What did Akiba Drumer ask the others to do for him?

Akiba Drumer has always been noted for his unshakeable optimism and unbending faith in God, even in the midst of the camp's unspeakable horrors. As well as a deep commitment to his faith, Akiba is also heavily into numerology, using it to predict immanent deliverance for the inmates from their terrible ordeal.
Eventually, however, Akiba is broken by his experiences of the camp, and he loses not just his faith but also his will to live. When he's selected by the Germans to be sent to the crematorium he asks his fellow inmates to say the Kaddish for him. In Judaism, Kaddish is the prayer for the dead. Although Akiba has lost his faith, he still feels it appropriate that the relevant religious rites should be observed. Unfortunately, however, no one remembers to say the Kaddish. The last few days had been particularly harsh and brutal, even by normal standards, so it's not surprising that the inmates' minds were focused elsewhere, on the daily struggle to survive.

What does "whose horrid image doth unfix my hair and make my seated heart knock at my ribs" mean in Shakespeare's Macbeth?

In act one, scene three, Macbeth receives a seemingly favorable prophecy from the Three Witches, who tell him that he will be named the Thane of Cawdor and become the future King of Scotland. Shortly after receiving the prophecy, Ross and Angus arrive to inform Macbeth that King Duncan has just given him the title Thane of Cawdor. Both Macbeth and Banquo are astonished by the news, and Macbeth immediately begins thinking about ways to attain the Scottish throne.
In an aside, Macbeth contemplates the positives and negatives associated with the witches' prophecy. Macbeth then begins to imagine assassinating King Duncan in order to become king, which is a horrifying, unsettling thought. Macbeth describes his feelings regarding the nature of the prophecy by saying,

If good, why do I yield to that suggestion Whose horrid image doth unfix my hair And make my seated heart knock at my ribs, Against the use of nature? (Shakespeare, 1.3.137-140)

Macbeth is essentially saying that the thought of committing regicide makes his hair stand on end and heart pound against his ribs in an unnatural way. These comments reveal Macbeth's ambitious nature and conscience. Judging from Macbeth's aside, the "horrid image" of murdering King Duncan is evidently disturbing and unsettling to him at this point in the play.

Macbeth was told by the Weird Sisters that he would become Thane of Cawdor and King of Scotland, and then, lo and behold, Ross and Angus arrive, bringing the news that he has, indeed, been named Thane of Cawdor. Now Macbeth really begins to believe, in earnest, that the more significant prophecy could come true, and he begins to entertain ways in which it might. He says,

I am thane of Cawdor.If good, why do I yield to that suggestionWhose horrid image doth unfix my hairAnd make my seated heart knock at my ribs,Against the use of nature?

In other words, he is now Cawdor, as the Weird Sisters said he would be. However, if this is a good thing, he asks himself, then why does he now find himself considering the murder of the current king, which is such a horrible idea that it makes his hair stand up on end and his heart pound loudly within his ribcage in such an unnatural way? Macbeth is already considering the nearest way to the throne, and he is unnerved by how quickly he has jumped to regicide as a possibility.

What was Pennsylvania's role in the abolitionist movement and the Civil War?

Quakers made up a significant portion of Pennsylvania's population. William Penn, the state's founder, was an English Quaker who had been granted a large piece of land by King Charles II in 1681 to pay off a land debt. Several thousand Quakers left England and followed Penn to the state that he would found. Initially, they were politically active, and they held positions of political influence until deciding that politics often compromised their values, particularly their pacifism.
Instead, they were early devotees of social justice. First, they pursued the protection of Native Americans' rights. Shortly thereafter, they reached an anti-slavery consensus. By the 1780s, slave ownership among Quakers was forbidden. Quakers were among the first abolitionists and participated in the Underground Railroad, harboring slaves until they reached their final destination which, after the passage of the Fugitive Slave Act in 1850, had to be Canada in order to avoid being captured and sent back to the South.
In regard to the Civil War, the most important battle—the Battle of Gettysburg—was fought in Pennsylvania. The battle was decisive, for it resulted in great losses on the Confederate side, as well as General Robert E. Lee's infamous retreat back into Virginia. Lee took his army north with the dual goals of gaining the support of Northern copperheads who were sympathetic to the Confederate cause and winning a battle in the interest of getting the Confederacy recognized by Britain and France.
Instead, 28,000 men were killed—a third of Lee's army. Union losses were not modest either. Union casualties amounted to 23,000. Lee was so dejected that he offered his resignation as general to Confederate president Jefferson Davis, who refused to accept it. The Confederacy went on to win other battles, but Gettysburg, along with Ulysses S. Grant's triumph at the Battle of Vicksburg in Mississippi, set the Union on the course to win the war.
https://www.history.com/topics/american-civil-war/battle-of-gettysburg

https://www.history.com/topics/immigration/history-of-quakerism

Did the last candidate die?

In the short story "The Knife Thrower," the last candidate is a young girl named Laura. During the night, Hensch performed a series of impressive knife throwing acts that left his audience in awe of his prowess. During the last segment of his performance, he inflicts the artful wound on three volunteers: his assistant, a high schooler named Susan, and a fifteen-year-old boy named Thomas. However, it is Hensch’s final performance that baffles his audience.
After the assistant invites a brave volunteer to come on stage for the "ultimate sacrifice," a mark that could be received only once in a person’s lifetime, the crowd is hesitant. Nevertheless, Laura raises her hand and makes her way to the front. The narrator states that after this, things happened so fast that they neither had time to protest nor stop what was about to happen. Soon after, Hensch released his knife and Laura’s body fell to the floor.
According to the narrator, it is unclear whether or not the last candidate died. The people believed that Hensch was so hell-bent on securing his reputation as the greatest knife thrower that he would be willing to stage the Laura act. However, the narrator also recounts numerous rumors involving the police and charges as well as countercharges that arose after Hensch’s performance. The narrator also asserts that even though they acknowledge that it is necessary for Hensch to develop new acts in order to stay relevant in a highly competitive environment, they agree that he crossed the line by endangering people’s lives.

y = sqrt(9-x^2) , -2

The function y = sqrt(9-x^2) is rotated about the x-axis and the surface area that is created in this way is a surface of revolution.
The area to be calculated is definite, since we consider only the region of the x-axis x in [0,3] , ie x between 0 and 3.
The formula for a surface of revolution A is given by
A = int_a^b (2pi y) sqrt(1 + (frac(dy)(dx))^2) dx
The circumference of the surface at each point along the x-axis is 2pi y and this is added up (integrated) along the x-axis by cutting the function into infinitessimal lengths of sqrt(1 + (frac(dy)(dx))^2) dx
ie, the arc length of the function in a segment of the x-axis dx in length, which is the hypotenuse of a tiny triangle with width dx , height dy . These lengths are then multiplied by the circumference of the surface at that point, 2pi y to give the surface area of rings around the x-axis that have tiny width dx yet have edges that slope towards or away from the x-axis. The tiny sloped rings are added up to give the full sloped surface area of revolution. In this case,
frac(dy)(dx) = -frac(x)(sqrt(9 -x^2))  
and since the range over which to take the arc length is [-2,2] we have a = -2 and b=2 . Therefore, the area required, A, is given by
A= int_(-2)^2 2pi sqrt(9-x^2) sqrt(1 + frac(x^2)(9-x^2)) dx
which can be simplified to
A = int_(-2)^2 2pi sqrt(9-x^2 + x^2) dx = int_(-2)^2 6 pi dx
so that 
A = 6pi x|_(-2)^2 = 6 pi (2 + 2) = 24pi
 
http://mathworld.wolfram.com/SurfaceofRevolution.html

An undergraduate engineering student, Ann, wants to secure a prestigious internship with company C in the summer before her senior year. Ann believes—rightly, let’s suppose—that if she secures that internship she will be hired by company C once she graduates, and she will go on to do important (and well-paid) work designing and building safe and useful objects for years to come. In her quest to get this internship, Ann comes to learn that one of company C’s current employees named Beth is a graduate of Ann’s college. A positive word from Beth can go a long way in helping a person get the coveted internship. Ann also comes to learn that Beth is a friend of a friend of hers (more precisely: an acquaintance of a friend of an acquaintance of hers) and that Beth will be at a party that Ann is going to this weekend. Intrigued, Ann looks around online for info about Beth. (For example, she checks out her LinkedIn page.) At the party, Ann goes out of her way to meet and speak with Beth, not about company C or the internship, but about general life stuff. Ann charms Beth quite successfully, which is not surprising given how much Ann knows about Beth, their shared college, the fact that they are both engineers, and so on. They exchange phone numbers and, in short order, they are hanging out regularly. Their budding friendship, if you can call it that, is initially built and sustained by Ann. Ann typically sends the first text, Ann requests to be Facebook friends with Beth, and so on. Over the course of a couple of months, it comes to be mutual and balanced. Eventually, they see each other a few times a week and talk (at least via text) almost every day. A few weeks after meeting Ann, Beth learns that Ann is applying for the internship. Ann does not make a big deal about it—and neither does Beth—but Beth wishes her luck. She also mentions how cool it would be if they could work together. Ann eventually applies for the internship and, unfortunately, does not get it. Beth even puts in a good word for Ann, as Ann really hoped she would—that’s why she tried to befriend Beth in the first place, after all—but it is not enough. Once Ann finds out that she did not get the internship, she cuts Beth off completely. She stops responding to her (many) texts, she unfriends her on Facebook, and so on. Ann is not angry at Beth. Ann just no longer sees any reason to keep talking to her, given that she did not get the internship. Why would Immanuel Kant almost certainly think that Ann acted immorally in this scenario?

One would be safe to conclude that Immanuel Kant would have disapproved of Ann’s actions. By meticulously cultivating a relationship with Beth over a period of time solely for the purpose of securing an important internship and then, upon failing to secure said internship, precipitously and rudely terminating all vestiges of that relationship, Ann violated Kant’s “categorical imperative” regarding human relations.
In his Grounding for the Metaphysics of Morals, Kant addresses the definition of morality and how it should, optimally, constitute the rules under which humans interact. In one of this treatise’s most frequently cited rules, the late German philosopher wrote, “Act so that you use humanity, as much in your own person as in the person of every other, always at the same time as end and never merely as means.” Kant was, in a sense, postulating a variation of the oft-cited “Golden Rule” or “ethic of reciprocity,” which can be traced to antiquity and which commands one to love his or her neighbor as he or she loves himself or herself. The “Golden Rule’s” most well-known variation is in the New Testament, Matthew 7-12: “Therefore all things whatsoever ye would that men should do to you, do ye even so to them: for this is the law and the prophets.” Kant, of course, had a complicated view of religion. He believed it in direct conflict with scientific reasoning but did not discount the presence of God in his life. His philosophy of ethics, however, represented a continuation of the “Golden Rule.”
In summary, Ann has deliberately exploited another human being for her own purpose and then further betrayed that human being’s trust by cavalierly cutting off all communications between Beth and herself. There is no question that Kant would disprove of Ann’s highly-questionable sense of morality. He would probably repeat another of his more frequently cited comments: “If man makes himself a worm, he must not complain when he is trodden upon.” Ann has violated the categorical imperative and has invited some form of retribution upon herself, whatever form that retribution might take.

According to Justice Harlan, what did the railroad claim was its motivation for the decision to separate passengers?

Justice Harlan wrote the dissenting opinion in the 1896 Supreme Court case Plessy v. Ferguson. This case stated that it was constitutional for states to have "separate but equal" public facilities, including schools, until it was overturned (related to schools) in the 1954 Supreme Court case Brown v. Borad of Education. 
In Plessy v. Ferguson, the court ruled that Louisiana could have separate railroad cars for black people and white people. In Harlan's dissent, he dismissed the idea that the railroad did not discriminate against either race but used the same rules to apply to both races, as they had claimed. Harlan wrote:

"The thing to accomplish was, under the guise of giving equal accommodations for whites and blacks, to compel the latter to keep to themselves while travelling in railroad passenger coaches. No one would be so wanting in candor as to assert the contrary."

In other words, Harlan said that under the pretense of giving separate accommodations to whites and blacks, the railroad's real motivation was to keep black people in their own coaches. The railroad intended to discriminate against blacks. Harlan wrote, "But in the view of the Constitution, in the eye of the law, there is in this country no superior, dominant, ruling class of citizens." That is, he said that under the Constitution, no race is superior and that all citizens have equal rights under the law. 

How are the themes of industrialism and self-discovery/knowledge during the Romantic Era portrayed in "The Mortal Immortal" by Mary Shelley?

"The Mortal Immortal" is a short story by Mary Shelley, whose protagonist, Winzy, drank, in his youth, half of a flagon of elixir, believing it to be a cure for love. On his deathbed, Winzy's master, the philosopher, informed him that the elixir had in fact been the elixir of immortality. Outliving his wife and never changing in appearance from a man of twenty, Winzy becomes tormented by his eternal youth and preoccupied with the hope that, having drunk only half of the elixir, he has surely acquired only longevity, rather than immortality. The idea of being truly immortal is anathema to him: he dwells on the fact that he has found a single grey hair on his head, and at the end of the story has set himself to undergo a quest which even a young man could not survive, so that he, the "mortal immortal," can finally be freed.
The Romantic theme of self-discovery and self-knowledge is the core of this story. The protagonist, Winzy, is not the creator of the elixir which has led him into his current sorry state, and yet, importantly, it was not his master who administered the draught. Winzy, feeling lovesick, drank the liquid himself in the hope that it would be an easy solution to a difficult problem, without full knowledge of what he was drinking or the effect it would have. We can see in this situation, then, a ready analogy: Winzy, an ordinary man, hopes that science will provide quick solution for him to an age-old problem. With only minimal knowledge of his own, he trusts that others will have provided him with the answers he needs, but he does not have sufficient self-knowledge to pause and consider the consequences of his actions. In an age of ever-increasing scientific discovery, then, the story implies that it is those ordinary people who come to believe in the god-like power of scientists to fix their problems who will suffer most.
Winzy is not a prideful man—he has not struggled personally to create an elixir which will stave off death. And yet the effects of the philosopher's unnatural endeavors have been widespread. While he himself has not suffered from his art, he and Winzy together, by their own ill-informed choices, have put Winzy into a situation which is too terrifying for the human man to understand. A chief preoccupation of Romanticism and early Gothic is the idea that science should beware of making advances which put man into the territory that should be reserved for God. In this story, we find Winzy struggling with the idea that he must now become his own god, and yet is completely ill-equipped to do so. Throughout his life with his once-beautiful wife, Winzy began increasingly to feel the ill effects of his actions: those around him begin to shun him, believing that he must be a witch. Even his wife becomes "jealous" and obsessed with Winzy's state, living in the hope and expectation that his unnatural youth will one day fall away. Winzy, having made the decision to drink the solution, has no idea of how to handle its effects upon him. Its creator has died, leaving the ordinary man to fend for himself, a situation in which we might find some analogy to the idea of God having left the world alone, and man finding it very difficult to fend for himself.
Winzy's mental state at the end of the story is a sorry one. His body has become "a cage for a soul which thirsts for freedom, to the destructive elements of air and water" and he is resolved either to free himself from it or to find that he is indeed immortal, in which case "my name shall be recorded as one of the most famous among the sons of men." Winzy is about to make another leap without knowing where it will take him. One leap into the unknown, without adequate understanding, then, simply drives us towards another. Having begun to overreach, humans find themselves in a situation from which further overreaching seems the only possible answer, and yet we cannot know where this motion will take us. As in the areas of industry and eighteenth-century science, progress is seemingly becoming closer and closer to magic, and this story suggests that its ultimate outcome may not be what was wished for.

For what are Georg and Ulrich fighting?

Besides the obvious reason that underlies the feud between Ulrich von Gradwitz and Georg Znaeym, which the other response eloquently describes for you, one could argue that the real reason for their feud goes deeper than a land dispute.
Both men are the patriarchs of their families, and both men feel responsible as the leader of their clans to make the right choices in the families’ best interests. For each, this means claiming the disputed tract of land for his family. Is this land really any better than a similar tract that the Znaeyms’ could obtain? Do the Gradwitz' honestly need the small patch of land? The answer to both of these questions is a resounding no.
Therefore, it becomes clear that the land is not what is most important here. Rather, each man wants to demonstrate his prowess and superiority over the other, proving to himself and his family that he “wins.” This dispute is more about male ego and dominance than the land dispute they use as an excuse to feud, which is why Saki’s ending is darkly humorous. In the end, it takes death for these relentless, misguided men to finally quash their quarrel.

Ulrich von Gradwitz and Georg Znaeym are engaged in a territorial dispute over a narrow strip of steep woodland, which is technically owned by the Gradwitz family. The dispute between the two families has lasted for three generations and stems from the Znaeym family's refusal to acknowledge the court's decision to grant the land to the Gradwitz family. The territorial dispute between the two neighbors is known throughout town and becomes personal between Ulrich and Georg. Both men accuse the other of illegally poaching on their territory, and the ill will between their families has been passed down to their sons.
At the start of the story, Ulrich is wandering through the steep slopes of the disputed territory in hopes of finding Georg and killing him. However, both men meet face-to-face, and a massive tree falls on them before either man can harm the other. While stuck underneath the fallen tree, the two men reconcile their differences and become friends before they are devoured by wolves.

Why is John Proctor arrested?

In act 3, John Proctor arrives at Salem's court with Mary Warren and a petition signed by landholding citizens who support Elizabeth, Rebecca, and Martha. John Proctor attempts to prove the witch trials are corrupt by having Mary Warren tell the truth and expose the girls as frauds. Unfortunately, Proctor is met with resistance and the court officials accuse him of attempting to undermine the court's authority. They end up dismissing Proctor's petition and also arrest Giles Corey when he presents a deposition against Thomas Putnam. In a final attempt to ruin Abigail's reputation and prove that she is a fraud, Proctor publicly admits that he had an affair with her. Unfortunately, Elizabeth lies to the court on John's behalf and Abigail begins to act like Mary's spirit is attacking her. Mary becomes overwhelmed with emotions and accuses John Proctor of colluding with the devil. When Deputy Governor Danforth begins questioning Proctor about his affiliation with the devil, John cannot control his anger and yells, "God is dead!" John is then arrested after making his declaration and is charged with colluding with the devil and attempting to undermine Salem's court.

In act 3, John Proctor comes to the court with a deposition containing nearly a hundred signatures of people who are willing to serve as character witnesses for Elizabeth Proctor, Martha Corey, and Rebecca Nurse. This is an act that does not endear him to the authorities. When Proctor continues to push for his wife's release, he is forced into the position of confessing his adulterous affair with Abigail Williams. This is enough to get him arrested (and executed under Salem's law), but it is not until Mary Warren accuses him of witchcraft that Proctor is actually arrested. Mary Warren points at John Proctor in the courtroom and says, "You are the devil's man." Because Proctor is frustrated at the illogicality of the proceedings (particularly the admission of spectral evidence) and the fact that the girls' accusations are condemning innocent people, Proctor yells, "God is dead!" and the marshals take him into custody.

Is Rakesh a devoted son throughout? Support your answer by giving example from text.

It can be argued that Rakesh is a devoted son throughout, but his extreme devotion later results in unintended, negative consequences for his aging father.
We are told that Rakesh has always shown a high degree of filial loyalty to his father, Varma. When the national examination results were announced, Rakesh bowed down and touched his father's feet in reverence. In fact, we are told that this is the first thing Rakesh did after seeing the results in the newspaper.
Not only is Rakesh a devoted son to his father, he also shows a great degree of tender regard for his mother. Even though he studied in America, Rakesh did not bring back a foreign bride to his parents' home. In fact, he did not stray from the Indian tradition of allowing his mother to choose his bride. The text tells us that Rakesh married an uneducated, old-fashioned village girl of his mother's choosing.
It can be seen that Rakesh met all the fond expectations of his parents. Because of Rakesh's filial loyalty, his parents are the envy of the whole village.
Later, however, Rakesh's extreme devotion results in unintended consequences. After his father has a health scare, Rakesh begins to exert stricter control over the older man's diet. He prohibits Varma from having any desserts or fried food. As a result, Varma's quality of life decreases. In the end, the old man begins to contract actual diseases. This leads to Rakesh doubling down on medicines for Varma.
Rakesh is a devoted son throughout, but his devotion blinds him to his father's true needs. In the end, his medical training fails him. He is so focused on treating physical ailments that he forgets to tend to his father's emotional needs.

What was the connection between increased trade in the Mediterranean and artistic output during the Renaissance?

By the early fifteenth century, trade throughout the Mediterranean had reached levels not seen since the collapse of the Roman Empire one thousand years earlier. Improvements in shipbuilding and navigation led to swifter and safer sea routes. This, combined with new mercantile connections made during the Crusades, meant that large amounts of wealth were pouring into Europe's port cities. This all led to the growth of a new merchant class, as well as the bankers that supported them.
With the influx of new capital in Europe—and Italy, in particular—the old class of nobles was no longer the only wealthy members of society. Now merchants were able to compete for prestige and power. These merchants, eager to show off their new wealth, commissioned works of art from the leading artists in their communities. Several leading merchant families in each trade city would often compete with each other to commission the greatest works of art in their community. Chief among these artistic patrons was the House of Medici of Florence, who supported nearly every type of art of the Renaissance, from painting and sculpture to music and poetry. Among the artists they supported were Michelangelo, da Vinci, and Botticelli. As patrons of the arts, they, like other wealthy families, used their position to become well-known and respected members of their cities. They used their vast wealth and popularity to gain political power in their city-states. In a sense, their support of the arts was a method for gaining further prestige and power.

The short answer is: money! 
During the Renaissance, trade by sea and land brought luxury goods to Europe, which were then sold for a profit. Hauling the thousands of pounds necessary to meet market demand was very difficult to accomplish on land. Improvements in navigation and shipbuilding enabled traders to travel much more quickly to far off places with exotic goods (like spices, silk, and precious metals) and return with hardly any increase to their burden. Once they arrived in port, the people who had commissioned the journey (wealthy merchants) or the travelers themselves would in turn sell their goods at marked-up prices. The increase in trade not only brought wealth to the Mediterranean, "stimulating" the economy-- it also provided the wealthy with enough money to invest in the arts.
Patronizing the arts was a way for wealthy individuals to "build up" or invest in their own cities, and such conspicuous consumption drove competition among the elite. With regards to religious art of the Renaissance, many of the people to have such works completed did so as a way of improving their standing with the Church or perception in society. Especially in Italy, a wealthy man might drink, gamble, and visit sex workers, but he could essentially clear his name and moral slate by paying for a very expensive piece of religious art to be created. 
https://www.britannica.com/art/Renaissance-art

https://www.encyclopedia.com/humanities/encyclopedias-almanacs-transcripts-and-maps/economy-and-trade

In "The Totalitarian Movement," Hannah Arendt attempts to explain what makes totalitarianism different. Briefly discuss 4 points made in her essay which help us understand totalitarian logic and how it is applied in practice.

Arendt contends that when totalitarianism takes over a country, it uses indoctrination and terror rather than propaganda to maintain control. Propaganda is then aimed at foreign governments and populations or at internal elite groups that have not yet been "reliably dominated." Propaganda is thus mainly a way totalitarian regimes deal with the non-totalitarian world. Arendt notes that rather than use propaganda, totalitarian regimes rely on terror over their own subdued masses. She writes this was particularly and strikingly standard in the Nazi concentration camps, where there was no "education" (propagandizing) of inmates, only "discipline" (terror).
Totalitarian governments, she says, differ sharply from other governments in being anti-utilitarian. For example, Hitler began murdering the mentally ill at the beginning of World War II not because of any necessity to do so, but as part of his long range vision of a purified Germany that would emerge in the distant future. Totalitarian governments are more concerned with realizing their own fictions of how the world should be than living in a practical, realistic universe, as other governments  do. 
According the Arendt, totalitarian leaders must be seen as infallible, even if this quest leads to strange distortions of truth, such as Stalin denying Trotsky's existence. 
Further, totalitarian regimes find consistency more important than visible experience.  Arendt calls totalitarian organization "completely new" because its aim is to turn the previous propaganda lies and fictions the party developed while seeking power into a "functioning reality" when it gains power. Totalitarians believe they can mold reality rather than be molded by it. They believe that if they have enough power they can turn their fictions into reality. 
 

Single Variable Calculus, Chapter 3, 3.2, Section 3.2, Problem 49

Prove that the function $f(x) = |x-6|$ is not differentiable at 6. Find formula for $f'$ and sketch its graph.

From the definition of absolute value,

$
f(x) = |x-6|= \left\{
\begin{array}{c}
x-6 & \text{if} & x > 0\\
-(x-6) & \text{if} & x < 0
\end{array}\right.
\qquad
\Longrightarrow
\qquad
f(x) = \left\{
\begin{array}{c}
x - 6 & \text{if} & x > 0\\
-x+6 & \text{if} & x < 0
\end{array}\right.
$


From the definition of derivative,
$\displaystyle f'_+ (x) = \lim\limits_{h \to 0^+} \frac{f(x+h) - f(x)}{h} \qquad \text{ and }
\qquad f'_- (x) = \lim\limits_{h \to 0^-} \frac{f(x+h)-f(x)}{h}$

For Right Hand,

$
\begin{equation}
\begin{aligned}
f'_+ (x) & = \lim\limits_{h \to 0^+} \frac{x+h-6-(x-6)}{h}\\
f'_+ (x) & = \lim\limits_{h \to 0^+} \frac{\cancel{-6}-\cancel{x}+\cancel{6}}{h}\\
f'_+ (x) & = \lim\limits_{h \to 0^+} \frac{\cancel{h}}{\cancel{h}}\\
f'_+ (x) & = \lim\limits_{h \to 0^+} 1\\
f'_+ (6) & = 1
\end{aligned}
\end{equation}
$


For Left Hand,

$
\begin{equation}
\begin{aligned}
f'_- (x) & = \lim\limits_{h \to 0^-} \frac{-(x+h)+6-(-x+6)}{h}\\
f'_- (x) & = \lim\limits_{h \to 0^-} \frac{\cancel{-x}-h+\cancel{6}+\cancel{x}-\cancel{6}}{h}\\
f'_- (x) & = \lim\limits_{h \to 0^-} \frac{\cancel{h}}{\cancel{h}}\\
f'_- (x) & = \lim\limits_{h \to 0^-} -1\\
f'_- (6) & = -1
\end{aligned}
\end{equation}
$


$f'_+ (6) \neq f'_- (6)$; Therefore, $f$ is not differentiable at 6.
We can find the formula for $f'$ using $f'_- (x) = -1$ and $f'(x) = 1$
Therefore, we can rewrite $f'(x)$ as

$
f'(x) = \left\{
\begin{array}{c}
1 & \text{if} & x \geq 6\\
-1 & \text{if} & x < 6
\end{array}\right.
$

How John Rupert Firth describe the context and the utterance in linguistics? Please use examples.

How does John Rupert Firth describe the concept of context of utterances in linguistics? Please provide examples. 
A leading figure in linguistics in the 1950s, John Rupert Firth’s work gave rise to the London School of linguistics. He believed the main role of linguistics was analyzing the meaning of spoken expression. At the center of Firth’s work was the inextricable connection of language and situational context. He posited that the meaning of an utterance cannot be separated from the cultural and social event in which it exists. Firth is noted for having said, “You shall know a word by the company it keeps.” This quote shows that his understanding of linguistic meaning rests on the context in which the language occurs.
Firth believed factors such as status, the personal history of the speaker, and the social tone of the situation must be considered in understanding meaning. An example of a “typical” context would be the use of common, socially prescribed phrases to be used in particular situations such as the exchange, “How are you?” “I’m fine, thanks. How are you?”. Firth’s study of context-dependent linguistics focused on speech events in which speakers were responding to social cues within a culturally acceptable mode of behavior.

How did World War I end, and what impact did the conclusion of this war have on the rest of the world?

World War I ended rather suddenly, with hostilities officially ending on November 11, 1918 at 11:00 a.m., though the Central Powers of Austria-Hungary and Bulgaria signed armistices with the Allies a few weeks prior to this. The official treaty that ended the war was not signed until 1919, as Germany had to accept war guilt and pay reparations in the Versailles Treaty. The war ended with the abdication of the German Kaiser Wilhelm II amid threats of leftist revolution at home. The German people could not believe that the war ended, since the government-controlled press had convinced them that the war was going well; in reality, the German army was retreating through France when the peace deal was struck. German soldiers and civilians alike were starving due to the British blockade of Germany and two bad harvests. Even between November 1918 and the ratification of the Versailles Treaty, Britain did not lift its blockade, and Germans continued to starve. Germany was never invaded, and this allowed Adolf Hitler to claim that communists and Jews sold out the German army while it was in the field.
The sudden end of the war had far-reaching implications. Woodrow Wilson had an idea for the League of Nations but he was not yet clear on what its role would be in world security. This would lead to debate in Europe and in the United States on the league and would ultimately end with the United States not joining the international body. Millions of Europeans clamored for their own nations as the Russian, German, Austro-Hungarian, and Ottoman Empires collapsed. This would lead to the formation of Yugoslavia, Estonia, Latvia, Lithuania, Finland, Czechoslovakia, Poland, and the independent nations of Austria and Hungary. Britain and France got mandates from divided German territory. While these places were supposed to be prepared for self-government in the future, the victorious nations ruled them similarly to how they had ruled their own colonies. Germany would use the sudden end of the war as incentive to get back at the Allied Powers, especially France, twenty years later. Germany would initially claim that it was only redressing the issues caused by the Versailles Treaty when it split German-speaking people in Austria and Czechoslovakia away from their mother countries. Germany would later sign a non-aggression pact with the Soviet Union—another nation that was treated unfairly at the Versailles Conference—in which Germany and the Soviet Union agreed to split Poland. This was the spark that began World War II in Europe.

Does the narrator interact with the other characters?

The narrator in Melville's tale does interact fully not only with Bartleby himself but with the other characters. He attempts to reason with Bartleby to discover the reason for the scrivener's unorthodox and increasingly alienated behavior. In fact, he seems to do this much more than would most others in his position, who would probably have fired Bartleby after the first or second reply of "I would prefer not to."
The narrator's interactions with people are of course not limited to Bartleby himself. At every juncture the lawyer intervenes with people—the other clerks in the office, the next occupier of the office, and the prison authorities—in order to protect Bartleby and save him from physical injury or death. The problem, if we can posit that Bartleby could have somehow been saved, is that the lawyer's actions are meant well, but are unhelpful.
From a twenty-first century perspective, it would be appropriate for the narrator to bring a physician to the office to examine Bartleby and offer some explanation for his behavior. Psychiatry as we know it did not yet exist at the time of the story (the 1850s), but physicians dealt in their way with mental disorders. However, the conditions of asylums at that time were appalling, with the patients often chained to the walls. So one cannot blame the lawyer for not reporting Bartleby's condition to the medical authorities.
One would almost think that a greater display of anger by the narrator might have yielded results, but this is to miss the point of the story. Bartleby has reached a point of alienation from which he cannot be brought back. In some sense the narrator understands this—that the hapless clerk is a symbol of despairing humanity, for whom no amount of interaction with others will do anything to relieve his suffering.

y=x^(2/3), y=0, x=8 Find the x and y moments of inertia and center of mass for the laminas of uniform density p bounded by the graphs of the equations.

For an irregularly shaped planar lamina of uniform density rho , bounded by graphs y=f(x) ,y=g(x) and a<=x<=b , the mass (m) of this region is given by:
m=rhoint_a^b(f(x)-g(x))dx=rhoA
where A is the area of the region.
The moments about the x and y-axes are given by the formula:
M_x=rhoint_a^b1/2([f(x)]^2-[g(x)]^2)dx
M_y=rhoint_a^bx(f(x)-g(x))dx
The center of mass (barx,bary) is given by barx=(M_y)/m  and bary=M_x/m ,
barx=1/Aint_a^bx(f(x)-g(x))dx
bary=1/Aint_a^b1/2[f(x)]^2-[g(x)]^2)dx
Now we given y=x^(2/3),y=0,x=8
The plot of the functions is attached as image and the bounds of the limits can be found from the same.
Area of the region A =int_0^8x^(2/3)dx
Use the power rule,
A=[x^(2/3+1)/(2/3+1)]_0^8 
A=[3/5x^(5/3)]_0^8
A=[3/5(8)^(5/3)]
A=[3/5(2^3)^(5/3)]
A=[3/5(2)^5]
A=(3/5(32))
A=96/5
Now let's evaluate the moments about the x and y-axes,
M_x=rhoint_a^b1/2([f(x)]^2-[g(x)]^2)dx
=rhoint_0^8[1/2(x^(2/3))^2]dx
=rhoint_0^8 1/2x^(4/3)dx
Take the constant out and apply the power rule,
=rho/2int_0^8x^(4/3)dx
=rho/2[x^(4/3+1)/(4/3+1)]_0^8
=rho/2[3/7x^(7/3)]_0^8
=rho/2[3/7(8)^(7/3)]
=rho/2[3/7(2^3)^(7/3)]
=rho/2[3/7(2)^7]
=rho(3/7)(2)^6
=rho(3/7)(64)
=192/7rho
M_y=rhoint_a^bx(f(x)-g(x))dx
=rhoint_0^8x(x)^(2/3)dx
=rhoint_0^8x^(5/3)dx
=rho[x^(5/3+1)/(5/3+1)]_0^8
=rho[3/8x^(8/3)]_0^8
=rho[3/8(8)^(8/3)]
=rho[3/8(2^3)^(8/3)]
=rho[3/8(2^8)]
=rho(3/8)(256)
=96rho
Now let's find the center of mass,
barx=M_y/m=M_y/(rhoA)
Plug in the value of M_y and  A ,
barx=(96rho)/(rho(96/5))
barx=5
bary=M_x/m=M_x/(rhoA)
Plug in the values of M_x and A ,
bary=(192/7rho)/(rho(96/5))
bary=(192/7)(5/96)
bary=10/7
The coordinates of the center of mass are,(5,10/7)
 

In "Blue Winds Dancing" by Thomas S. Whitecloud, how does the speaker feel when he first reaches Woodruff? Why does he feel that way?

The writer is apprehensive and a little afraid of how he will be received when he first arrives in Woodruff.
This is because the writer has presumably been away for a while. He hasn't seen his family since he's been enrolled in college. While he appreciates the opportunity to learn new ways, the young writer misses his home and his people. He reasons that, where he lives, there's no need to listen to lecturers droning on and on about obscure topics just to "hear their own words come back to them from the students." At home, the speaker doesn't need to concern himself with grades or whether he's earned enough academic honors. In short, when he's home, there are no anxieties to plague his peace.
Lonely and homesick, the writer decides that he will return home in time for Christmas. When he gets off the train, he feels great joy in tramping through the woods of his childhood years. Yet, on initially arriving at Woodruff, he's apprehensive and fearful of how his family and village will receive him. He's afraid that they will think him less of an Indian. At the same time, he feels that he has no place among the white people he associates with on a daily basis.
In short, the writer feels alienated from both groups. He even wonders about his identity ("Am I Indian, or am I white?"). However, when he enters the village lodge, he soon finds that his deepest fears have been unfounded. The older people receive him with great joy, and everyone makes him feel at home. At long last, the writer joyously concludes that he's indeed home, where he's yearned to be for a while.

What is the Black Belt of Georgia?

In chapter 7 of The Souls of Black Folk, Dubois describes his journey through Georgia, which included an area in a region known as the Black Belt.
The Black Belt was originally used to describe a part of the United States known for its rich black soil. Because of the fertility of the soil, African and African American slaves were imported to the region in large numbers to work on cotton plantations. For this reason, slaves were profitable there.
The large numbers of African slaves that were imported to the region for plantation labor eventually reached, "...half a million at the time of the war," as is recorded by Dubois.
Eventually, according to Booker T. Washington in his book, Up From Slavery, the black belt became less a description of the fertile soil and more a political term for counties where the population of black people outnumber the population of white people. Areas that historically produced rice, tobacco, and sugar were also considered a part of the Black Belt.
In The Souls of Black Folk, chapter 7, Dubois focuses on a county in Georgia, south of the city of Macon, that is considered the Black Belt. In his description of the landscape and the people during his travels, he emphasizes how the region is highly populated by black people, or Negroes, who at the time were mostly tenant farming lands that were owned by the descendants of former plantation owners. He describes the vestiges of the cotton farming industry that apparently left the people indebted and the land largely neglected due to the reduction of demand and dismantling and replacement of the slave labor system by sharecropping and tenant farming.
Today, the Southern Black Belt refers to 623 counties throughout the south that remain among the most impoverished in the United States. They continue to be rural and agricultural, but due to mechanized technology, farming now requires fewer workers. The population of black or African Americans in the Southern Black Belt remains high, and there has been a return migration of educated black citizens to the region.
So, the term Black Belt, as referred to by Dubois in The Souls of Black Folk has a dual meaning for a region of rich, fertile soil that was largely cultivated to produce cotton and, later, other cash crops in the southern part of the United States. It was in this region that slave labor was in high demand, and a large population of the descendants of those slaves continued to reside in the area after the Civil War. They farmed the land under the subsequent labor systems of sharecropping and tenant farming, which was in practice during Dubois's writing of The Souls of Black Folk.
Perhaps, the term symbolizes debt, impoverishment, oppression, disintegration, shame, exploitation, and ill-gotten gains that led to loss. The allusion to the Bible verse from the book of Song of Solomon at the opening of the chapter provides a clue to the central idea of the chapter, "Of the Black Belt." "I am black, but comely...They made me the keeper of the vineyards; But mine own vineyard have I not kept."
https://southernspaces.org/2004/black-belt/

The Great Awakening of the 1740’s refers to ?

The Great Awakening was a massive religious revival that took place in the United States in the 1730s and 40s. The inspiration for the movement came from the Methodists in Great Britain and was an attempt to purify Christianity of its more worldly elements.
At the forefront of the Awakening was the charismatic minister Jonathan Edwards. He sought to bring the faithful back to more important matters, the age-old religious principles of worship and doctrine established by Reformers such as John Calvin. The American colonies were becoming increasingly prosperous. But the headlong dash for wealth was corrupting souls, thought Edwards, making people start to question some of their traditional beliefs.
Like any orthodox Calvinist, Edwards passionately believed that everyone needed to be reminded of how deeply sinful they were. He was a powerful, compelling preacher and used his considerable oratorical skills to drive home the message to growing audiences. Soon thousands were gathering from all around to the hear the old-time Evangelical religion being preached with vigor and passion by Edwards as well as the English minister George Whitefield.
The Great Awakening had considerable political, as well as religious, significance. Thanks to the likes of Edwards and Whitefield, the ministry was no longer seen as the preserve of a social and cultural elite. A people's religion began to emerge, unleashing a spirit of democracy and religious liberty that helped lay the foundations for the American Revolution.

What is the significance of George Bernard Shaw's Arms and the Man being written in three acts instead of the usual five?

The division of plays into “acts” has three functions: the social need for pauses in the entertainment experience, both physical and psychological; the theatrical necessities of costume change, set change, actor breaks, and the like; and, most importantly, the division of the “narrative” into parts whose relationship is part of the artistic experience.  It is not quite accurate to say that plays are “usually” divided into five acts; history has shown that the stage has favored three acts ever since the 19th century, and ever since the 20th century the two-act play is more common.  The important difference is what the playwright was trying to do: the five-act play is a full historical account, as in Shakespeare’s English histories.  The three-act play subtly follows the Socratic method of argument, with a thesis (Act I), an anti-thesis (Act II) and a conclusion (Act III).  Arms and the Man follows this pattern.  In modern times, starting with Beckett’s Waiting for Godot, playwrights have found the 2-act play structure best, to illustrate the dualities presented by Existentialism and other dualistic views of the world.  The whole argument is complicated and requires study in both philosophy and dramaturgy.

Who is she referring to in this poem? Thanks

Translated into English by Mary Barnard, this poem is one of the few we still have that was written by Sappho, one of history's most famous female poets. It is told from her own perspective. 
She starts off with a direct focus on a man, but the poem is truly about her love for another woman. 
"He is more than a hero he is a god in my eyes— the man who is allowed to sit beside you—he
who listens intimately 
to the sweet murmur of your voice," 
In this excerpt, the "you" Sappho is referring to is a woman that she clearly has very passionate feelings for. The man in the poem is a "hero," because he can do what Sappho cannot—gain the love and attention of this woman. In context, the titular "He" in the poem is much less important than the woman he sits with, who is driving Sappho wild with desire.

In Margaret Atwood's "Death by Landscape," how have the significant losses throughout Lois' life created isolation in her life?

Lois is isolated in the sense that, at the end of her life, she is alone in a condo. Her husband is dead, and her children are grown. She is glad to “not to have to worry about the lawn,” or any of the other responsibilities of owning a house, or, presumably, of caring for a family. In fact, her whole life has been one of disengagement. As Atwood writes,

Even at the time she never felt she was paying full attention. She was tired a lot, as if she was living not one life but two: her own, and another, shadowy life that hovered around her and would not let itself be realized, the life of what would have happened if Lucy had not stepped sideways and disappeared from time.

Lois’s isolation, or the life she is missing, is connected to Lucy’s disappearance. The pictures in her condo, “everyone of them a picture of Lucy,” are portals into that alternate life. Lois’s fixation on Lucy, even after all these years, is based on the assumption that something about her inalterably changed the day of the accident. Cappie’s gentle suggestion that perhaps Lois “did something” to Lucy—like push her off the cliff—is more than an injustice: it transforms her identity. Others think of Lois as having “done something,” but the bitter irony is that Lois’s inaction, or her need to follow camp etiquette by giving Lucy privacy while she pees, is what haunts her. Because she was not present, she can never know what happened to Lucy, or what her life might have been if she had not disappeared. In this sense, Lois’s isolation is as much from herself, and her own sense of agency, as it is from other people.

In "Death By Landscape" loss and isolation are inextricably linked. Indeed, the main theme of Margaret Atwood's short story is arguably the way in which loss, if not properly dealt with, can lead to a profound sense of isolation.
Loss of one kind or another is a permanent fixture in Lois's life. Her husband Rob has passed away; her children have grown up and flown the nest; she finds herself constantly haunted by the memory of her lost childhood friend, Lucy. All alone in her apartment, Lois is also isolated from nature, her only experience of which is a view of Lake Ontario from the window.
However, something inside her constantly draws her back to the wilderness, even though it cannot bring her any semblance of peace. She adorns her walls with wilderness landscapes, despite the fact that these paintings fill her with a sense of unease. As an adult, Lois now attempts to do something she could never do as a child: reconcile herself to the wilderness to which Lucy was lost all those years ago. Sadly, the very nature of that landscape has now changed completely. No longer is it seen as a place of beauty, fun or recreation; now it takes on a truly sublime appearance, at once majestic and terrifying.
On the face of it, it may appear that Lois's behavior is masochistic. Why on earth would she surround herself with paintings depicting an environment which so unnerves her and evokes such deeply traumatic childhood memories? On closer inspection, however, we see that the overall picture is much more complicated. By hanging so many wilderness landscapes on the wall, Lois is attempting to create her own little world, a world of artificial nature which, unlike the wilderness of Camp Manitou, she hopes to control.
Unfortunately, she does not. Lois's admission that the paintings make her feel uneasy would seem to suggest that the artificial landscapes exert as much control over her as the real one continues to do.
At the same time, Lois looks upon her painting collection as a way of keeping Lucy alive. We never find out exactly what happened to Lucy, but Lois is so profoundly affected by her friend's disappearance that she grieves over her loss as if she were dead. Additionally, she can never fully come to terms with her loss. Why? She cannot because she has isolated herself from reality, meaning that she will never be able to confront the traumas of her troubled past and achieve some measure of peace.
So long as Lois fails to confront her demons, she will remain forever trapped in a dark place between a real wilderness and a fake one. Whichever way she turns, the painful loss she suffered and the debilitating isolation that goes with it will forever endure.

Calculus: Early Transcendentals, Chapter 7, 7.1, Section 7.1, Problem 6

You need to solve the integral int (x-1) sin (pi*x) dx = int x*sin (pi*x) dx - int sin (pi*x)dx
You need to use substitution pi*x = t => pi*dx = dt => dx = (dt)/(pi)
int x*sin (pi*x) dx = 1/(pi^2) int t*sin t
You need to use the integration by parts for int t*sin t such that:
int udv = uv - int vdu
u = t => du = dt
dv = sin t=> v = -cos t

int t*sin t = -t*cos t + int cos t dt
1/(pi^2) int t*sin t = 1/(pi^2)(-t*cos t + sin t) + c
Replacing back the variable yields:
int x*sin (pi*x) dx = 1/(pi^2)(-pi*x*cos(pi*x) + sin (pi*x)) + c
int (x-1) sin (pi*x) dx = 1/(pi^2)(-pi*x*cos(pi*x) + sin (pi*x))+ (cos (pi*x))/(pi) + c
Hence, evaluating the integral, using integration by parts, yields int (x-1) sin (pi*x) dx = 1/(pi^2)(-pi*x*cos(pi*x) + sin (pi*x))+ (cos (pi*x))/(pi) + c.

Why does John insist that Mary Warren testify in Elizabeth's defense?

John's wracked with guilt over Elizabeth's arrest. He feels that he's in some way responsible—which, to a large extent, he is. The level of hysteria has reached fever pitch in Salem, destroying lives and setting neighbor against neighbor. John knows just how serious this is; he knows that Elizabeth is in real danger of being arraigned as a witch. He's got to do whatever it takes to save his beloved wife from such a terrible fate.
Somehow, John has to try and undermine the credibility of Abigail Williams's testimony. That shouldn't be too hard, one might think, given that her whole story has been nothing but a tissue of lies from the start. But Abigail's become a very powerful figure in Salem thanks to the witch-craze she started, and she's not about to relinquish the power she's accrued to destroy others. Truth be told, people are scared stiff of her, and with good reason, too. Just one word from her lying mouth and some poor soul could end up dangling on the end of a rope.
Mary Warren's only one of many townsfolk absolutely petrified by Abigail and the diabolical power Abigail wields with such wanton recklessness. She knows full well that Abigail's made up the whole witchcraft business, but she daren't let on. When John pleads with her to testify against Abigail, Mary flatly refuses, saying that Abigail will turn against her immediately and falsely accuse her of being a witch instead.

How does the sub-plot involving Jessica and Lorenzo support the main plot of Shakespeare's The Merchant of Venice structurally and thematically?

Jessica's eloping with Lorenzo helps motivate Shylock's hatred against the main characters, but it also reveals certain sympathetic elements of his character. He is deeply upset by her marrying without his consent, especially to a Christian. For Shylock, whose fury at Christians comes from their prejudice against the Jewish minority, this strengthens his resolve to get that pound of flesh from Antonio, the Christian he hates most.
Shylock's reaction to Jessica's actions also shows he has a more vulnerable side. He mentions that one of the valuables Jessica took with her was a turquoise ring his deceased wife, Leah, gave him before they were married. He claims he would not have given the ring up for anything, showing its value for him is sentimental rather than monetary. This goes against Solanio's mocking of Shylock's grief.
This shows that Shylock is not just weeping over blows to his wallet or self-respect, which people like Solanio believe to be the case. Shylock's heart has been broken as well, and this ties into his famous "Do we not bleed?" speech, where he condemns the Christian mainstream society that refuses to see Jewish people as human beings worthy of respect.

Structurally, Jessica's romance with Lorenzo helps drive Shylock over the edge.  
When the play opens, Shylock already feels hard-done-by. After Jessica runs away with Lorenzo, Shylock takes yet another hit, both in his pocketbook and in his self-respect. Jessica takes some money with her, which upsets Shylock. He also, of course, feels betrayed that his daughter left him, and her heritage, to marry a Christian. To make matters worse, everyone is laughing at his frustration. In Act 2, Scene 8 we see this exchange:

Solanio:
As the dog Jew did utter in the streets:
'My daughter! O my ducats [money]! O my daughter!
Fled with a Christian! O my Christian ducats!
Justice! the law! my ducats and my daughter!'
Salerio:
Why, all the boys in Venice follow him,
Crying his stones, his daughter, and his ducats.

Shylock has become a laughingstock. In Act III, Scene 1, we see he blames Salerio, Solanio, and Antonio for this turn of events: "You knew, none so well, none so well as you, of my daughter's flight." A few lines later, Shylock gives his "Revenge" speech. If there was any question before about whether Shylock would really take his pound of flesh from Antonio, his resolve to do so is now hardened.
Thematically, at least three things are occurring. 
First, Jessica's subplot confirms Shylock is not a gracious person. He is not even kind to his own daughter. He treats her harshly. She sees nothing attractive in his lifestyle, and is only too eager to leave it.
This leads in to the second theme, that of the contrast between Shylock's bitter way of life and Antonio's gracious one. Unfortunately, in this play that is also painted as the contrast between life as a Jew and life as Christian. Of course, this is an exaggeration and a stereotype at best. The underlying point is that it is better to live a life of giving and receiving mercy than a life of giving and receiving only one's rights under the law. In the play, Jessica is a gracious young woman, so she shows her good character by preferring a merciful life.
Finally, Jessica, like Portia, is a funny, clever, and strong-minded young woman who dresses as a boy and sneaks out of her house to do some good. Her behavior echoes Portia's, but in a minor key. Jessica is not quite as brave as Portia (she is afraid to be seen in the pageboy's costume), nor quite as selfless (she is running away mostly for her own benefit, not to help another). Still, between these two remarkable young ladies, Shakespeare shows a smart and spunky girl can come from any walk of life. 

Compare and contrast how empathy is evoked in the reader in "Follower" by Seamus Heaney and "The Farmer's Bride" by Charlotte Mew.

In terms of eliciting empathy from the reader, these two poems share multiple qualities. Perhaps the greatest is creating characters which are vulnerable. In "The Farmer's Bride," the speaker almost immediately concedes that he may have made a misjudgment and contributed to his own unhappiness. When the speaker says he married "Too young maybe—but more’s to do / At harvest-time than bide and woo," we can sense he is reasonable for admitting the potential for his own fault and was preoccupied with hard work. He was burdened and made a mistake; he was vulnerable.
The reader is similarly compelled to feel empathy for the speaker of "Follower." In Heaney's poem, the strong father character is juxtaposed to the speaker as a boy, who was "a nuisance, tripping, falling, / Yapping always." In short, he was young, clumsy, and vulnerable. By illuminating each speaker's weaknesses or faults, both "Follower" and "The Farmer's Bride" provoke empathy from readers.
However, even though both these poems attempt to paint sympathetic characters, the situations of each poem are fundamentally different. "The Farmer's Bride" is, quite simply, about an unhappy marriage and a sad situation. We feel pity for both husband and wife as the speaker says, "When us was wed she turned afraid / Of love and me and all things human."
"Follower," on the other hand, portrays a meaningful and healthy bond between father and son, only to abruptly introduce a devastating role change. As the speaker's father has aged, so the speaker has had to become the leader of the two. It is obvious that seeing his father's strength diminished has brought great sadness to both parties. One poem paints a sad portrait, and the other portrays a downfall from happiness to despair.

What literacy device is the author using to convey the following point of view? "In both countries it was clearer than crystal to the lords of the State preserves of loaves and fishes, that things in general were settled for ever."

The above quote is from the first chapter of A Tale of Two Cities, and it is what we call an allusion.
An allusion is a literary device which references ideas or people with political, religious, social, or literary significance. In the above, the quote is an allusion to Christ's two miracles of the loaves and fishes in the New Testament. The first miracle involved Christ feeding five thousand people by multiplying five loaves of bread and two fishes. The second miracle involved Christ multiplying seven loaves and a few fishes to feed four thousand who had gathered to hear him.
In the above quote, the French and English aristocracy were the "lords of the State preserves." They were the ones responsible for the general welfare of the people; yet, the irony is that they lived their lives oblivious to the true nature of the average citizen's struggles. While they presided over plenty, a majority of the populace in both countries lived subsistence lives. Basically, the aristocratic classes enjoyed lavish lifestyles and concluded that "things in general were settled for ever."
Additionally, many aristocrats had access to game preserves that average French and English citizens were forbidden to enter. In these preserves, the wealthy and the powerful indulged their love for game sport. The meat was not used to feed the hungry masses (hence the irony of the allusion to Christ's miracles), but to tease the palates of those who were already accustomed to good food on a daily basis. It was said that the English and French monarchy "trod with stir enough, and carried their divine rights with a high hand." In other words, the aristocrats acted like gods but failed to fulfill their responsibilities to their people.
http://dickens.stanford.edu/dickens/archive/tale/issue1_allusions.html

In what ways is Achilles a bit like John Gardner's Grendel?

Many similarities exist between the characters of Achilles and Grendel. One could begin by arguing that the two are, in effect, mirror images: Achilles is a man made superhuman by supernatural intervention, while the monster Grendel possesses human qualities in his level of intelligence, wit, and propensity for social commentary. Temperamentally, the two characters are alike: both have volatile tempers and can act rashly, even dangerously, when that temper is provoked. Driven by intense, sometimes rigid moral codes, both embark upon an heroic quest. Furthermore, both Achilles and Grendel can be arrogant in the assertion of their respective beliefs. Possessing superhuman strength, the two are fierce warriors who hate to lose or even admit defeat. One might also argue that both are tragic heroes who share a fatal flaw: pride.

Single Variable Calculus, Chapter 3, 3.1, Section 3.1, Problem 5

Determine the equation of the tangent line to the curve $\displaystyle y = \frac{x - 1}{x - 2}$ at the point $(3, 2)$

Using the definition $\text{(Slope of the tangent line)}$

We have $a = 3$ and $\displaystyle f(x) = \frac{x - 1}{x - 2}$, so the slope is


$
\begin{equation}
\begin{aligned}

\displaystyle m &= \lim \limits_{x \to 3} \frac{f(x) - f(3)}{x - 3}\\
\\
\displaystyle m &= \lim \limits_{x \to 3} \frac{\frac{x - 1}{x - 2} - \left( \frac{3 - 1}{3 - 2} \right)}{x - 3}
&& \text{ Substitute value of $a$ and $x$}\\
\\
\displaystyle m &= \lim \limits_{x \to 3} \frac{\frac{x - 1}{x - 2} - 2}{x - 3}
&& \text{ Get the LCD and simplify}\\
\\
\displaystyle m &= \lim \limits_{x \to 3} \frac{-x + 3}{(x - 3)(x - 2)}
&& \text{ Factor the numerator}\\
\\
\displaystyle m &= \lim \limits_{x \to 3} \frac{-1 \cancel{(x - 3)}}{\cancel{(x - 3)}(x - 2)}
&& \text{ Cancel out like terms}\\
\\
\displaystyle m &= \lim \limits_{x \to 3} \frac{-1}{x - 2} = \frac{-1}{3-2} = -\frac{1}{1} = -1
&& \text{ Evaluate the limit}\\
\end{aligned}
\end{equation}
$

Therefore,
The slope of the tangent line is $m = -1$
Using point slope form


$
\begin{equation}
\begin{aligned}

y - y_1 =& m ( x - x_1)\\
\\
y - 2 =& -1 ( x - 3)
&& \text{ Substitute value of $x, y$ and $m$}\\
\\
y - 2 =& - x + 3
&& \text{ Combine like terms}\\
\\
y =& -x+5
\end{aligned}
\end{equation}
$


Therefore,
The equation of the tangent line at $(3,2)$ is $y = -x +5$

Why did Europeans, and not Asians, undertake the voyages of discovery connecting Old World with New World?

One reason why the Europeans and not the Asians undertook the voyages to connect the Old World with the New World had to do with safety. There were times when the land routes to Asia were either blocked or unsafe due to possible attacks. Islamic Empires were often fighting for control of the areas where the land routes went. Also, robbery was common, and the caravans were often in danger of being raided.
Another factor dealt with the growing competition between the European powers. The Italian city-states were in a good location to profit from and dominate the trade with Asia. Spain, Portugal, and Great Britain hoped to break the Italian control by finding different water routes to Asia.
Finally, the Europeans were more interested in Asian products than the Asians were interested in European products. Silk and spices from Asia were highly demanded in Europe. Thus, the Europeans wanted to find multiple ways to get these products to Europe.

The answer is quite simply that the Asians had goods Europeans wanted very badly, and not vice versa. The Europeans were especially hungry for the spices the Asians could cultivate and they could not, such as pepper and cinnamon. In earlier years, the Europeans had made the overland journey to the Far East, but by the fifteenth century the Turkish Empire had gained control of those overland routes. They charged high tariffs for passage through their lands, and the Europeans also ran a higher risk of encountering pirates and bandits. An already costly overland journey became prohibitively expensive, taking much of the profit out of the spice trade.
Countries such as Portugal had been developing their navigational technology and improving their shipbuilding techniques. They wished to find a sea route to India by sailing around the tip of Africa, so as to circumvent dealing with the Turks. When they were able to successfully do this, it unleashed a frenzy of exploring activity as other countries also sought alternative overseas routes, seeking profits in trade with Asia. 
In the process of trying to find ways to Asia, the Europeans stumbled on the North and South American continents, and almost immediately realized the huge potential existing there in raw materials. This created competition for the New World's resources among European nations and thus more exploration. 

Considering that much of the technology that permitted Europeans to traverse the oceans came from Asia and the Far East, the reason is not found in any technical advantage that Europe possessed over Asia.  In answering this question, it is important to understand the motive for European exploration and discovery of America.  First, the Europeans wanted an easier and less expensive route to the East in order to acquire spices, drugs, perfumes, and silks that were in very high demand on their continent after the Crusades.  So through this perspective, the Asians would not be trying to find a sea route to their own lands.  Secondly, the Europeans were in the midst of the Renaissance, a period of time in which there was a belief in the unbelievable potential of humanity. This period brought about scientific discovery and reason.  Despite the fact that Europeans discovered a previously unknown world, this was done by complete accident and for years following the landfall of Columbus, Europeans still did not realize they were not in Asia. 
https://www.whoi.edu/page.do?pid=66617

Explain the differences between how the characters of Homer (Iliad) dealt with their monumental struggles as compared to how the characters in Oedipus the King and Euripides Medea.

As there are numerous different characters in all of these works, a comparison of all of them to each other would run to hundreds of pages.
The conflict between the Trojans and Greeks is handled by violence. Paris seized or abducted Helen. Menelaus, the jilted husband, has enlisted the support of other Greeks to reclaim her by violence.
Within the Greek forces, conflicts are normally handled by debate, but Agamemnon also has the power to make executive decisions. Achilles handles his conflict with Agamemnon by withdrawing from the fight, hoping that subsequent losses in battle will compel Agamemnon to return his war prize. Odysseus tends to favor subterfuge.
Oedipus exists within a more rational and legalistic framework. He consults oracles and follows laws. Medea takes justice into her own hands and resolves conflict with violence.

What is the main external conflict in this story ?

The main external conflict in "Contents of the Dead Man's Pocket" is involved in the problem of retrieving a sheet of yellow paper that has blown out the window. At first it seems like a relatively simple matter, even though the scene is set eleven floors above the street. The paper is only about five yards from Tom Benecke's apartment window. The ledge is about as wide as the length of his shoe. The weather is clement, which explains why he opened the window in the first place. But when Tom gets out on the ledge and sidles a short distance towards the paper, he realizes that he has more logistical problems than he had anticipated. He can only proceed by facing the wall and holding onto the bricks with his fingertips. And when he does get to the precious paper, he finds that he can't bend over to pick it up without risking losing his balance and falling to his death.
Up to that point his internal problems have been relatively minor. He had decided that he would just not look down. That way the height would not be a serious factor. But when he is finally forced to look down in order to pick up the yellow sheet of paper, he gets a full, horrible view of Manhattan at night from eleven stories up.

...he lowered his right shoulder and his fingers had the paper by a corner, pulling it loose. At the same instant he saw, between his legs and far below, Lexington Avenue stretched out for miles ahead.
He saw, in that instant, the Loew's theater sign, blocks ahead past Fiftieth Street; the miles of traffic signals, all green now; the lights of cars and street lamps; countless neon signs; and the moving black dots of people. And a violent instantaneous explosion of absolute terror roared through him. 

After this the story changes from an external conflict to an internal conflict. Tom has to start moving back towards his apartment window in spite of his nearly overpowering terror and the sense of vertigo which seems to be pulling him backward off the narrow ledge and out into empty space.

How does Thich Nhat Hanh use Buddhist practice, especially mindfulness, to combat suffering?

Thích Nhất Hạnh is a Vietnamese spiritual leader and peace activist who is widely credited as a key figure in introducing Buddhism to the western world. 
How did he do this, and what are his primary teachings and beliefs?
He believes that mindfulness is essential for peace.
The only way for individuals to find peace and contentment, Nhất Hạnh believes, is to practice mindfulness (the practice of focusing one's attention on the present moment). This is often achieved through meditation. The only way for a society to function peacefully is for individuals to have inner peace. So mindfulness is very important in the prevention of conflict.
He encourages nonviolent conflict resolution.
Nhất Hạnh is a peace activist, and the peace he is trying to achieve is not only on an societal or political level, but also on an individual level (see above). He encourages individuals to proactively pursue peace and to set a good example for others. To quote the spiritual leader,

In Buddhism we see that teaching is done not only by talking, but also by living your own life. Your life is the teaching, is the message.

Nhất Hạnh's approach to nonviolence even includes animals: unlike human beings, animals cannot be taught to behave proactively or pursue peace, so Nhất Hạnh believes in protecting their interests. He promotes refraining from the consumption of meat and animal products as a way of practicing nonviolence to animals.
The points above are all leading up to the major point here:
Thích Nhất Hạnh practices "Engaged Buddhism." 
What is this? It is a term that Nhất Hạnh actually coined himself: it refers to the application of Buddhist principles, including meditation and mindfulness practice, to larger issues in the world—such as social and political issues, environmental problems, economic recessions, racial injustice, and so on. By working on ourselves first and by being aware of ourselves and the present moment we live in, we can be more effective members of society and even become leaders who set the tone for the communities we live in.

Pretend you are a public defender (defense attorney). Your client is a resident of California. Last summer he was arrested in Yosemite National Park by the federal government for possession of marijuana. The marijuana was seized from his camping tent without a warrant. The officers removed a tarp from the top of the tent and found the marijuana inside. Your client is currently being charged with felony possession because this is his third offense, and he has chosen to plead the Fifth. Build a case for his defense using the equal protection clause of the Fourteenth Amendment and the exclusionary rule of the Fourth Amendment. Then explain if this defense would change significantly had he been arrested and charged by the Arizona state government and not the federal government. Some things to consider: Was the evidence obtained legally? Does federal policy supercede state law? Your client is facing three years in jail and a $5,000 fine. Is this punishment excessive? Can you find any recent cases that pertain, i.e., the development of jurisprudence in this area that may help build your case? Remember originally the Bill of Rights only applied to the federal government, and through the process of selective incorporation, most now apply to the states as well.

First, the key piece of material evidence in this case —the marijuana—must be excluded as it is "fruit of the poisonous tree." The fruit of the poisonous tree doctrine generally says that evidence obtained illegally is not admissible in court. In this case, the marijuana was discovered after the residence (the tent) of the defendant was searched without probable cause or a search warrant—the general requirements for police entry required by the fourth amendment.

Second, the equal protection clause of the 14th amendment establishes that all citizens of the United States should be treated equally under the law. While possession of marijuana may be a federal crime, it is legal in California and to prosecute a Californian within California for an act for which Californians in other parts of the state would not be subject to prosecution would be a violation of equal protection. However, were he arrested in Arizona, the equal protection argument might not apply, as no differential application would come into play, Arizona not having legalized marijuana in the first place.


The equal protection argument with respect to marijuana possession is currently being argued in the case of Washington, et. al v. Sessions.
Finally, the penalty of three years imprisonment and a $5,000 fine may or may not be excessive, however, the constitution only prohibits punishment which meets the two-part test of being (a) cruel, and, (b) unusual. In Furman v. Georgia the court set-out a high threshold of requirements for something to be both cruel and unusual, none of which are met by the penalty faced by the defendant in this hypothetical case.
http://www.hillerpc.com/wp-content/uploads/2017/07/Filed-Complaint-with-Dkt.-No.pdf

https://www.law.cornell.edu/wex/fruit_of_the_poisonous_tree

The Fourth Amendment of the US Constitution prohibits "unreasonable searches and seizures." Through the incorporation doctrine, the Fourth Amendment applies to the states as well as to the federal government (Mapp v. Ohio). Evidence found during an unreasonable search or seizure is excluded from court through the exclusionary rule.
Searches that are conducted without a warrant are unreasonable unless they fall into one of a small category of permissible exceptions. These are:
When police have to take immediate action to prevent evidence from being destroyed (the exigency exception).
Vehicle searches, which are permissible without a warrant because vehicles can be moved quickly, taking any evidence with them.
A search incident to an arrest, which allows police to search a suspect being apprehended, as well as his or her immediate surroundings.
A search done with a suspect's consent.
A search of areas that are within an officer's plain view, provided that the officer is legally standing in a public place.
The open fields exception, which allows police to search your land, provided you do not have a reasonable expectation of privacy in it.
Only the last two are closely applicable. The fact that the police needed to move a tarp to find the marijuana, though, eliminates these as a valid reason for the search. This makes the search unreasonable, in violation of the Fourth Amendment, and therefore illegal. It would be excluded from court and could not be used against the defendant.
The defense would not change significantly if the arrest had happened in Arizona by state law enforcement. The US Constitution provides civil rights that are considered the "floor": states can offer individual rights that surpass what the US Constitution offers, through their own state constitutions, but they can never offer less.
The three year, $5,000 fine punishment is far from excessive. In fact, it is relatively lenient for a third-time felony offense. Excessive punishment cases under the Eighth Amendment tend to involve extremely high sentences, and the bar is very high for the punishment to be excessive: A 25-years-to-life sentence under California's "three strikes law" in Ewing v. California for a defendant who stole three golf clubs was found to not be excessive.

Why can't the speaker enjoy the beauty of the woods?

The poem doesn't give readers an explicit and concrete answer to this question; however, the poem does offer enough evidence for a reader to hazard a guess or two as to why the man can't stay stopped by the woods. One possible reason as to why the man can't stay stopped is a straightforward and realistic reason. It's cold, he's getting cold, and he needs to get himself and his horse to shelter. We are told that the man stopped at night, and night temperatures are more often than not colder than day temperatures. Additionally, it is cold enough to snow. He's watching the woods fill with snow, and we are specifically told that the lake is frozen. In order to freeze a lake, it has to be quite cold for quite some time. We aren't given any indication as to how long the man has been riding or how much farther he has to go, but delaying any longer could potentially be life threatening.
The final lines of the poem give readers another option as to why the man can't stay staring at the woods. We are told that he has promises to keep. Maybe he promised his wife that he would be home by a certain time, and he had better not wait too long. We have no idea what those promises are, but we do know that he feels a strong need to get to his destination in order to keep those promises. He may want to stay looking at the "lovely, dark, and deep" woods, but his commitments to other people are more important than his own desires.

Which specific elements in Crane's "The Bride Comes to Yellow Sky" help to determine its theme, and how?

The central theme in "The Bride Goes to Yellow Sky" is the passing away of the Old West to make way for the future. The two elements which most emphasize this theme are the setting and characters.
The first scenes in the story are set on a train coming from San Antonio. It is a symbol of the fast-paced modern world. Jack Marshall and his bride are out of place on the train, uncomfortable in their wedding clothes and mocked by both the other passengers and the porters. Yellow Sky on the other hand is a frontier town, rougher in its manners. The train coming to Yellow Sky represents modernity catching up to the Old West and replacing it.
The characters are plays on Old West tropes: the law-abiding marshall bent on justice, the good woman with domestic influence, and the trigger-happy criminal sworn on vengeance. However, they are stripped of all their romance. Jack is more terrified of what the town will think of his marrying a woman without their consent than of any criminals that might threaten his new bride. His bride is a timid, middle-aged woman, not the youthful beauty one might expect.
Scratchy Wilson is the least glamorous of all. Initially presented as a menace, by the end of the story he is rendered pathetic. When he learns Jack is now married and has no time for their old cat-and-mouse game, he reacts like a little boy being told his best friend cannot play ball with him anymore. In fact, he is referred to as a child-like figure throughout, even though he asserts to Jack "I ain't no kid."
This last, anticlimactic defeat of Scratchy Wilson becomes a representation for how the wild ways of the Old West were being tamed by "civilization" in the late nineteenth century.

Crane's famous tale is a parable about the contrast and the clash between the old and new, the primitive and the civilized.
In the story, Potter is traveling by train with his bride from San Antonio to a remote town in Texas. The description of the interior of the railway carriage, and the mere fact of journeying by train, are meant to emphasize the new, civilized side of the frontier. The porters are overly attentive to Potter and his bride; the fixtures are of polished brass and wood that gleams "like oil;" the dinner costs a whole dollar. The disconnect between this new world of luxury and ease, and the wild frontier of Yellow Sky, is also evident in Potter's anxiety over how the town will receive his bride, about whom he has told them nothing. Potter himself isn't quite at ease with the advanced, comfortable world from which he's bringing her. He gives the porter a tip "as he had seen others do."
The theme of culture clash between old and new is further delineated in the rather comical description of the bar in Yellow Sky and the way everyone cowers before Scratchy Wilson. The town drunk who gets out of hand became a cliché of Western literature and film. If Scratchy represents the old untamed West, then his defeat, the vanishing of his species, so to speak, comes about when he sees that Potter has a bride with him. It's as if Potter's married status represents civilization. The title of Crane's story is emblematic of the taming of the Old West. When the bride comes to Yellow Sky, it's the beginning of the end for Scratchy and the wildness of the frontier, as Scratchy walks away, foregoing the planned fight with Potter.

Stephen Crane's 1898 short story was meant to explore, sometimes humorously, how the American West was changing near the turn of that century. 
Trains were making it easier for people to travel great distances, and Crane opens the story with the town policeman, Jack Potter, returning to Yellow Sky with the woman he has married earlier that day in San Antonio. She is an Easterner unused to the vast distances of the West and the unique pressures on her husband in his prominent role in Yellow Sky. So, the initial setting of the story, the train, illustrates how trains were bringing Easterners and Westerners together.
The fact that the story's protagonist is a lawman with enemies in a Western town is a familiar trope. Potter really has two "enemies:" the town, to whom he will have to answer for his choice in marrying an Easterner without their "permission;" and Scratchy, his "ancient enemy" and a living artifact of the Old West.
The fact that Scratchy walks away from his "showdown" with Jack Potter—who is described as a "city policeman," and not a sheriff—suggests that civilization and modern thinking have reached West Texas. 

What is an example of: A is a subset of B and B is a subset C, but C is not a subset of A?

Hello!
Actually, such a situation is typical. If A is a subset of B and B is a subset of C, then A is a subset of C (any element of A is an element of B and thus is an element of C).
Therefore for C to be a subset of A, A and C must coincide. And for C not to be a subset of A it is sufficient that B has at least one extra element compared to A, or C  has at least one extra element compared to B. This is easy to achieve.
For example, let A = {1}, B = {1,2} and C={1,2,3}. Then all the conditions are satisfied: A sub B sub C,  but not C sub A.
Or A = NN, B = ZZ, C = RR.
 
 

Do you agree with criticism that Hamlet should take action against Claudius sooner than he does?

As a matter of fact, I do agree with this criticism. Hamlet decides to act mad, and then waits for months before taking any other "action." Then, he seems only to make a plan once the traveling troupe of actors happens to show up at Elsinore. It surprises me that he would not be quicker to act, given the awful grief Hamlet feels upon the death of his father, the terrible way in which his father was murdered, and the fact that revenge means so much to to his father that his ghost returns to charge Hamlet with the responsibility of avenging him. 
Also damning, for me, is the way Hamlet feels about himself. If he were making progress and pleased with that progress, I might feel less critical of him. Hamlet thinks he's not acting the way he should, though. Consider his speech after he watches an actor emote during a performance: he asks himself, "Am I a coward?": a seemingly rhetorical question whose answer is, evidently, yes (Act II, Scene 2, line 598). He also calls himself a

dull and muddy-mettled rascal, [who] peak[s] Like John-a-dreams, unpregnant of my cause, And can say nothing—no, not for a king Upon whose property and most dear life A damned defeat was made (Act II, Scene 2, lines 594-598).

Hamlet criticizes and characterizes himself as someone without courage who is, at best, an absent-minded dreamer who accomplishes nothing, despite the fact that he loved his dear father who was defeated in such a despicable way.

In the New York City police Department (NYPD) Regarding Protest in the NYPD, what might police in other places learn from NYPD? What should they avoid that NYPD does?

Police departments all across the country have policies dealing with how to handle protests and demonstrations. In New York City, the policy is to try to protect the First Amendment rights of all people at a demonstration. People have the right to voice their opinion, whether it is popular or unpopular. All police departments should follow this policy.
In New York City, there is no set policy regarding how many police officers would be present at a protest. Generally, the larger the anticipated number of protesters, the larger the police presence will be. While it would be nice to have some set guidelines, it is often difficult to determine the exact number of protesters who will arrive. Generally, the main goal of the NYPD will be to protect the public as well as members of the police force.
The NYPD will meet with the people who want to protest in advance of the day of the protest. They will ask for information about the protest, including collecting flyers and other printed materials. They also will look at the past history of any group that wants to protest. This is a good policy for all police departments to follow.
The NYPD also will establish what is known as "barrier pens" in order to effectively patrol the protesters and maintain some control over them. This may or may not be effective in every city. Other cities have tried to establish a perimeter area in order to control the protesters instead of using "barrier pens."
In New York City, any protesters who break the law will be arrested. Any person arrested will be taken to a mobile facility for processing.
Developing a police policy for demonstrations for a given city depends on many factors. What may be good for one city might not be effective for another city.
https://sfbos.org/police-facilitation-mass-protests

Which organ of government is known as the judiciary?

I think you are referring to the form of government that the United States and some other countries have, with a legislative organ, an executive organ, and a judicial organ.  We usually refer to these as branches of government.  When we make reference to the judiciary, we often mean the Supreme Court of the United States, which is meant to have nine members, although there is a vacancy at the moment.   The Supreme Court was established by Article III of the Constitution.  The legislative branch, Congress, has established other courts below the Supreme Court, federal district courts and federal circuit courts.  The district courts are throughout the United States, and they are trial courts to make determinations about federal laws and the Constitution.  The circuit courts are appellate courts, and anyone has the right to appeal a district court decision to the circuit court.  From the circuit court, one may ask the Supreme Court to review the decision, but it is up to the Supreme Court to agree to do so or not.  At the state level, there is also a judiciary, established by each state's constitution.  There are three levels here as well, a trial court level, an appellate court level, and a state supreme court level.  As in the federal judiciary, one has the right to appeal the decision from the trial court to the appellate court, but the state supreme court decides whether or not to hear an appeal from the appellate court decision. 
https://www.fjc.gov/history/home.nsf

Even though The Other Side of Truth has a positive ending, Beverly Naidoo still succeeds in disturbing the reader. How does the author achieve this?

The entire premise of the story could be considered disturbing, even though the ending is a positive one. For example, the two children in the story become refugees after their mother's murder. Naidoo delves into the brutal experience and all the emotions and fears that accompany it for the children. Her description of the shooting that resulted in the death of the children's mother is disturbing on its own, especially since it is told from the perspective of young children. Immediately after learning that their mother will die from her gunshot wound, Sade receives a vague threat over the phone, increasing the tension in the story and creating an atmosphere of disturbing suspense.
Another disturbing element is introduced to the story when the children are forced to flee Nigeria to escape their father's political enemies with a woman who is already flying to London. Naidoo describes their pain and fear of leaving their father with heart-wrenching depth, making the story both disturbing and poignant. Sade and her brother are later abandoned at a cafe in London and they face the disturbing reality of being cold and alone in a strange place. They are treated unkindly and with suspicion by the locals, and face the harsh reality of being refugees without parents to care for them. After being taken into the foster care system, the children are assigned a kind social worker, but they have a frightening experience when immigration services gets involved. Throughout their experiences in the foster care system and at a strange school, Naidoo effectively showcases the emotional turmoil the children go through.
Later, after the children are reunited with their father in jail, they learn that he has been falsely accused of their mother's murder by Nigerian leaders. Dealing with the death of one parent and the incarceration of another is difficult enough, but the false accusation introduces another disturbing element to the story. While the story comes to an uplifting resolution in the end, with the children being permanently reunited with their father, the trauma they go through in order to get to their happy ending is significant. The author uses the gradual buildup of these traumatic experiences to create a tense and disturbing atmosphere throughout the story. Naidoo also uses the juxtaposition of the children's innocence and their horrific circumstances to disturb the reader.

Single Variable Calculus, Chapter 7, 7.6, Section 7.6, Problem 32

Determine the derivative of the function $y = \tan^{-1} \left( x - \sqrt{1 + x^2} \right)$ and simplify if possible.
If $y = \tan^{-1} \left( x - \sqrt{1 + x^2} \right)$, then

$
\begin{equation}
\begin{aligned}
y' &= \frac{1}{1+\left( x- \sqrt{1+x^2} \right)^2} \cdot \frac{d}{dx} \left( x - \sqrt{1+x^2} \right)\\
\\
y' &= \frac{1}{1 + \left( x^2 - 2x \sqrt{1+x^2} + (1 + x^2) \right)} \cdot \left( 1- \frac{2x}{2\sqrt{1+x^2}} \right)\\
\\
y' &= \frac{1- \frac{x}{\sqrt{1+x^2}}}{2 + 2x^2 - 2x \sqrt{1+x^2}}\\
\\
y' &= \frac{\frac{\sqrt{1+x^2}-x}{\sqrt{1+x^2}} }{2\left( 1 + x^2 - x \sqrt{1+x^2} \right)}\\
\\
y' &= \frac{\sqrt{1+x^2}-x}{2\sqrt{1+x^2}\left( 1 + x^2 - x \sqrt{1+x^2}\right)}
\end{aligned}
\end{equation}
$

What scene or incident from Voltaire's Candide illustrates an aspect of Voltaire's understanding of human nature?

Voltaire had a pessimistic view of human nature, finding it largely irrational. This is illustrated in chapter 28 in a scene where Candide has a conversation with Pangloss. Pangloss recounts that he has survived a hanging and only managed not to be dissected by screaming on the autopsy table at the first incision. Then, he tells Candide, he entered a mosque and picked up the nosegay a woman there had dropped. He appeared to be looking at her cleavage as he returned it and so was sentenced to one hundred lashes on the soles of his feet. Then he was made a galley slave, and in his words:

We were continually whipped, and received twenty lashes a day with a heavy thong

In this particular scene, Pangloss recalls all these horrors. Candide asks him if his recent sufferings have caused him to reconsider his adherence to Leibniz's theory that all is for the best in the best of all possible worlds:

"Well, my dear Pangloss," said Candide to him, "when You were hanged, dissected, whipped, and tugging at the oar, did you continue to think that everything in this world happens for the best?"

Remarkably, Pangloss does adhere to this philosophy, saying:

it would not become me to retract my sentiments; especially as Leibnitz could not be in the wrong: and that preestablished harmony is the finest thing in the world

Clearly, this is highly irrational, and Voltaire is pointing out how senseless human beings are to value a theory above the reality of lived experience. Today, we call this confirmation bias, and unfortunately, this tendency to "know what we know" in the face of overwhelming evidence to the contrary is still prevalent.