating we get

$
\begin{equation}
\begin{aligned}
F(x) &= \left( -3x^2 + 4x \right) \left( 7x^{\frac{1}{2}} + 1 \right)\\
\\
F(x) &= -21x^{\frac{5}{2}} - 3x^2 + 28x^{\frac{3}{2}} + 4x
\end{aligned}
\end{equation}
$


Thus,

$
\begin{equation}
\begin{aligned}
F'(x) &= \frac{d}{dx} \left( -21x^{\frac{5}{2}} - 3x^2 + 28x^{\frac{3}{2}} + 4x \right)\\
\\
&= -21 \cdot \frac{d}{dx} \left( x^{\frac{5}{2}} \right) - 3 \cdot \frac{d}{dx} (x^2) + 28 \cdot \frac{d}{dx} \left( x^{\frac{3}{2}} \right) + 4 \cdot
\frac{d}{dx} (x)\\
\\
&= -21 \cdot \frac{5}{2} \left( x^{\frac{5}{2} - 1} \right) -3 \cdot 2 \left( x^{2 - 1} \right) + 28 \cdot \frac{3}{2} \left( x^{\frac{3}{2} - 1} \right)
+ 4 \cdot (1)\\
\\
&= \frac{-105}{2} x^{\frac{3}{2}} - 6x + 42x^{\frac{1}{2}} + 4\\
\\
&= \frac{-105}{2} \sqrt{x^3} - 6x + 42 \sqrt{x} + 4
\end{aligned}
\end{equation}
$

How does Ponyboy react to Johnny’s death?

I think that Ponyboy reacts in a way that is similar to how many people react when a close friend or family member dies unexpectedly. Ponyboy simply can't bring himself to believe and accept the fact that his friend is dead. Johnny dies at the end of chapter 9, and chapter 10 sees Ponyboy denying the fact that Johnny has just died. Deep down Ponyboy knows it is true, but he can't bring himself to fully understand and embrace the concept:

Johnny was dead. But he wasn't. That still body back in the hospital wasn't Johnny. Johnny was somewhere else -- maybe asleep in the lot, or playing the pinball machine in the bowling alley, or sitting on the back steps of the church in Windrixville. . . He isn't dead, I said to myself. He isn't dead. And this time my dreaming worked. I convinced myself that he wasn't dead.

Even after Ponyboy tells the other Greasers that Johnny is dead, Ponyboy still inwardly tells himself that Johnny isn't dead. Ponyboy turns even more inward than normal, and he ends up staying fairly inactive for another week. He simply can't bring himself to focus on anything, but his denial is still strong. Randy comes over to Ponyboy's house in chapter 11, and Ponyboy once again states that Johnny isn't dead. Even throughout most of chapter 12, Ponyboy simply isn't moving on and dealing with the fact that Johnny is dead. Ponyboy's grades begin slipping, and he is quite irritable. It isn't until Ponyboy finds the note Johnny left him that Ponyboy starts to come out of his mental fog.

When Johnny dies at the end of chapter 10, Ponyboy and Dallas are right next to him in his hospital room. Dallas reacts to Johnny's death with violent emotion, slamming his body and his fists against the wall of the room, while Ponyboy reacts with silence and shock.
Chapter 11 opens with a description of Ponyboy's experience. He uses words like "daze" and "stupor" to describe his state of mind. As well, Ponyboy's thoughts take him through imaginings of Johnny while Johnny was still alive; he imagines Johnny playing pinball and sitting on the steps of the church, for example. Ponyboy explains that his dreams and his imagination are able to convince him that Johnny isn't dead. Ponyboy's denial of Johnny's death is a reflection of Ponyboy's pain and sense of loss. Unfortunately, the reader knows that Ponyboy's dreams of Johnny and his sense that Johnny must still be alive are only temporary; soon, the reality of the situation will hit Ponyboy, and he will suffer his loss deeply.

How can the poem “On Killing a Tree” be interpreted as a protest?

Gieve Patel, the author of “On Killing a Tree,” grew up in Mumbai, India. India gained its independence in 1947 and the 1960s saw the city of Mumbai expand rapidly into an urban metropolis. Using this background for context, one can read Patel’s poem as an environmental protest against urban expansion. He seems to be arguing that Mother Nature’s claims to the land are just as valid as any human’s. It takes immense effort to fully uproot a tree, and once destroyed, nature never returns to the way it once was. Patel seems to lament the idea that nature is viewed as an inconvenient enemy to urban sprawl, and that it has to be treated with complete, surgical extraction, like a pest infestation or a cancer. Patel’s imagery of genocidal “scorching and choking” seems to be a strong protest against destroying Mother Nature’s defenseless presence.

Calculus: Early Transcendentals, Chapter 4, Review, Section Review, Problem 22

y=x/(1-x^2)
a) Asymptotes
Vertical asymptotes are the zeros of the denominator of the function.
1-x^2=0rArr(1+x)(1-x)=0
x=-1 , x=1
Vertical asymptotes are x=1 and x=-1
Degree of numerator=1
Degree of denominator=2
Since degree of denominator degree of numerator,
So, Horizontal asymptote is x-axis i.e. y=0
b) Maxima/Minima
y'=((1-x^2)-x(-2x))/(1-x^2)^2
y'=(1-x^2+2x^2)/(1-x^2)^2
y'=(1+x^2)/(1-x^2)^2
To find critical numbers , solve for x at y'=0
(1+x^2)/(1-x^2)^2=0 rArr1+x^2=0
x^2=-1rArrx=+-i
Since there is no real solution , so there are no critical points.
Domain : -1< x< 1
Check the sign of y' by plugging test points in the intervals (-oo ,-1),(-1,1) and (1,oo )
y'(-2)=(1+(-2)^2)/(1-(-2)^2)^2=5/9
y'(0.5)=(1+(0.5)^2)/(1-0.5^2)^2=2.22
y'(2)=(1+2^2)/(1-2^2)^2=5/9
There is no change in sign of y' , so there are maxima and minima.
c) Inflection points
y''=((1-x^2)^2(2x)-(1+x^2)(2)(1-x^2)(-2x))/(1-x^2)^4
y''=((1-x^2)((1-x^2)2x+4x(1+x^2)))/(1-x^2)^4
y''=(2x-2x^3+4x+4x^3)/(1-x^2)^3
y''=(2x^3+6x)/(1-x^2)^3
y''=(2x(x^2+3))/(1-x^2)^3
For inflection points y''=0
(2x(x^2+3))/(1-x^2)^3=0
2x(x^2+3)=0
x=0 , x^2=-3
ignore the points that are complex,
So , Inflection point is at x=0

Why does the average total cost slope upward at the end?

The average total cost (ATC) curve slopes upwards at the end because of the law of diminishing marginal returns.  At first, as production increases, a firm will become more efficient at producing a given good.  This will cause its ATC to drop.  However, at some point, the law of diminishing marginal returns comes into play and the ATC starts to increase once again.
In the short run, this happens because, at some point, a firm cannot work as efficiently when it tries to produce a larger quantity.  Let us imagine that I own a restaurant with a fixed kitchen size and fixed appliances.  I start out small, with only one or two people working in my kitchen.  Those two are trying to do all the work in my whole kitchen.  As business gets better, I hire more people.  The first few that I hire can really help me.  Each time I hire a new person, they fill in another empty spot in the kitchen.  They make it so each cook can specialize in one thing and can work exclusively in one area of my kitchen.  In essence, I create an assembly line. 
However, at some point, I have hired one cook for each space/task in my kitchen.  What happens if I try to produce still more food each day?  This is where the law of diminishing returns comes in.  I hire another worker for the kitchen, but my kitchen is not really big enough to give them a place to work.  They do not have an empty spot that they can fill.  They help as much as possible, but they do not add as much to our output as previous cooks did.  Because I tried to increase my output, I ended up lowering my marginal returns.
When marginal returns drop, ATC starts to rise.  I increase my costs by hiring more workers, but they do not create enough extra output to offset the wages I pay them.  Therefore, my average cost per unit of output (which is my ATC) rises.  This causes my ATC curve to slope upwards as output rises.
Please follow the links below for further discussion of this topic.
http://www.amosweb.com/cgi-bin/awb_nav.pl?s=wpd&c=dsp&k=average+total+cost+curve

http://www.amosweb.com/cgi-bin/awb_nav.pl?s=wpd&c=dsp&k=law+of+diminishing+marginal+returns

Describe the rationalization process of the Erinyes in "The Eumenides" by Aeschylus.

The Erinyes are the Furies and usually consist of three deities of destruction and vengeance. They are understood to be advocates for the dead.
In the play, the Erinyes want Orestes to pay in blood and suffering for his mother Clytemnestra's murder. The Erinyes/Furies rationalize their thirst for blood vengeance by referencing the ancient Greek codes of blood-pollution. Because Orestes killed his mother, they claim that he has polluted his legacy; the Erinyes emphatically argue that this kind of familial pollution can never be erased. On the other hand, the Erinyes do not interest themselves in pursuing Clytemnestra for killing Agamemnon (her husband) because the two are not blood kin.
According to the Erinyes, guilt can only be effaced through the execution of equivalent violence on behalf of the victim. Furthermore, the Erinyes maintain that Orestes deserves to be driven mad for his matricide; they hound him mercilessly with the miasma of Clytemnestra's dead spirit. The dead spirit is believed to be a polluted presence, and therefore poses a danger to the larger community. Here, the Erinyes reference the ancient Greek belief that murder can render a perpetrator insane. During the trial, the Erinyes stress that Orestes can never remove the blood-taint of his matricide, and they pronounce him unclean and unworthy to perform any religious rituals in his city. Essentially, the Erinyes reject the claim that anything other than blood atonement can purify Orestes.
Sources:
Inner Purity and Pollution in Greek Religion: Early Greek Religion, Volume 1 by Andrej Petrovic, Ivana Petrovic.
Restless Dead: Encounters Between the Living and the Dead in Ancient Greece by Sarah Iles Johnston

How did the ability to domesticate animals help a civilization's ability to become powerful and rich ?

The domestication of animals provides a handy source of food, meat and dairy products, in one place, allowing people to settle in that place, no longer expending all their energy on traveling for game to sustain them.  Concomitantly, if one is settled in one spot, one can grow food, which has the same consequence, less time and energy moving about foraging for food. When people stay in one area, they are inclined to build permanent structures, homes, shelter for animals, places to store excess food.  They begin to have a greater sense of community in one place, as well, and the elimination of the need to travel far and wide for food allows for a little more "specialization" of tasks.  In combination, these elements set the stage for community structures to be built, religious institutions and community storage facilities, for example.  Infrastructure emerges, means of dealing with sewerage, paths or roads, the community well.  All of this leads to what we think of as civilization.   

What is the authors purpose in writing Skipping Christmas?

We can probably guess why the author wrote the story, based on his words during the premier of Christmas With The Kranks.
The movie Christmas With The Kranks is adapted from Grisham's story Skipping Christmas. During his interview at the movie premier, John Grisham lamented the commercialization of Christmas. Although he admits that skipping Christmas entirely isn't the answer, he expresses his belief that there should be a better way to celebrate the holiday.
The commercialization of Christmas often leads to unnecessary stress for many families during the holidays, especially in financial terms. Essentially, the reason for the holiday has been lost, and Grisham points this out in his story. In Skipping Christmas, Luther Krank daydreams about the joy it would give him to avoid all the stresses commonly associated with Christmas:

No trees, no shopping, no meaningless gifts, no tipping, no clutter and wrappings, no traffic and crowds, no fruitcakes, no liquor and hams that no one needed, no "Rudolph" and "Frosty," no office party, no wasted money...

Luther reminds his wife, Nora, that they spent sixty-one hundred dollars on Christmas the year before and have "precious little to show for it." He also admits that he isn't too happy about the loss of time, "the traffic, stress, worry, bickering, ill-will, [and] sleep loss" associated with celebrating the holiday.
Luther's words echo Grisham's in his interview. In the story, certain materialistic traditions have become so entrenched in the social consciousness that the Kranks suffer great disapproval from members of their community for wanting to skip celebrating the holiday. So, it can be inferred that Grisham's humorous story is an attempt at highlighting the problems associated with commercializing Christmas.

From the poem "Phenomenal Woman" by Maya Angelou, please explain the stanzas beginning "I walk into a room" and "That's me."

In the second stanza and the two-line third stanza, the speaker explains how she is a "phenomenal woman." These stanzas are a response to the wonder in the minds of women who wish to know "where [her] secret lies."
Strangely enough, the speaker seems to be the only one who comprehends the source of her compelling attractiveness. Rather than stating one attribute such as dazzling eyes or an amazing figure, the speaker identifies her feminine power as emanating from a certain elusive quality. This quality cannot be defined, but is subtly communicated to those who perceive her in the combination of her physical traits along with her graceful movements that are generated by her energy and inner beauty:

It's the fire in my eyes,And the flash of my teeth,The swing in my waist,And the joy in my feet.

From certain words that the speaker uses, such as "fire," "flash," "swing," and "joy," the inner strength and confidence of this woman are conveyed, as these words suggest the energy and happiness that seem to charge the air when she enters a room or passes by.
Having asserted simply that she is a "Phenomenal woman" in the two-line third stanza, Angelou's speaker acknowledges that she cannot formulate her attractiveness. 
Not unlike ideas expressed in another poem of Angelou's entitled "Woman Me," the features that the speaker of "Phenomenal Woman" possesses are those that provide her an indefinable attractiveness. Her "certain something," her "phenomenon," derives from an inner source and attractiveness formed by a combination of movements and features which, though not conforming to any ideal, certainly attract men and cause women to "wonder where [her] secret lies." 

When does Nhamo return to the science station?

Nhamo goes back to the science station after living with her uncle. When she first arrives at the station, Nhamo wants to stay, but she is advised by the scientists to attend school. The scientists contact Nhamo's uncle Industry, who at first believes that Nhamo is an imposter who wants his wealth. Once Nhamo is able to convince Industry about her lineage, he allows Nhamo to stay with him and attend school with his children.
Although her new life is better than her life back at the home village, she still feels distant from her family. As a result, the scientists begin to fulfill the supportive aspects of family that Nhamo has lacked throughout her life. Not only do they nurse her back to health, they also teach her to read and write. Also, the head scientist saves the gold nuggets that Nhamo got from Ambuya in case Nhamo needs them in the future.

Did Montag and Mildred divorce?

Montag and Mildred do not get a divorce, but they do separate in Part Three of the novel. After Montag interacts with his intuitive neighbor, Clarisse McClellan, he realizes that he is not in love with Mildred and becomes aware that his marriage is a failure. Montag and his wife even struggle to remember where they first met each other, and Mildred does not share Montag’s interest in literature.
In Part Two, Montag returns home after visiting Faber and reads poetry aloud to his wife and her two friends. After Montag makes them cry, Mildred calls in an alarm on him. In Part Three, Montag arrives at his home with Captain Beatty, and Mildred rushes out of the house without acknowledging her husband. Mildred leaves Montag because of his affinity for literature and refuses to speak to him while she is getting into a cab.
Unlike Montag, Mildred has no desire to examine or change her superficial, shallow life. The two characters do not get a formal divorce, but they do separate. Towards the end of the story, Montag escapes to the wilderness, and Mildred ends up dying in the nuclear attack.

In Fahrenheit 451, Montag and Mildred do not get divorced but they do separate from each other. In fact, Mildred leaves Montag because she becomes increasingly frustrated with his desire to read books and to bring an end to the system of censorship.
The real turning point for Montag and Mildred's marriage comes in Part Two when he reads a poem out loud to Mildred and her friends. Not only does Montag really upset Mildred's friends when he does this, but he makes her angry enough to report his activity to Captain Beatty. Shortly after, Mildred packs her things and leaves him without offering any explanation.
Montag and Mildred do not get the opportunity to either fix their marriage or divorce since she is killed in Part Three of the novel when the city is destroyed.

Single Variable Calculus, Chapter 8, 8.1, Section 8.1, Problem 58

Find the volume generated by rotating the region bounded by $y = e^x$,$ y =e^{-x}$ and $x = 1$ about $y$-axis. Use cylindrical shells method.
By using vertical strips have distance to the $y$-axis as $x$. Such that if you rotate these length about the $y$-axis, you'll get a circumference of $c = x$. Also, the height of the strips resembles the height of the cylinder as $H = y_{\text{upper}} - y_{\text{lower}} = e^x - e^{-x}$, Thus, the value is



$
\begin{equation}
\begin{aligned}
V &= \int^1_0 c (x) H(x) dx\\
\\
V &= \int^1_0 (2 \pi x) \left(e^x - e^{-x}\right) dx\\
\\
V &= 2 \pi \int^1_0 x \left(e^x - e^{-x}\right) dx
\end{aligned}
\end{equation}
$

By using integration by parts
$\displaystyle V = \frac{4\pi}{e}$ cubic units

In the first part of Twilight, Bella sees Edward standing in her room in the dark, but when she turns on the light, he is gone. Was she dreaming, or was this really Edward watching her?

Although neither Bella nor the reader can possibly know the answer to this question at this point in the story, we do find out the actual answer in chapter 14. By this point in the story, Bella knows that Edward and the other members of the Cullen family are all vampires. She is incredibly curious about them, their habits, and how they came to be. As the conversation continues, Bella notices that Edward knows more about her house than he should. She finds out that Edward has "spied" on her at night. Bella is taken aback for a moment by this information, but she is more curious than anything else. Bella asks Edward how often he visits her at night while she sleeps, and Edward confesses that he comes just about every night. This confirms for readers that Bella more than likely really saw Edward in her room earlier.

I still didn't turn around. "How often did you come here?"
"I come here almost every night."
I whirled, stunned. "Why?"
"You're interesting when you sleep." He spoke matter-of-factly. "You talk."

Single Variable Calculus, Chapter 2, 2.3, Section 2.3, Problem 1

Determine the limits that exist. If the limits does not exist, explain why. Given that
$
\quad \lim\limits_{x \rightarrow 2} f(x) = 4 \qquad \lim\limits_{x \rightarrow 2} g(x) = -2 \qquad \lim\limits_{x \rightarrow 2} h(x) = 0
$


$
\begin{equation}
\begin{aligned}
\text{(a) }& \lim\limits_{x \to 2} \quad [f(x) + 5g(x)] &
\text{(b) }& \lim\limits_{x \to 2} \quad [g(x)]^3\\
\text{(c) }& \lim\limits_{x\to 2} \quad \sqrt{f(x)} &
\text{(d) }& \lim\limits_{x\to 2} \quad \frac{3f(x)}{g(x)}\\
\text{(e) }& \lim\limits_{x\to 2} \quad \frac{g(x)}{h(x)} &
\text{(f) }& \lim\limits_{x\to 2} \quad \frac{g(x)h(x)}{f(x)}
\end{aligned}
\end{equation}
$



a.) $\lim\limits_{x \to 2} \quad [f(x) + 5g(x)]$

$
\begin{equation}
\begin{aligned}
\lim\limits_{x \rightarrow 2} \quad[f(x) + 5g(x)] & = \lim\limits_{x \rightarrow 2} f(x) + \lim\limits_{x \rightarrow 2} 5 g(x) && \text{(Substitute the given values.)}\\
\lim\limits_{x \rightarrow 2} \quad[f(x) + 5g(x)] & = 4 +5(-2) & &\text{(Simplify.)}\\
\end{aligned}
\end{equation}\\
\boxed{\lim\limits_{x \rightarrow 2} \quad[f(x) + 5g(x)] = -6 }
$


b.)$ \lim\limits_{x \to 2} \quad [g(x)]^3$

$
\begin{equation}
\begin{aligned}
\lim\limits_{x \rightarrow 2} \quad [g(x)]^3 &&& \text{(Substitute the given value.)}\\
\lim\limits_{x \rightarrow 2} \quad [g(x)]^3 &= (-2)^3 && \text{(Simplify)}\\
\end{aligned}
\end{equation}\\
\boxed{\lim\limits_{x \rightarrow 2} \quad [g(x)]^3 = -8}
$


c.) $\lim\limits_{x\to 2} \quad \sqrt{f(x)}$

$
\begin{equation}
\begin{aligned}
\lim\limits_{x \rightarrow 2} \quad \sqrt{f(x)} &&& \text{(Substitute the given value)}\\
\lim\limits_{x \rightarrow 2} \quad \sqrt{f(x)} &= \sqrt{4} && \text{(Simplify)}\\
\end{aligned}
\end{equation}\\
\boxed{\lim\limits_{x \rightarrow 2} \quad \sqrt{f(x)} = 2}
$


d.) $\lim\limits_{x\to 2} \quad \frac{3f(x)}{g(x)}$

$
\begin{equation}
\begin{aligned}
\lim\limits_{x \rightarrow 2} \quad \displaystyle\frac{3f(x)}{g(x)} &&& \text{(Substitute the given values)}\\
\lim\limits_{x \rightarrow 2} \quad \displaystyle\frac{3f(x)}{g(x)} &= \frac{3(4)}{-2} && \text{(Simplify)}\\
\end{aligned}
\end{equation}\\
\boxed{\lim\limits_{x \rightarrow 2} \quad \displaystyle\frac{3f(x)}{g(x)} =-6}
$


e.) $ \lim\limits_{x\to 2} \quad \frac{g(x)}{h(x)} $

$
\begin{equation}
\begin{aligned}
\lim\limits_{x \rightarrow 2} \quad \displaystyle \frac{g(x)}{h(x)}& \qquad \qquad \qquad \text{(Substitute the given values)}\\
\lim\limits_{x \rightarrow 2} \quad \displaystyle \frac{g(x)}{h(x)}& = \frac{-2}{0}\\
\end{aligned}
\end{equation}\\
\boxed{\text{Limit does not exist, the function is undefined because denominator is zero.} }
$


f.) $\lim\limits_{x\to 2} \quad \frac{g(x)h(x)}{f(x)}$

$
\begin{equation}
\begin{aligned}
\lim\limits_{x \rightarrow 2} \quad \displaystyle \frac{g(x)h(x)}{f(x)} & && \text{(Substitute the given values)}\\
\lim\limits_{x \rightarrow 2} \quad \displaystyle \frac{g(x)h(x)}{f(x)} &= \frac{(-2)(0)}{4} && \text{(Simplify)}
\end{aligned}
\end{equation}\\
\boxed{\lim\limits_{x \rightarrow 2} \quad \displaystyle \frac{g(x)h(x)}{f(x)} = 0}
$

What are some character traits of Peyton Farquhar in An Occurence at Owl Creek Bridge?

Peyton Farquhar is the protagonist in Ambrose Bierce's short story entitled "An Occurrence at Owl Creek Bridge." He is described as a wealthy plantation owner from a highly respected Alabama family. He was a secessionist, meaning that he supported the Southern cause of leaving the union. The story is set during the American Civil War, when the issue of slavery divided the country. Bierce describes Farquhar as "ardently devoted to the Southern cause."
Peyton Farquhar was a husband and a father. Readers can infer that he was devoted to his wife and children. Right before his death by hanging, his family occupies his thoughts. The narrator mentions later in the story that it is the thought of his wife and children that spurs Farquhar on.
Bierce describes him as one who longed to be a soldier fighting on the front lines, which he imagined released pent-up energy and carried honor and glory with it. But his services were apparently needed as a spy, so he was unable to fulfill this desire. Because of their work, spies must be able to lie, to deceive, and to gain the trust of the enemy. Readers can infer that these were characteristics Farquhar possessed.

"Circumstances of an imperious nature, which it is unnecessary to relate here, had prevented him from taking service with that gallant army which had fought the disastrous campaigns ending with the fall of Corinth, and he chafed under the inglorious restraint, longing for the release of his energies, the larger life of the soldier, the opportunity for distinction. That opportunity, he felt, would come, as it comes to all in wartime. Meanwhile he did what he could. No service was too humble for him to perform in the aid of the South, no adventure to perilous for him to undertake if consistent with the character of a civilian who was at heart a soldier, and who in good faith and without too much qualification assented to at least a part of the frankly villainous dictum that all is fair in love and war."

It's interesting to note that he considers himself a "student of hanging." That could be due to his work as a spy, but one wonders if it also has something to do with his life as a plantation owner.

Calculus of a Single Variable, Chapter 8, 8.3, Section 8.3, Problem 34

(ds)/(d alpha) = sin^2(alpha/2)cos^2(alpha/2)
To solve, express the differential equation in the form N(y)dy = M(x)dx .
So bringing together same variables on one side, the equation becomes
ds =sin^2(alpha/2)cos^2(alpha/2) d alpha
To simplify the right side, apply the exponent rule (ab)^m=a^mb^m .
ds =(sin(alpha/2)cos(alpha/2))^2 d alpha
Then, apply the sine double angle identity sin(2 theta)=2sin(theta)cos(theta) .

sin (2*alpha/2)=2sin(alpha/2)cos(alpha/2)
sin(alpha)=2sin(alpha/2)cos(alpha/2)
sin(alpha)=2sin(alpha/2)cos(alpha/2)
(sin(alpha))/2=sin(alpha/2)cos(alpha/2)

Substituting this to the right side, the differential equation becomes
ds = ((sin (alpha))/2)^2 d alpha
ds = (sin^2 (alpha))/4 d alpha
Then, apply the cosine double angle identity cos(2 theta)=1-2sin^2(theta) .

cos (2alpha) = 1 - 2sin^2(alpha)
2sin^2(alpha) = 1-cos(2 alpha)
sin^2(alpha) = (1-cos(2 alpha))/2

Plugging this to the right side, the differential equation becomes
ds = ((1-cos(2 alpha))/2)/4 d alpha
ds = (1-cos(2alpha))/8 d alpha
ds = (1/8 - cos(2alpha)/8) d alpha
Then, take the integral of both sides.
int ds = int (1/8 - cos(2alpha)/8) d alpha
int ds = int 1/8 d alpha - int cos(2 alpha)/8 d alpha
Apply the integral formulas int adx = ax + C and int cos(x) dx = sin(x) + C .
s+C_1 = 1/8alpha - (sin(2alpha))/16 + C_2
Then, isolate the s.
s = 1/8alpha - (sin(2alpha))/16 + C_2-C_1
Since C1 and C2 represents any number, it can be expressed as a single constant C.
s = 1/8alpha - (sin(2alpha))/16 +C

Therefore, the general solution of the differential equation is s = 1/8alpha - (sin(2alpha))/16 +C .

Explain this quote ¨Yet this government never of itself furthered any enterprise, but by the alacrity with which it got out of its way. It does not keep the country free. It does not settle the West. It does not educate¨

This quote needs to be understood within the context of the overall essay.

"On the Duty of Civil Disobedience" by Henry David Thoreau extols individuality and disparages government. Thoreau states that ideally, there should be no government, and that people should be free to govern themselves as they see fit. Although government is meant to serve a practical purpose, it usually does more harm than good.


It finally amounts to this, which I also believe, - "That government is best which governs not at all;" and when men are prepared for it, that will be the kind of government which they will have. Government is at best but an expedient; but most governments are usually, and all governments are sometimes, inexpedient.


The above quote speaks of governments in general, but in the quote within the question - "Yet this government never of itself furthered any enterprise but by the alacrity by which it got out of its way..." Thoreau is writing specifically about the government of the United States in the mid-19th century. He is saying that the government interfering in the affairs of its citizens does not contribute to education, commerce, and the settlement of the West, and that if the government backed off and became less involved, people would be able to accomplish more. Thoreau makes it clear, though, that the United States is not in a position or stage of growth to abolish government completely when he says in the next paragraph: "I ask for, not at once no government, but at once a better government."

This is an example of Thoreau's individualism and strong stand of the importance of conscience above the unjust dictates of government that later profoundly influenced people such as Leo Tolstoy, Mahatma Gandhi, and Martin Luther King, Jr.

This quote from Thoreau’s essay “Civil Disobedience” succinctly summarizes one of the key sentiments negotiated in the text. In the essay, Thoreau argues against governmental overreach and governmental involvement in the affairs of American citizens. In the second paragraph, Thoreau calls the government “a sort of wooden gun” and a “complicated machinery” which serves “to satisfy that idea of government which they [the citizens] have.” What Thoreau seems to suggest here is that the government serves a symbolic function, or that it is an abstract idea necessary for citizens to have a sense of security and perhaps a shared purpose. In light of this, the quote under consideration here seems to suggest that it is not the government itself but rather the citizens, who populate the social, economic, geographic, and cultural space that represents the power of the country. In other words, Thoreau seems to think of the government as an empty shell that only receives its power and authority from people who do the work.     

In Tuck Everlasting, what three things happen that seem to have no connection between the Tucks and the Fosters?

The prologue to Tuck Everlasting lists three seemingly unrelated things that happen one August day. At dawn, Mae Tuck sets out for the woods at the edge of the village of Treegap, where she intends to meet her sons, Miles and Jesse, as she does once every ten years. At noon, Winnie Foster begins to think about running away. And at dusk, a stranger appears at the Fosters' door looking for someone.
The three events turn out to be very much interrelated, and they produce a conflict disastrous enough to cause "this weary old earth" to "trembl[e] on its axis like a beetle on a pin." The plot of the book unfolds as these three events come together.
The next day, Winnie acts on her plan to run away by heading into her family's wood, which is where Mae plans to meet Miles and Jesse. Winnie meets Jesse first and sees him drinking the miraculous water. In order to keep their secret, Mae, Jesse, and Miles kidnap Winnie.
The stranger who had appeared at the Fosters' gate the previous night was looking for the Tucks. Because Mae carried her music box into the wood and played it as he was standing at the Fosters' gate, the man suspects that one of the Tucks is in the wood, so he observes as the Tucks set out on the road with Winnie toward their home. He follows them and eavesdrops on the story when the Tucks explain the secret of the water to Winnie.
Now the three events have intersected, and with the stranger's nefarious intentions to sell the water to the world, a cataclysm looms that only Winnie can prevent.

The Prologue, or the introduction section of the novel, sets up the mystery of the Tucks and the major changes that come to Winnie Foster's life by describing three events that seem to have no connection. The events in question, take place on a summer day, during the first week of August. The readers are told of how Mae Tuck, at dawn, sets out on her traditional trip to Treegap woods. The narrator tells us that Mae makes this trip every 10 years. This is the start of the mystery of the Tuck family and introduces the reader to this strange family. The reader starts to question how old is Mae and her sons and why do they meet every 10 years. The reader is then introduced to Winnie Foster, who's family owns the Treegap woods, and who is considering running away. This draws the reader into Winnie's world and mind set, at the start of the novel. The last event, that takes place near sunset, is the arrival of a stranger. Just as the narrator set up the mysterious Tuck family, this stranger also comes with a mystery. He appears at the Foster's gate and he has a mission to find someone, but he would not say who.

The three things that the question is asking about can be found in the story's opening prologue.  It is there that readers are told that three things happened that appeared to have no connection to each other at all.  
The first thing that happened was Mae Tuck began to head toward the town of Treegap.  The narrator tells readers that this is something that she does every ten years.  This event happened at dawn.  
The second thing that happened was Winnie Foster decided that she would begin thinking about running away.  This event happened at noon.  
The third thing that happened was a stranger arrived at the Foster home looking for someone; however, he would not say who exactly he was looking for.  This event happened at sunset. 
The events are connected to each other because Mae is going to Treegap to meet her sons.  Winnie runs away and meets the Tucks, and the stranger follows Winnie and the Tucks in order to learn their secret.  

What is the meter of "Sonnet 73"?

If you have read any of Shakespeare's other sonnets—or indeed, any sonnet in the traditional form—you may recognize this meter. It is iambic pentameter, a meter in which each line contains five iambic feet, or iambs.
An iamb is an unstressed beat followed by a stressed beat (or emphasized syllable). So, iambic pentameter does not mean that there are only five syllables in a line, but that there are five points of emphasis. Let's look at a line from this poem poem:

That TIME of YEAR thou MAYST in ME beHOLD.

The capitalized syllables represent the places where we'd give stress to the sentence if we were reading it aloud.
Now, the meter in this poem is perfect—all the lines conform exactly to the iambic pentameter guideline. However, sometimes we will find a poem written in iambic pentameter where one or two of the lines doesn't quite fit—maybe it has four iambs, or six. In such a case, we would still describe the poem as being written largely in iambic pentameter.

I am going to assume that the question is asking about "Sonnet 73" by William Shakespeare.  Being a Shakespearean sonnet, this poem's rhythm and meter is iambic pentameter.  An iambic foot is composed of an unstressed syllable followed be a stressed syllable.  Shakespeare will use this rhythmic foot five times per line, and that gives each line 10 total syllables or five iambic feet.  That is why it is called iambic pentameter.  Let us look at the first line of the poem to illustrate this point.  I will use bold to illustrate the stressed syllables.  

That time / of year / thou mayst / in me / behold 

"Sonnet 73" will use this particular rhythm and meter through most of the poem. However, line 13 messes with the iambic foot at the beginning of the line. The first syllable is stressed, and the following syllable is unstressed.  This is called a trochee, and it is the opposite of the iambic rhythm.  

This thou / perceiv'st / which makes / thy love / more strong.

Why does Helen consider the old-fashioned garden the paradise of her childhood?

From her early years, Keller, as she describes in her memoir, had a love of nature. Being blind and deaf, she enjoyed going into the garden near her house, Ivy Green, because she liked the scents of the flowers and the boxwood hedges. She says it was a "joy" to go from place to place in the garden until she found a particular vine that meant she had arrived at the summer house at the garden's far end. This suggests that the garden was a place of mystery and wonder to her—she wasn't quite sure where she was at any given time, and she had to rely on her senses of smell and touch to guide her.
She writes of loving the clematis, jessamine, and butterfly lilies, but especially the climbing roses. She says she has never, in northern greenhouses, found roses like those that bloomed at her childhood home, describing them as

filling the whole air with their fragrance, untainted by any earthy smell; and in the early morning, washed in the dew, they felt so soft, so pure, I could not help wondering if they did not resemble the asphodels of God's garden.

It must have been a pleasure to escape a domestic world, where it was difficult for her to communicate, and enter into a place where she could feel free and experience the beauty of nature.

Helen inherits her father's love for gardens. And for her, the garden near her home becomes a haven from a dark and troubled world. Spending time among all those flowers with their soft, smooth textures and their delicate fragrances allows Helen to develop two of her remaining senses. The garden becomes a true paradise for Helen, a sanctuary of peace and repose where she can engage with the outside world in a way that simply isn't possible elsewhere. The delights of the garden crucially foreshadow an event of great significance in Helen's life. The connection she establishes with the world around her in the garden is developed further when Annie teaches her the rudiments of language during that extraordinary day at the water-pump.

In lord of the flies, how does golding use the setting to explore ideas and themes

One theme in Lord of the Flies is the question of what it means to be part of a society or to be civilized. The wild, unfamiliar, setting presents challenges to the boys' understanding of societal expectations and leads them to act in ways that would have been impossible or unacceptable in their home environment.
One element of the setting that influenced the boys' behavior is the isolation of the island on which they land. After their plane crashes, they find themselves without the supervision of adults or the comforts of home. While the older boys attempt to replicate some of the social structures they are familiar with by organizing a hunting party and assigning boys to make and watch the signal fire, they resort to violence and harsh treatment of weaker boys. Without the guidance of adults or the oversight of a larger community with laws and consequences, the boys' activities quickly get out of hand. An example is when their fire burns out of control and the causes a blaze in the forest, in which one of the younger boys disappears.
The wildness of the setting, an uninhabited island, also contributes to the exploration of what what it means to be civilized. Events that would be nearly unthinkable in the populated, controlled, setting where they came from become accepted in the wild setting of the island. In their excitement over the wild sow that Jack's hunting party has caught and killed, the hunting party fails to recognize Simon coming out of the jungle and kills him. In a wild world where they must kill to survive, the boys lose perspective and are unable to figure out where to draw the line between survival and aggression.
While the boys are alone on the island, they are also not completely isolated from the world at large, a point that is brought home when a soldier escaping from an airplane battle over the island lands, dead, by their signal fire. Although the reader may be horrified by the violent actions of the boys, this element of the setting, its proximity to the war raging in the "civilized" world nearby, highlights the parallels between the violence perpetuated among the boys on the island and the violence of the war the adults are engaged in back in civilization.
The setting of The Lord of the Flies makes it possible for the reader to explore the themes of what it means to be civilized by removing a group of boys from the constraints of societal expectations as well as the supports of their community. By placing the boys in a wild, uninhabited place just out of reach of adults and their war, William Golding leads readers to question what it means to be part of a civilization.

One of the themes of the book is savagery vs. civilization. The boys have been raised within a civilization. There are rules and order that govern their lives, and the boys act accordingly within that structure in order to succeed; however, that society governed by civilized people is removed by setting the story on a deserted island. There are no people on the island; therefore, there's no society, civilization, no rules, no order, etc. The boys are free to set up their own governing body, and they attempt to mimic what they know. Unfortunately, with no additional societal support to help enforce civility, savagery begins to take over. The boys are forced in some ways to behave like savages. They are forced to hunt and scavenge for food, but their savagery escalates. The boys turn their savagery and blood lust toward each other. Had the plane crashed outside some small rural town, I do not believe the boys would have changed so drastically. The setting helps readers believe in the character changes.
I think another theme that the novel explores is isolation. While the group of boys is somewhat large, the group itself is isolated from any external influences. The setting is an island that doesn't see a lot of passing traffic, and that allows Golding to keep the boys on the island for quite some time. It's never clear exactly how long the boys are on the island, but we are told about hair lengths becoming much longer and clothes being very tattered. The isolation creates changes in the boys. They lose their innocence much sooner because of their isolation and turn toward savagery.

Explain why Pip feels disappointed as he leaves Miss Havisham's house.

Pip has recently learned the true identity of his benefactor. For years, he'd always assumed it was Miss Havisham. For her part, she had done absolutely nothing to disabuse him of this notion; indeed, she positively encouraged it. It was all part of Miss Havisham's little game to toy with her greedy relatives, to make them jealous by giving the impression that she favored Pip over them. Pip feels like a fool, feels like he's been used—and he has. It's not surprising, then, that he's so thoroughly disappointed with Miss Havisham. Worse still, he's emotionally crushed, devastated by the cruelty of Estella, who's also been playing her own little games, toying with his affections. Estella has learned well the lessons of her mistress, as she was always intended to.

What are the differences between Abraham and Moses?

Abraham and Moses are fundamental figures in both Judaism and Christianity. They each played an integral role in the development of these religious traditions.
The most basic differences between Abraham and Moses are the facts that they were two very different men living hundreds of years apart.
Biblical scholars date Abraham's lifetime to sometime around 2000 BCE. Most of what is known of Abraham's life comes from the book of Genesis in the Christian Old Testament of the Bible. These writings are also included in the Tanakh (Hebrew Bible). Interestingly, Moses is traditionally given credit for the authorship of Genesis, along with the other books that comprise the Pentateuch (first five books of the Bible). In other words, Moses may have been Abraham's biographer.
According to the Genesis account, Abraham was called by God (Yahweh) out of Ur in what is now Iraq. Abraham entered a covenant with God in which his descendants would be the "chosen people" (Hebrew people) and would demonstrate their unique relationship with God through the outward act of circumcision. This is know as the Abrahamic Covenant.
According to Biblical tradition, Abraham became the patriarch of the Hebrew (Jewish) people through his son, Isaac, by his wife, Sarah, as well as the patriarch of the Arab people through his son Ishmael, by his Egyptian concubine, Hagar.
The book of Genesis contains many details of Abraham's life and deeds, the most famous of which is his attempted sacrifice of Isaac. Abraham is commanded to kill his son as a sacrifice to the Lord, but is prevented from completing the act at the last moment. God provided a ram for a sacrifice instead. Most Hebrew and Christian scholars regard this event as either a test of Abraham's faith and obedience, or as possibly a prelude to the coming of Christ--when God sacrificed His own Son.
Because of his obedience and faithfulness to God, Abraham is rewarded with many descendants, great wealth, and a long life.
Moses was the son of a Hebrew slave in Egypt. According to Genesis, the Hebrew people moved to the land of Goshen in Egypt during a terrible famine. This was during the time of Joseph, Abraham's great-grandson. Over time, the Hebrews were enslaved by their Egyptian hosts.
Scholars believe that Moses lived around 1300 or 1200 BCE. Moses is saved from death (Hebrew boys were being thrown into the Nile) by the quick thinking of his mother and sister and the compassion of an Egyptian princess. In order to save her baby, Moses' mother hides him in a basket among the reeds. While bathing in the river, an Egyptian princess finds the baby and decides to raise him as her own. Moses' older sister was keeping watch nearby and when she learns the princess intends to adopt her brother, fetches her mother to serve as a wet nurse. 
According to the account of Moses' life, found in the book of Exodus, Moses was raised as an Egyptian prince. When he is a young man he is told of his true origins and ends up murdering an Egyptian who is beating a Hebrew slave. After this, Moses is exiled to the desert. He eventually rescues and marries the daughter of the priest of Midian. Moses spent several years as a shepherd before being called by God.
According to the Biblical account, Yahweh appeared to Moses in the form of a burning bush and revealed his name to him. He commanded him to return to Egypt and convince Pharaoh to let the Hebrew people go. Moses was reluctant but eventually agreed. The book of Exodus gives the dramatic story of Moses and the ten plagues, the last of which was the death of every firstborn male, that finally convince the Pharaoh to let the Hebrews go.
Through a series of miraculous events Moses eventually leads his people on a 40+ year journey to the promised land of Israel. Most significnt during this journey is the giving of the law (the Ten Commandments) and the instructions to buid the ark or the tabernacle (God's dwelling on earth). The giving of the law and the covenant it represented between Yahweh and the Hebrew people is known as the Mosaic Covenant.
Moses' relationship with the Lord was more turbulent than that of Abraham. Moses was not allowed to enter the promised land due to a lack of faith he had shown many years previous. Moses is credited with writing the first five books of the Bible/ Tanakh and with laying the foundation of Hebrew and Christian morality through the Ten Commandments.

Both Abraham and Moses are considered men of deep faith, and both have strong devotion to the Hebrew God. Other than simple time period differences or differences in the events that they lived through, there is a difference in their initial faith and willingness to serve God's call. Abraham is a man of incredible devotion to God. He rarely, if ever, argues with God, and he is always willing to do what God tells him to do. There might be times when he takes matters in to his own hands, but he is still going to where God called him. Abraham's faith and devotion to God is so deep that he unquestioningly took his son, Isaac, up a mountain to be sacrificed. God eventually supplies an animal to be sacrificed, but Abraham was willing to let his long awaited for son die instead.
On the other hand, Moses is not as quick to obey God's commands. A good example of this is when God appears to Moses in the burning bush. God tells Moses that he is being called to help free the people of Israel from their Egyptian masters. Moses argues against God and claims that he won't be an effective enough communicator to deliver God's message to the Egyptians. Unlike Abraham, Moses struggled with taking God at his word and doing things exactly the way that God said to do them. A good example of this is in Numbers 20. God told Moses to speak to a rock in order to get water to spring forth from the rock; however, Moses struck the rock with his staff instead. As punishment, God would not allow Moses to enter the promised land.

7The Lord said to Moses, 8“Take the staff, and you and your brother Aaron gather the assembly together. Speak to that rock before their eyes and it will pour out its water. You will bring water out of the rock for the community so they and their livestock can drink.”
9So Moses took the staff from the Lord’s presence, just as he commanded him. 10He and Aaron gathered the assembly together in front of the rock and Moses said to them, “Listen, you rebels, must we bring you water out of this rock?” 11Then Moses raised his arm and struck the rock twice with his staff. Water gushed out, and the community and their livestock drank.
12But the Lord said to Moses and Aaron, “Because you did not trust in me enough to honor me as holy in the sight of the Israelites, you will not bring this community into the land I give them.”

What was happening at the time that can provide insight into the motivations and perspective of the Montesquieu when he wrote The Spirit of the Laws?

The Spirit of the Laws (originally De l'esprit des loix) was released in 1748. It is a bit surprising that this was so far before the French Revolution, because many of the ideas in The Spirit of the Laws about liberty, republic, and constitutional government would go on to be vital in influencing the French Revolution. Yet it took over a generation for this revolution to really take hold.Montesquieu was writing toward the end of what would come to be called the Ancien Regime, where France was governed by a monarchy with essentially absolute power. The king in 1748 was Louis XV, who had been officially king for decades but only really took the reins of power on his own after the death of his mentor and chief minister in 1744. Louis XV was widely regarded as incompetent and untrustworthy, and became a symbol of all that was wrong with absolute monarchy. This was probably one of the largest influences on Montesquieu, as he tried to envision new forms of government that would be superior to monarchy and turned to what he knew about the republics of Classical Greece and Rome. 1748 was also when the War of the Austrian Secession had just concluded with a result that was not very favorable to France, further discrediting the government.
https://books.google.com/books?id=aTqQ9vCTMHAC&pg=PA44

https://oll.libertyfund.org/titles/montesquieu-complete-works-vol-1-the-spirit-of-laws

https://www.britannica.com/biography/Louis-XV

The African slaves who arrived in the English colonies in the seventeenth century________. a) had no prior exposure to slavery in Africa b) were often Christians when they were enslaved c) often were brought to North America from Brazil or the Caribbean d) came from societies with no class divisions

The correct answer is C.
There was a slave system that had existed in West Africa prior to the Age of Exploration and Conquest. However, the slave system that existed bore no resemblance to that which developed in the New World in the 18th- and 19th-centuries. Firstly, one would not be in bondage for a lifetime. Secondly, the slave system more closely resembled a system of apprenticeship. A young man would be captured from a neighboring tribe, as part of the spoils of war, then kept as a slave for a number of years. During those years, he would learn a skill, then would be freed and allowed to apply that skill toward making a living for himself and his family. Thirdly, there is no evidence showing that the system of cruel and inhumane retribution that existed in the New World also existed in West Africa. There was also no concerted effort to keep slaves in states of ignorance and degradation.
West Africans who were captured and brought to the New World were followers of Islam, not Christianity. The Kingdom of Mali, for example, accepted Islam in the early fourteenth century. Islam reached West Africa as a result of trade with North African states.
Lastly, as with many societies, there were class divisions in West African kingdoms. Kingdoms are defined by class division. Each kingdom was comprised of village states headed by a particular family. Village states were formed by clans, or families, who shared common ancestry. Each African king had a group of ministers and advisers. Strong village states, which were comprised of a strong military, good leadership, and ample resources (e.g., livestock) could grow into powerful kingdoms. The kingdoms of Mali and Songhay were characterized by such strength.
Now, let's focus on why "C" is the correct answer. The first Africans were brought to the New World in the 16th-century. The Norton Anthology of American Literature and John Hope Franklin's From Slavery to Freedom: A History of African Americans claim that the first slaves were brought to Hispaniola (the island now comprised of both Haiti and the Dominican Republic) in 1502, and into other parts of Latin America in the second decade of the sixteenth century. Most West Africans were taken to Brazil and the Caribbean.
Brazil, a nation which currently has the largest population of black people outside of Nigeria, received about forty-five percent of the slaves transported across the Atlantic. Islands in the Caribbean, particularly the Barbados, which had a thriving sugar trade, received another forty-five percent. The thirteen colonies only received around five percent, while the other five percent of slaves were scattered throughout the Americas. 
The response in Answer C is slightly misleading. For, the Caribbean is, of course, a part of North America. Slaves who first disembarked in the Barbados might have been shipped North to other thriving commercial colonies, such as South Carolina or Virginia. By 1834, the British abolished slavery in all of its colonies. Demand for slaves declined in Virginia, though not in South Carolina, in the 1820s as a result of dropping prices for tobacco. As a result, many Virginia slaves were frequently shipped to the Deep South (e.g., East Texas, Mississippi, Arkansas, and Alabama) where the cotton trade thrived. 

What is the structure of tragedy in Oedipus Rex?

The dramatic structure used by Sophocles in Oedipus Rex is essentially the same five-part structure found in tragic plays written by other ancient Greek playwrights, including Aeschylus and Euripides.
Prologos. The play opens with a prologos (prologue) which is the first entrance of one or more actors in the play. These actors provide "exposition" (background information) on the play for the audience (although the audience is very familiar with the myths and legends on which the play is based), and they set the play in motion.
In Oedipus Rex, a Priest appeals to Oedipus, King of Thebes, on behalf of the Theban people who are suffering from a drought and plague. Creon returns from the Oracle at Delphi to report that Apollo commands that in order for the drought and plague to be lifted, Thebans must find and banish from Thebes the murderer of their former King, Laius. Oedipus vows to do so.
Parodos. Following the prologos, the Chorus enters, dancing and singing the parados—a choral ode. The Chorus in Oedipus Rex describes how the drought and plague are affecting the people of Thebes and prays to Apollo, Athena, and Artemis to help them find the murderer and end their suffering.
Episode. An episode is what we know as a "scene." In the Greek tragedies of the 5th century, the number of episodes varied from play to play. In the 4th century, tragedies usually had five episodes, from which the five-act play structure of the plays of Shakespeare and other playwrights evolved. Oedipus Rex was written in about 429 B.C., and has six episodes. The episodes in Oedipus Rex contribute to the "exposition" of the play, as well as the" rising acting," composed of the complications and conflict in the play, and the "climax" of the play.
Stasimon. After each episode, the actors leave the stage, and the Chorus returns and sings and dances another choral ode called a stasimon. The stasimon usually comments on the preceding episode, and sometimes expands on the story and provides further information for the audience, as is the case in Oedipus Rex. The play then alternates between episodes and stasimon until the final scene.
Exodus. The exodus is the final scene of the play consisting of the "resolution" or "denouement" of the play, in which all of the issues of the play are resolved. In Oedipus Rex, Creon becomes King, restoring order to Thebes, and Oedipus is exiled (although Oedipus actually exiles himself).
The actors leave the stage, the Chorus sings one last choral ode imparting to the audience the lesson of the play, and the Chorus leaves the stage for the final time.
The last lines of the Chorus in Oedipus Rex are very interesting. The Chorus points out the moral of the play, as expected.

CHORUS: Look ye, countrymen and Thebans, this is Oedipus the great,He who knew the Sphinx's riddle and was mightiest in our state.Who of all our townsmen gazed not on his fame with envious eyes?Now, in what a sea of troubles sunk and overwhelmed he lies!

The Chorus provides some further guidance for the audience, and at the same time, in the last two lines of the play, gives a hint of a sequel to Oedipus Rex.

CHORUS: Therefore wait to see life's ending ere thou count one mortal blest;Wait till free from pain and sorrow he has gained his final rest.

This is a fairly precise description of the plot of Oedipus at Colonus, although Sophocles didn't write Oedipus at Colonus until about 406 B.C, and it wasn't performed until 401 B.C., five years after his death.

In addition to adhering to the classical unities, as well described in the other answer, the play is structured so that it begins "in media res," which means in the middle of the action. A plague has already erupted in Thebes—we come into the play to find Oedipus addressing his citizens about it and then to find Creon returning from the oracle of Delphi with information that a sin must be rooted out to end the plague.
The play also starts many years after what precipitated the plague, which was Oedipus murdering his father and marrying his mother. We start at the moment of crisis that causes the backtracking in time that reveals the awful truth about the plague's origin.
As the unravelling leads closer and closer to the final revelation that even Oedipus can't deny, the play reaches its cathartic—and tragic—high point as Jocasta hangs herself and Oedipus puts out his eyes, at which point he achieves the insight and wisdom he could not achieve when he could see.

The dramatic structure of Oedipus Rex is intimately related to its status as a tragedy. In other words, the way in which the play is structured is designed to serve the time-honored demands of Greek tragedy. To this end, Sophocles sticks to the traditional three-fold unity of time, place and action. Why were these norms of classical drama considered so important to the Greeks? And how do they relate to the tragedy of Oedipus Rex?
Unity of time- The play must take place over the course of a single day. It needs to be dramatically plausible, making the action on stage appear as realistic as possible. The shorter the period of time involved, the more real the drama will appear.
In relation to Oedipus Rex Sophocles concentrates upon the latter part of Oedipus's life for maximum dramatic impact. The tragedy of the play lies in the revelation that Oedipus has unwittingly killed his father and married his mother. That all this is revealed in such a short space of time makes this tragic outcome all the more intense.
Unity of place- The events of the play must happen in one place. In the case of Oedipus Rex that means the palace of Oedipus. Again, credibility is an important consideration here. However, what's also important is that unity of place gives us no breathing space, as it were. For everything happening in one place means that there's nowhere to hide, either for ourselves or the characters. We can see how this heightens the tragedy further in Oedipus Rex as everyone is confronted with the terrible truth in a dramatically enclosed, claustrophobic environment.
Unity of action- Everything that happens in the play should be related to its overriding theme. In Oedipus Rex this means the question of Oedipus's birth, his past actions and how they will impact on his fate. All action in the play points to one thing, which is a tragic end for Oedipus and Jocasta.
 
 

What were the outcomes of the American revolution?

The primary outcome of the American Revolution was the independence of fourteen formerly British colonies in North America; thirteen of which would immediately form the United States and the fourteenth, Vermont, which would accede to the United States shortly thereafter.
An additional outcome of the American Revolution was an ideological cleansing of royalists in the fourteen formerly British colonies, many of whom were compelled to relocate to Canada. Among these were a number of slaves who had fought on the side of the British.
The Six Nations Confederacy, a 500-year-old alliance of the Seneca, Cayuga, Onondaga, Oneida, Tuscarora, and Mohawk tribes, was also splintered and ended as a result of the American Revolution, the Oneida and Tuscarora having sided with the Americans, with the other tribes having made a ruinous decision to ally with the defeated British.
Returning French soldiers evangelized some of the ideological underpinnings of the American Revolution in Europe through groups such as the Society of the Thirty. This proselytizing encouraged, in part, the later French Revolution with the Declaration of the Rights of Man and the Citizen inspired heavily by the United States Declaration of Independence.
https://www.history.com/topics/american-revolution/american-revolution-history

https://www.nps.gov/fost/learn/historyculture/the-six-nations-confederacy-during-the-american-revolution.htm

There were many outcomes of the American Revolution. The immediate result was the achievement of independence from Great Britain for the colonies. Longer-term effects include the creation of the United States after the ratification of the Constitution in 1787, the influencing of the French Revolution, beginning in 1789, and the expansion of the territory of our new country Westward. This last effect, the expansion of US territory, made it possible for the new country to absorb large numbers of immigrants. It also created conditions for a significant expansion of slavery in the US, which set the stage for the US Civil War, which began in 1860.
Other outcomes, which had mainly international effects, were the growth of trade and industry related to cotton, as its cultivation increased, along with slavery in the American South, the growth of banking and manufacturing in New England, and the mid-Atlantic states. The American Revolution also had powerful exemplary effects internationally in the nineteenth- and twentieth-centuries. This means the Revolution was used as an example, or imitated, by rebellions and protests the world over.

The main outcome that came out of the 1783 Treaty of Paris was that the colonists gained their independence from Britain.  The United States gained the territory between the Appalachian Mountains and the Mississippi River.  The new nation was also responsible for paying all of its outstanding debts to British merchants incurred before the war.  Britain still maintained forts along the Great Lakes, which it used to arm Native Americans in the region against encroaching American settlers. This was a clear violation of the treaty.  
Internationally, a spirit of democracy seemed to take hold in the Atlantic World.  Haitian slaves overthrew their French masters in the spirit of all men being created equal.  The United States, afraid that such an uprising would inspire insurrection in Southern slaves, did not recognize the existence of the Haitian nation until 1862.  The French monarchy was bankrupted by helping the Americans in this war, and many commoners sought to overthrow the French thrown. The French Revolution began in 1789, which then transformed into the Reign of Terror. Ultimately, this would lead to the rise of Napoleon and a very costly war which engulfed all of Europe.  
As a result of the American Revolution, other colonies of European powers sought their independence, often using the same rhetoric of the Declaration of Independence.  As late as the twentieth century, Ho Chi Minh, the leader of North Vietnam, created the Vietnamese Declaration of Independence; he sought to create a nation of equality under the law that did not have to worry about foreign interference.  He used a great deal of the rhetoric used in the Declaration of Independence—demonstrating the continuing influence of the colonists' struggles in 1776.  

When the group of men arrives, Atticus confirms that Tom Robinson is inside the jailhouse sleeping and tells the men not to awaken him. Scout reports: “In obedience to my father, there followed what I later realized was a sickeningly comic aspect of an unfunny situation: the men talked in near-whispers” (202). What is “sickeningly comic” about the situation? Why is it ironic that the men agree to talk in whispers?

In Chapter 15 of To Kill a Mockingbird, Scout, Jem, and Dill venture downtown at night and find Atticus sitting in front of the jail. Unaware of their presence, Atticus is sitting in a chair and reading a newspaper. As the children begin to leave, a line of cars approaches and stops in front of the jail. Hiding near the hardware store, Scout, Jem, and Dill watch as the men exit the cars and approach Atticus. One of the men says, "He in there, Mr. Finch?" Atticus confirms that Tom Robinson is indeed inside but cautions them, "He's asleep. Don't wake him up." What follows is what Scout refers to as a "sickeningly comic aspect of an unfunny situation."
The men are there to participate in a violent and uncivilized act. However, while their goal is to lynch Tom, they are respectful of Atticus and do as he says by whispering when they speak. It is ironic that they plan to hurt Tom and may even hurt Atticus in the process; they speak to him respectfully and whisper out of obedience to him. They even refer to Atticus as "Mr. Finch." Though there is nothing funny about the events, Scout refers to the situation as "sickeningly comic." This is because the men are managing to be respectful while at the same time planning to do bodily harm.

Thoreau is known for his aphorisms. Find one you like and explain its relevance for living today.

Thoreau is one of the better known sources of aphorisms in American literature, and his sometimes witty, sometimes reflective sayings are often quoted in essays, on posters, and even on t-shirts and bumper stickers. He has provided readers with many quips that package his philosophy into smaller, more memorable terms.
While many of his aphorisms have relevance in contemporary life, one example is from a letter to a friend. In his letter, Thoreau references the lack of jobs due to a depression the county was facing at that time. He notes the lack of jobs because of this, but states that perhaps these jobs were not worth having in the first place. Thoreau closes out the letter writing, "It is not enough to be industrious; so are the ants. What are you industrious about?" This quote reflects Thoreau's concern about industrialization and the changes in modern society. He did not believe that industry and mass production were necessarily beneficial for the country. He writes about this concern in many of his works, perhaps most notably Walden.
This quote certainly reflects the situation Thoreau describes in his letter; however, it could easily apply to modern day society. Industrious can be defined as "constantly, regularly, or habitually active or occupied." Take a look around at any public place, and it is obvious that everyone is "habitually occupied" with their phones and tablets. But are they occupied in something worthwhile? Answering constant emails, texting, posting on social media, playing games, and shutting out the natural world are probably things that Thoreau would not value. Thoreau would probably suggest that people step back and examine how beneficial busying themselves with these tasks truly is. He spends many pages in his writings discussing the value of self-exploration through solitude and the power of being in nature (away from society and technology) to bring meaning to his life. Modern usage of devices is a prime example of the type of "industry" Thoreau would question.

An aphorism, as defined by Merriam-Webster, is "a concise statement of principle," so it is a short line or phrase that illustrates some belief of the speaker. Henry David Thoreau was absolutely fond of confidently stating his point of view and offering neat, plain advice on how others could live the way that he did: more simply and more fully. An example of one of his aphorisms from his famous text Walden is

A man is rich in proportion to the number of things which he can afford to let alone.

This statement illustrates Thoreau's belief in simplicity, that man should try to reduce his possessions to that which he truly needs and nothing else. This idea is essential to his experience at Walden Pond, where he lived in a cabin he built himself and strived to reduce distractions from his life. Normally in a consumer culture, a man is considered rich if he owns too many things and he can call his life luxurious. But Thoreau rejects such thinking and instead emphasizes the great advantage of freedom over responsibility. The less things the man has to fiddle with, the more time and energy he will have for nobler pursuits.
This idea is obviously relevant in today's American society, as consumerism, ever-changing technology, and wealth disparities tend to plague the population with distractions and extra responsibility. People who are constantly taking care of their possessions or updating them do not have time for much else. And people who are working multiple jobs have no time or energy for much else. Thoreau's statement reminds us that, ultimately, we need much less than we think we do, and he urges us to insist on simplicity.
Thoreau's aphorisms span his writing, so besides Walden: Life in the Woods, look through Civil Disobedience for more examples to choose from.

Should memories recalled as the result of hypnosis be admitted as evidence in court? Why or Why not

Short answer: legally, possibly. In practice, and as a matter of ethics, almost certainly not.
Legally, the question of repressed memories being admissible evidence at all is highly contentious. See reference for a detailed breakdown of the legal standard for repressed memories in the United States, but the short version is that in most circumstances, its admissibility and weight are determined on a case-by-case basis. In addition, the general attitude of the legal system has consistently moved away from repressed memory as reliable.
Hypnosis compounds that problem. Depending on the court, one of three different standards may be applied to the use of evidence obtained under hypnosis: "credibility," which leaves the question of reliability to the jury; "discretionary admission," which leaves the question to the judge; and "procedural safeguards," which set specific, formal rules about what evidence, under what circumstances, can be admitted. 
Ethically, as noted in the Department of Justice reference below, the question of repressed memory being admissible as evidence is "in flux," after several convictions based on that evidence were overturned after factual evidence proved the "memories" to be false. It is broadly accepted throughout the psychological community that memory is suggestible, and hypnosis by definition places the patient in a suggestible state. Indeed, courts have used the mere use of hypnosis to call into question a witness's mental state.
In the context of a court of law, my conclusion is the same as Paul Giannelli's, whose abstract is cited below: "Unless the advantages of hypnotically refreshed testimony are significant, why add more problems?" In the current state of play of both psychology and the law, the use of evidence based on repressed memories obtained under hypnosis is ethically troubling and pragmatically more trouble than it's worth.
https://www.ncbi.nlm.nih.gov/pubmed/7737764

Was the Reign of Terror in France justified?

The Reign of Terror came out of a period of great political turmoil and conflict. The crowned heads of Europe had waged war on revolutionary France, and there was a growing sense of patriotism among the French people who felt they needed to defend "their" revolution against the imminent threat of foreign invasion.
When people decide to take on a foreign enemy, they invariably also look for enemies within. As well as fighting against the armies of Austria and Prussia, the revolutionaries were also engaged in a bloody, bitter conflict with domestic counterrevolutionaries who wanted to restore the ancien regime. The army was on the verge of defeat, and the revolutionaries were utterly convinced that the deposed monarch and his followers were conspiring with foreign powers to destroy the Revolution once and for all. The very existence of the newly-forged nation was at stake.
It is little wonder then that in an environment of suspicion and paranoia, those in power wished to impose a Reign of Terror to crush their enemies. Desperate times called for desperate measures.
At the same time, however, there was undoubtedly an ideological edge to the use of terror as a revolutionary tactic. Leading revolutionaries such as Robespierre openly justified the use of terror not just on practical grounds, but also on moral grounds. Robespierre was obsessed with the idea that the purity of the Revolution was under constant threat, both from internal and external opponents. Virtue was the governing idea in peacetime, but it needed to be linked to the implacable use of terror in times of conflict. Robespierre regarded himself as the most virtuous of revolutionaries, so he naturally saw it as his duty to spearhead the campaign of terror which he and the other Jacobins unleashed upon France.
The Reign of Terror, forged in the heat of war, was ultimately undone by it. As the French Revolutionary Army notched victory after victory against foreign counter-revolutionary forces, it became harder to justify mass repression. Yet, if anything, Robespierre intensified the terror even more. In the process, he alienated many of his former comrades, who feared that they would be next for the guillotine. The radical revolutionaries had overplayed their hand and their fate was sealed. 
Whatever the justification, there can be no doubt of the immense suffering caused by the Reign of Terror. Tens of thousands perished. The overwhelming majority of people killed were not, as legend would have it, aristocrats or conspiring traitors, but ordinary men and women often sent to their deaths on the flimsiest of evidence.
https://www.historytoday.com/archive/robespierre-and-terror

How has Oscar Wilde explored the corruption of the human soul in the Picture of Dorian Gray

Any analysis of The Picture of Dorian Gray must start with a recognition that the novel is in some sense autobiographical. Because Oscar Wilde was gay or bisexual, he lived a double life in Victorian England, and eventually was tried and imprisoned for his "immoral" behavior. In the nineteenth century there was, in fact, "underground" literature, but Wilde was a very public and famous person, and, as the feminist author Kate Millet wrote in her book Sexual Politics, Wilde "wanted to publish and to shine." Therefore Dorian Gray can be seen as a novel in which Dorian's homosexuality is implicit, veiled, and, in keeping with the morality of the time, associated with crime and degradation. Perhaps it was Wilde's own latent guilt (impossible not to have in that repressed era) about being gay that made him identify Dorian's behavior with moral corruption.
Dorian's cruel rejection of Sybil after she gives an embarrassingly bad performance in Romeo and Juliet is the first downward plunge of his "soul." He is aware that Sybil loves him, but he allows the judgement of Lord Henry and his other friends to override his own feeling for Sybil. He later regrets his behavior and intends to marry her, but when he learns that she has committed suicide, this news paradoxically leads him to begin the "immoral" lifestyle into which Lord Henry has been trying to lead him all along. The supernatural mechanism by which the portrait both "ages" and shows the corruption in Dorian's soul, while his own face continues to look both young and innocent, facilitates Dorian's descent into a new and sordid world, in which he not only gives free reign to his sexual desires, but also apparently uses drugs and engages in blackmail.
The ultimate step in Wilde's exploration of this corrupted soul is the murder of Basil, which Dorian commits as a kind of climax to his whole life of crime and as an inevitable result of his downward spiral. It is ironic, but not surprising, that he should blame Basil for his own descent, thinking that the picture Basil painted is what has caused him, Dorian, to become unhinged. It is also a corollary to Dorian's "sins" that instead of acknowledging his own responsibility for his crimes, he blames Basil as the one who has made him a "victim." And finally, Dorian mistakenly thinks that he can be redeemed by destroying the portrait itself.
The last scene is a puzzle, for it implies that there is essentially no difference between the picture and the man. The destroyed portrait becomes the destroyed human being, as the servants find Dorian, an old withered man, dead with a knife in his heart. Although Wilde has infused the book with a "moral" message, the ending is another example of the eternal theme of illusion vs. reality, and what difference there is, if any, between the two.

y = cos2x , y = 0 , x = 0 , x = pi/4 Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis.

Given
y=cos(2x), y=0 x=0,x=pi/4
so the solid of revolution about x-axis is given as
V = pi * int _a ^b [R(x)^2 -r(x)^2] dx
here
R(x) =cos(2x)
r(x)=0 and the limits are a=0 and b=pi/4
so ,
V = pi * int _a ^b [R(x)^2 -r(x)^2] dx
= pi * int _0 ^(pi/4) [(cos(2x))^2 -0^2] dx
=pi * int _0 ^(pi/4) [(cos(2x))^2 ] dx
 
as we know cos^2(x) = (1+cos(2x))/2
so ,
cos^2(2x) = (1+cos(4x))/2
now
 
=pi * int _0 ^(pi/4) [(1+cos(4x))/2 ] dx
 
=pi *  (1/2) int _0 ^(pi/4) [(1+cos(4x))] dx
 
=pi *  (1/2)  [(x+(1/4)sin(4x))]_0 ^(pi/4)
 
=pi/2 [pi/4 +(1/4)(sin(pi))-[0+0]]
 
= (pi/2)[pi/4]
 
=pi^2/8

is the volume

What gives Vera confidence to weave her story about the tragedy in "The Open Window" by Saki?

In "The Open Window," Vera gains the confidence to fabricate her tale about her aunt's brothers and husband after Framton Nuttel says he knows "[H]ardly a soul" in the area. 
When Framton first arrives at the Stappleton's house, he finds himself talking to Vera, a girl of fifteen, who is the niece of Mrs. Stappleton and a "self-possessed young lady." She asks Framton if he knows many people in the area, and Framton replies,

"Hardly a soul. . . My sister was staying here, at the rectory, you know, some four years ago, and she gave me letters of introduction to some of the people here."
"Then you know practically nothing about my aunt?" the girl asks.
"Only her name and address."

With the knowledge that Framton Nuttel will not know what is true and what is not, Vera spins a tale of how Mrs. Stappleton suffered the tragic loss of the male members of her family, and now delusionally believes they will return. Knowing Mrs. Stappleton will watch for her husband and her brothers to return through the open window, Vera hopes to play a practical joke on Mr. Nuttel.
Vera's ruse works so well at blurring the lines between what is imaginary and what is real that when Mr. Stappleton, his sons, and the dog return, Framton Nuttel flees in terror, and Vera's joke is complete.

What are the key points from chapters 22-27 in Harper Lee's To Kill a Mockingbird?

Chapter 22 of To Kill a Mockingbird picks up after Tom has been convicted of rape. The key event in this chapter is that they discover that Bob Ewell threatened Atticus and spat in his face. Another important event occurs in chapter 24 when we discover that Tom has been killed in an attempt to escape from prison. The appeal Atticus hopes to bring before a judge will never happen, and justice will never be served for Tom. Atticus has the unenviable task of going to tell Tom's mother in chapter 25.
In chapter 27 we learn that Bob Ewell is still up to no good, and that he has not yet given up on avenging what he perceives as Atticus's attempt to humiliate his family in court. It is also announced that Scout will participate in a school pageant, dressed as a ham. This leads to a very important event in the novel, which occurs in chapter 28—Bob Ewell's fateful attack on the children on the way back from the pageant.

How did the end of the war bring social and economic instability to the US and world in WWI?

The end of WWI brought about economic instability for the whole world. The sudden end of the war did not give the United States enough time to transition to a consumer-driven economy. As a result, the prices for food and clothing increased so much that it was an election issue in 1920. Farmers and speculators had done well during the war by selling wheat to war-torn Europe; the sudden end of the war meant that prices fell and farmers began to plant more in order to pay off loans they took out for machinery and more land during the war. As a result, the price tumbled more. The tilling of marginal land in the Great Plains would become one of the leading causes of the Dust Bowl. Farmers were losing their land well before the Great Depression started officially in 1929. Millions of American servicemen returning home often had no job to return to, and many resented the munitions workers who made more money than the soldiers who were actively using the munitions. Business was able to use patriotism in order to cut down on strikes and the ensuing Red Scare after the war made life difficult for the worker who hoped for better wages.
Internationally, the war made a shambles of the European economy. Britain and France were heavily in debt to the United States, and they leaned on Germany to help pay the bill. The German economy was essentially ruined, and it was once a major import and export market. The Russian economy was closed during the early days of the Russian civil war and the United States would not officially recognize the Bolshevik government under the Franklin Roosevelt administration. The Republican presidents who came after Wilson—Harding, Coolidge, and Hoover—enacted heavy protectionist tariffs, most notably the Hawley-Smoot Tariff during the Hoover administration. This put Europe further behind in terms of paying its debt, and it reduced the purchasing power of one of the United States's most valuable trading regions.

How would you oppose the pessimism of science in Robert Louis Stevenson's Dr. Jekyll and Mr. Hyde and Nathaniel Hawthorne's "The Birthmark"?

Nineteenth-century literature is replete with depictions of scientific experiments and prophesies of new inventions and discoveries. Given that this was an era, like our own digital age, in which the world was being transformed by technology, this particular obsession of writers was only natural. While much of their fiction portrays negative and tragic results of scientific research, it's generally not science itself that is criticized but rather man's own inherent weaknesses and moral failings.
Hawthorne's "The Birthmark" is a parable of man's inability to accept imperfection as an inevitable part of life. Aylmer is a brilliant researcher who has created (interestingly enough, in the previous century, where Hawthorne sets the tale) fantastic inventions which, if used correctly, could benefit mankind immeasurably—just as the actual inventions of Hawthorne's lifetime, such as the telegraph, gas lighting, and railway travel, were doing in a way that understandably was seen as spectacular during those years. But Aylmer, in his obsession with Georgiana's "flaw," misuses the power he has created in the laboratory. This is not the fault of "science" or even of Aylmer's scientific activities, but of his failure as a man in refusing to value his wife as she is, and for what she is, instead focusing on the birthmark which doesn't bother anybody else, including Aylmer's "uncouth" lab assistant. As in other works, Hawthorne is also criticizing the mindset that creates a dichotomy between the spiritual and the physical. Aylmer's unrealistic attitude, including the rarefied way he speaks and the horror he begins to feel when looking at his wife's face, is basically one of disgust with the physical world. Like Mr. Hooper in "The Minister's Black Veil," who cuts himself off from life by covering his face, Aylmer seeks purity but ends up destroying Georgiana and himself.
Stevenson's famous story is a parable as well, in which a man splits himself into two beings. It would be simplistic to give the usual interpretation that Jekyll represents good and Hyde evil. As with Aylmer, Jekyll's brilliance as a researcher is beyond question. But his flaw, again, is the non-acceptance of the real world and a misguided striving for something beyond it, which he believes science can produce for him. The descriptions of his pathetic attempts again and again to find the right formula to restore him to normalcy are a metaphor of man's having succumbed to his own weaknesses and his inability to restore the real but imperfect self with which he should have been satisfied.
Both Hawthorne and Stevenson, by showing hypothetical scenarios in which science can produce results no one could have dreamed of, are actually showing their faith in man's ability to advance. It is not science per se, but its misuse due to human failure that is at fault and that brings on the catastrophe in each of these stories.

Calculus and Its Applications, Chapter 1, 1.2, Section 1.2, Problem 16

Determine the $\displaystyle \lim_{x \to -1} \left( 3x^5 + 4x^4 - 3x + 6 \right)$ by using the Theorem on Limits of Rational Functions.
When necessary, state that the limit does not exist.


$
\begin{equation}
\begin{aligned}
\lim_{x \to -1} \left( 3x^5 + 4x^4 - 3x + 6 \right) &= \lim_{x \to -1} 3x^5 + \lim_{x \to -1} 4x^4 - \lim_{x \to -1} 3x + \lim_{x \to -1} 6
&& \text{The limit of a difference is the difference of the limits and the limit of a sum is the sum of the limits}\\
\\
&= 3 \cdot \lim_{x \to -1} x^5 + 4 \cdot \lim_{x \to -1} x^4 - 3 \cdot \lim_{x \to -1}x + \lim_{x \to -1} 6
&& \text{The limit of a constant times a function is the constant times the limit}\\
\\
&= 3 \cdot \left( \lim_{x \to -1}x \right)^5 + 4 \cdot \left( \lim_{x \to -1}x \right)^4 - 3 \cdot \lim_{x \to -1} x + \lim_{x \to -1} 6
&& \text{The limit of a power is the power of the limit}\\
\\
&= 3 \cdot \left( \lim_{x \to -1}x \right)^5 + 4 \cdot \left( \lim_{x \to -1}x \right)^4 - 3 \cdot \lim_{x \to -1}x + 6
&& \text{The limit of a constant is the constant}\\
\\
&= 3(-1)^5 + 4(-1)^4 - 3(-1) + 6
&& \text{Substitute } -1\\
\\
&= -3 + 4 +3 + 6\\
\\
&= 10
\end{aligned}
\end{equation}
$

Single Variable Calculus, Chapter 3, 3.3, Section 3.3, Problem 49

Find the equation of the tangent line of the curve $\displaystyle y = \frac{2x}{x + 1}$ at Point $(1,1)$

Required:

Equation of the tangent line to the curve at $P(1,1)$

Solution:

Let $y' = m$ (slope)


$
\begin{equation}
\begin{aligned}

\qquad y' = m =& \frac{\displaystyle (x + 1) \frac{d}{dx} (2x) - \left[ (2x) \frac{d}{dx} (x + 1) \right]}{(x + 1)^2}
&& \text{Apply Quotient Rule}
\\
\\
\qquad m =& \frac{(x + 1) (2) - (2x)(1)}{(x + 1)^2}
&& \text{Simplify the equation}
\\
\\
\qquad m =& \frac{\cancel{2x} + 2 - \cancel{2x}}{(x + 1)^2}
&& \text{Combine like terms}
\\
\\
\qquad m =& \frac{2}{(x + 1)^2}
&& \text{Substitute value of $x$ which is 1}
\\
\\
\qquad m =& \frac{2}{(1 + 1)^2}
&& \text{}
\\
\\
\qquad m =& \frac{2}{4}
&& \text{Reduce to lowest term}
\\
\\
\qquad m =& \frac{1}{2}
&&

\end{aligned}
\end{equation}
$


Solving for the equation of the tangent line:


$
\begin{equation}
\begin{aligned}

\qquad y - y_1 =& m(x - x_1)
&& \text{Substitute the value of the slope $(m)$ and the given point}
\\
\\
\qquad y - 1 =& \frac{1}{2} (x - 1)
&& \text{Add 1 to each side}
\\
\\
\qquad y =& \frac{x - 1}{2} + 1
&& \text{Get the LCD}
\\
\\
\qquad y =& \frac{x - 1 + 2}{2}
&& \text{Combine like terms}
\\
\\
\qquad y =& \frac{x + 1}{2}
&& \text{Equation of the tangent line to the curve at $P(1, 1)$}
\\
\\

\end{aligned}
\end{equation}
$

Single Variable Calculus, Chapter 2, Review Exercises, Section Review Exercises, Problem 10

Determine $\displaystyle \lim \limits_{v \to 4^+} \frac{4 - v}{| 4 - v|}$

Recall


$
\begin{equation}
\begin{aligned}

|x| =& \left\{ \begin{array}{ccc}
x & \text{ if } & x \geq 0 \\
-x & \text{ if } & x < 0
\end{array} \right.
\end{aligned}
\end{equation}
$


So,


$
\begin{equation}
\begin{aligned}
|4 - v| =& \left\{ \begin{array}{ccc}
-(4-v) & \text{ if } & v \geq 4 \\
(4-v) & \text{ if } & v < 4
\end{array} \right.

\end{aligned}
\end{equation}
$

Since $v$ approaches 4 from the right-hand limit. We use $-(4 - v)$ to eliminate the absolute sign.


$
\begin{equation}
\begin{aligned}

\lim \limits_{v \to 4^+} \frac{4 - v}{| 4 - v|} &= \lim \limits_{v \to 4^+} \frac{\cancel{4 - v}}{-\cancel{(4 - v)}} = \frac{1}{-1}
&& \text{Cancel out like terms}
\\
\\
& \fbox{$= -1$}
&&


\end{aligned}
\end{equation}
$

What might a 2016 Magna Carta look like?

Signed in 1215, the original Magna Carta was one of the first Western legal documents to protect the rights of the individual against the power of a despotic ruler. The rights it offered--such as the right to a swift and fair trial--seem rather basic to us today, but in 1215 they were radical. A 2016 Magna Carta would hopefully preserve the radical spirit of the original and present a robust protection of the liberties of the individual. Here are some ways a new Magna Carta might seek to do this:
Prohibit forced service in the armed forces (conscription, more commonly known as "the draft")
Prohibit government surveillance of citizens without a warrant
Prohibit civil asset forfeiture, which allows the government to confiscate a person's property without convicting him or her of a crime
Prohibit official government discrimination against individuals for any reason, such as belonging to an unpopular or anti-government group
 

Since the Magna Carta was a charter designed to protect the individual rights of barons and regular English citizens, you would want to focus on creating a document that pertained to the rights of individuals today.  The goal of the Magna Carta was to challenge the unlimited authority of kings as well, so you can also focus on areas where our government and individuals leading our nation have overstepped the power and authority given to them.
Some individual rights that are currently in the news today are the rights of gay people, transgender individuals, gun owners, women and minorities.  Compiling a list of problem areas of power and a list of rights that are being infringed upon or threatened would be a great way to create your “modern” Magna Carta.

Single Variable Calculus, Chapter 1, 1.3, Section 1.3, Problem 25

Use the figure below to find a function that models the number of hours of daylight at
New Orleans as a function of the time of year assuming that the city of New Orleans is
located at latitude $30^{\circ}\rm{N}$. Use the fact that on March 31, the sun rises at 5:51 AM
and sets at 6:18 PM in New Orleans.




Referring to the figure for latitude of New Orleans at $30^{\circ}\rm{N}$, we see that the daylight lasts about 14 hours sometime
in June and 10 hours sometime in December, so the amplitude of the curve is $\displaystyle \frac{1}{2} (14-10) = 2$

Recall that the general equation of sine function is $y = A \sin (2 \pi \rm{ ft})$ or $y = A \sin \displaystyle \left(\frac{2 \pi}{T} t\right)$


$
\begin{equation}
\begin{aligned}
\text{Where } A &= \text{amplitude}\\
f &= \text{frequency}\\
T &= \text{period}
\end{aligned}
\end{equation}
$


Let's say that the curve begins on March 21, the 80th day of the year, therefore the graph of the function
is shifted 80 units to the right and shifted 12 units upward as shown in the figure. Also, we assumed that there are 365 days in a year.
Therefore, the model of the number of hours of daylight at New Orleans as a function of time of year is...

$f(t) = 2 \sin \displaystyle\left[ \frac{2 \pi}{365} (t-80)\right]+12$

What examples did Henry give to show that Britain had no intention of peaceful reconciliation with the colonies?

Patrick Henry's "Give me Liberty or give me Death" speech of 1775 is one of the most famous and memorable orations in American political history. At the time, revolution was in the air, and the great and the good of Virginia had come together in a statewide Convention to determine their political strategy. Inevitably, there was a wide variety of opinions on how to deal with the growing threat. Strange as it may seem today, there were many at the Convention who still held out the hope of a peaceful reconciliation with the British.
Henry, for his part, was certain that war was an inevitability and that it was therefore absolutely essential for Virginians to form themselves into militias to resist the British. Despite the martial rhetoric of his speech, he nonetheless puts forward a number of rational arguments for taking the fateful step of armed resistance.
Henry is guided by "the lamp of experience." In his experience, there is absolutely nothing that the British have done in the last ten years to suggest any hope of reconciliation. He illustrates his point by citing the example of British troops mobilizing across the colonies:

Ask yourselves how this gracious reception of our petition comports with these war-like preparations which cover our waters and darken our land. Are fleets and armies necessary to a work of love and reconciliation? Have we shown ourselves so unwilling to be reconciled, that force must be called in to win back our love?

If the British were really serious about peaceful reconciliation, as some at this Convention believed, they had a funny way of showing it.

Has Great Britain any enemy, in this quarter of the world, to call for all this accumulation of navies and armies? No, sir, she has none. They are meant for us; they can be meant for no other.

Henry uses incontrovertible logic to press home his point. If the British are building up their army and navy, it can only be to suppress the American colonists. They have no other enemies in that part of the world.
Trying to reason with the British has been a complete waste of time. Time and time again the colonists have presented their grievances only to have them completely ignored and treated with utter disdain:

We have petitioned; we have remonstrated; we have supplicated; we have prostrated ourselves before the throne. . . Our petitions have been slighted; our remonstrances have produced additional violence and insult; our supplications have been disregarded; and we have been spurned, with contempt, from the foot of the throne.

We tried to achieve peaceful reconciliation with the British, suggests Henry, but they just did not want to know. If they had really wanted to achieve better relations, they would at least have made meaningful efforts at negotiation.

It is in vain, sir, to extenuate the matter. Gentlemen may cry, "Peace, Peace" but there is no peace. The war is actually begun!

The time for talking is over. We must now fight for our liberty and, if necessary, be prepared to die for it:

I know not what course others may take; but as for me, give me liberty or give me death!