Why is the fact that the Americans are helping the Russians important?

In the late author Tom Clancy’s first novel, The Hunt for Red October, the assistance rendered to the Russians by the United States is important because avoiding a nuclear war is of paramount importance.
In Clancy’s story, the Americans are put in the awkward position of having to help Captain Marko Ramius in his efforts to defect to the United States with his nuclear-powered ballistic missile submarine and having to help the Soviet Union to “find” the highly-secret submarine—in order to avoid a panicked reaction against the United States. The Hunt for Red October was written during a period of intense and extraordinarily dangerous relations between the United States and the Soviet Union. The early-1980s were characterized by a large build-up in American military capabilities after a period of degradation. Modernization of American nuclear forces was a very prominent component of that build-up. In addition, both sides were adept at carrying out sophisticated naval operations intended to both collect intelligence on the other side while enabling ship and submarine crews to prepare for an actual war—a war that thankfully never materialized. Submarines and anti-submarine warfare were among the most secretive elements of the military competition between the two superpowers, and Clancy’s novel accurately captured the technological intricacies and political machinations that played out daily in the world’s oceans and seas.
The United States, under the circumstances depicted in The Hunt for Red October, helped Captain Ramius because the Navy and intelligence community desperately wanted to know as much as possible about Soviet submarine design and construction: the Red October represented the pinnacle of Soviet engineering. In addition to the intelligence that could be gleaned from examining the submarine firsthand, enormously valuable information could be conveyed by Captain Ramius after his arrival in the United States. As Admiral Greer points out at one point regarding the Soviet naval officer, "He's about the best sub driver they have, a real charger.” Captain Ramius could provide the West with invaluable insights into the thought processes of the Soviet Navy, as well as information on Soviet naval tactics. In short, the Americans had powerful incentives to help the defecting Soviet officers aboard the Red October.
The more important question regards the decision to help the Soviet government track its missing submarine. Here is where Cold War machinations and intelligence-gathering methodologies come into play. Until Ryan can convince his superiors, all the way up to the presidency, that Captain Ramius is a genuine defector, the United States must cooperate with the Soviet Union in locating the Red October so that it can be captured or destroyed before it is able to launch an attack on the United States. It is, in short, in both sides’ interests that the submarine be located and neutralized.  As Ryan notes in his meeting with the president,

The SS-N-20 has a range of six thousand miles. That means he could have hit any target in the Northern Hemisphere from the moment he left the dock. He's had six days to do that, but he has not fired. Moreover, if he had threatened to launch his birds, he would have to consider the possibility that the Soviets would enlist our assistance to locate and sink him.

Once the American government becomes convinced, however, courtesy of Ryan’s persuasiveness, that Captain Ramius is defecting and is not a rogue officer intent on starting a war, the United States still must be seen cooperating with the Soviet Union to enable the surreptitious capture of the submarine and its commanding officers without the Soviets knowing it has succeeded. This requires a deft touch; the Navy has to be perceived as helping the Soviet Union while simultaneously conspiring against it.
American assistance to the Soviet Union is significant because it is considered mutually advantageous and because it is part of a ruse to secure possession of the submarine without the Soviets knowing it.

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

Evaluate $\displaystyle \int x^2 \cos mx dx$ by using Integration by parts.
If we let $u = x^2$ and $dv = \cos mx dx$, then
$du = 2x dx$ and $\displaystyle v = \int \cos mx dx = \frac{1}{m} \sin mx$

So,

$
\begin{equation}
\begin{aligned}
\int x^2 \cos mx dx = uv - \int vdu &= \frac{x^2}{m} \sin (mx) - \int \left( \frac{1}{m} \sin mx \right) (2x dx)\\
\\
&= \frac{x^2}{m} \sin (mx) - \frac{2}{m} \int x \sin (mx) dx
\end{aligned}
\end{equation}
$


To evaluate $\displaystyle \int x \sin (mx) dx$, we must use integration by parts once more, so...
If we let $u_1 = x$ and $dv_1 = \sin (mx) dx$, then
$ du_1 = dx$ and $\displaystyle v_1 = \int \sin (mx) dx = \frac{1}{m} \left(-\cos (mx) \right)$

Thus,

$
\begin{equation}
\begin{aligned}
\int x \sin (mx) dx &= u_1 v_1 - \int v_1 du_1 = \frac{-x}{m} \cos (mx) - \int \frac{-\cos (mx) dx}{m}\\
\\
&= \frac{-x \cos (mx)}{m} + \frac{\sin(mx)}{m^2} + c
\end{aligned}
\end{equation}
$


Therefore,



$
\begin{equation}
\begin{aligned}
\int x^2 \cos mx dx &= \frac{x^2}{m} \sin (mx) - \frac{2}{m} \left[ \frac{-x \cos (mx)}{m} + \frac{\sin (mx)}{m^2} + c\right]\\
\\
&= \frac{x^2 \sin (mx)}{m} + \frac{2x \cos (mx)}{m^2} - \frac{2 \sin (mx)}{m^3} + c
\end{aligned}
\end{equation}
$

Single Variable Calculus, Chapter 7, 7.8, Section 7.8, Problem 92

Prove that $\displaystyle f''(x) = \lim_{h \to 0 } \frac{f(x+1)-2f(x) + f(x-h)}{h^2}$ suppose that $f''(x)$ is continuous.

By applying L'Hospital's Rule
$\displaystyle f''(x) = \lim_{h \to 0 } \frac{f(x+1)-2f(x) + f(x-h)}{h^2} = \lim_{h \to 0} \frac{f'(x+h)(1)+f'(x-h)(-1)}{2h}$

Again, we must apply L'Hospital's Rule since the limit is an indeterminate form

$
\begin{equation}
\begin{aligned}
\lim_{h \to 0} \frac{f'(x+h)(1)+f'(x-h)(-1)}{2h} &= \lim_{h \to 0} \frac{f''(x+h) - f''(x-h)(-1)}{2}\\
\\
&= \lim_{h \to 0} \frac{2f''(x+h)}{2}\\
\\
&= \lim_{h \to 0} f''(x+h)\\
\\
&= f''(x+0)\\
\\
&= f''(x)
\end{aligned}
\end{equation}
$

What is a theme of Touching Spirit Bear and textual evidence that explains the theme?

Touching Spirit Bear by Ben Mikaelsen is a coming-of-age story about a young man named Cole who undergoes a healing treatment on a deserted island as punishment for violently attacking another boy. Cole is taken under the wings of two men: 
Garvey—Cole’s parole officer who got him into the rehabilitation program called Circle Justice.
Edwin—He is one of the Native Americans in charge of Circle Justice.
It’s not surprise that isolation would become a central theme to the book since Cole is put on an island alone to work out his problems. The ideal goal for Cole is to reflect on his actions and reenter society as a changed person. Isolation is explored in several ways—mostly through Cole’s experiences.
 First, Cole feels social isolation from the community. For example, Cole believes that people in his community try to help him be a better person only because they want to get rid of him. Mikaelsen writes, “He hated their fake concern. They didn't really care what happened to him. They were gutless—he could see it in their eyes. They were afraid, glad to be rid of him. They pretended to help only because they didn't know what else to do.” Do you see how Cole is isolated from society? He does it to himself, but his community also pushes him away too.
Second, Cole experiences physical isolation. He is physically placed on an island alone. The separation from others really gets to him. Mikaelsen says, “Some nights he cried himself to sleep from loneliness. He couldn't help it. The silence became overpowering, and he longed to hear another human voice.” It’s not that Cole even wants to interact with others; he just wants to hear them to know that he isn’t alone. 
Isolation persists throughout the book until the end when Cole returns to society. From there, he must use his new skills to reenter his community.

While the "circle" theme (or, "karma") is a great and prominent theme in Mikaelsen's Touching Spirit Bear (as outlined above), there are also a myriad of other themes Mikaelsen weaves through his narrative that are worthy of exploration.
Healing is a major theme of the novel. The urge and necessity to "heal" spans across dimensions, both physical and spiritual. Some textual examples are:

Cole's initial assault on Peter. This attack is a necessary step towards healing, and is a physical and spiritual endurance on both characters thereafter.

When the Spirit Bear attacks Cole. This instance explores Cole's pain and path to healing that parallels his initial assault on Peter.

Edwin and Gavey's atonement for their past sins. This highlights a prominent struggle towards peace that promotes healing.

Cole's Mother, and her broken heart. In "letting go" of her troubled marriage, Cole's Mother embarks on a very tenuous path to healing.
Along with healing, comes forgiveness. This is another theme Mikaelsen explores, and almost works hand-in-hand with "healing". Each of the examples above insight pain, healing, and forgiveness as the ultimate goal. A vital asset in healing is forgiveness, and each character is on their own path towards enlightenment.
In choosing a theme above (or creating your own) I'd advise you to consider which theme speaks to you, and investigate your own reasoning into why the author uses this theme. This will help you create a strong thesis statement and argument.

There are several wonderful themes in Ben Mikaelsen's novel. Touching Spirit Bear. 
One dominate symbol and theme in the novel is the circle and traveling in circles. In literature, circles can mean wholeness or healing.  Cole Matthew's life moves in a full circle as he is sent to the Alaskan island as a 15-year old juvenile delinquent who assaulted a boy for telling on him and later returning to the island and living with Peter Driscal, the boy he assaulted.
Some additional textual evidence of circles as a theme are:
Cole keeps getting himself in trouble and his parents and their high-priced lawyers usually rescue him.
Cole burns down the hut and later rebuilds it.
Cole continuously tries to swim off the island, running from his problems, only to return to the island to complete his healing.
Through flashbacks, Mikaelsen shows events that led Cole to being on the island and how his parents' actions contributed.  Later during physical therapy he reconciles with his mother.
Cole blames everyone for his anger and later learns to forgive.
Peter beats up on Cole in anger and later heals
Cole and Peter carve a circle symbol as the last symbol on the totem pole symbolizing their healing.

Edna Pontellier could not have told why, wishing to go to the beach with Robert, she should in the first place have declined, and in the second place have followed in obedience to one of the two contradictory impulses which impelled her. A certain light was beginning to dawn dimly within her—the light which, showing the way, forbids it. At that early period it served but to bewilder her. It moved her to dreams, to thoughtfulness, to the shadowy anguish which had overcome her the midnight when she had abandoned herself to tears. In short, Mrs. Pontellier was beginning to realize her position in the universe as a human being, and to recognize her relations as an individual to the world within and about her.This may seem like a ponderous weight of wisdom to descend upon the soul of a young woman of twenty-eight-- perhaps more wisdom than the Holy Ghost is usually pleased to vouchsafe to any woman. But the beginning of things, of a world especially, is necessarily vague, tangled, chaotic, and exceedingly disturbing. How few of us ever emerge from such beginning!How many souls perish in its tumult! The voice of the sea is seductive; never ceasing, whispering, clamoring, murmuring, inviting the soul to wander for a spell in abysses of solitude; to lose itself in mazes of inward contemplation. The voice of the sea speaks to the soul. The touch of the sea is sensuous, enfolding the body in its soft, close embrace. 1. The “it” in line 9 refers to: a) “ the two contradictory impluses” b)“a certain light...beginning to dawn” c) “the way” d) ”the shadowy anguish” 2. In line 23,”vouchsafe” can be best replaced by: a) bestow b) inform c) refuse d) deign 3. The final paragraph of the passage(lines 34-36) foreshadow a) Edna’s affair with Arobin b) Robert’s shipwreck on his way to Mexico c) the sucide at the end of the novel d) doctor Mandalet’s disapperance 4. Which of the following lines best describes Edna’s journey from this point to the end of the novel? a) “the voice of the sea speaks to the soul.” b)”this may seem like a ponderous weight of wisdom” c)”it moved her to dreams, to thoughtfullness, to shadowy anguish...” d)”of a world especially,is necessarily vague, tangled, chaotic and exceedingly disturbing.” 5. Line 30 contains an example of which literacy device? a) polysyndeton b)asyndeton c)anthropomorphism D) metonymy 6.the final two paragraphs depict a sea that is: a) anthropomorphised b) didactic c) personified d) dynamic 7.which of the following best describes edna’s characterization in the passage: 1. She is firm in her resolve to do as she pleases. 2. She is confused and lost regarding who she is and what she wants. 3. She is young and a bit naive. a) 2 only b) 1 and 3 c) 2 and 3 d) 1,2, and 3 8. The shift in perspective in the sentence beginning on line 26 and ending on line 27 does all of the following except a) give the reader a direct connection to the emotions Edna is feeling. b) imply that the situation is not uncommon c) give the narrator the opportunity to insert her commentary and experiences d) describe a situation for Edna to be a part of something greater than she. 9. The ”anguish in line 12,most likely refers to a) Edna’s distress over the creole culture and her lack of understanding with it. b)the heartbreak Edna felt when she listened to Madame Ratignolle reveal the intimate details of her delivery, knowing she would never be a “mother-women” c) the torment of knowing that is on the beach with Robert and the moment,though beautiful to her, would have repercussions. d) the sadness Edna felt when she realized, after being scolded by Leonce and checking on Raoul, that she is trapped. 10. The tone of the passage the best be described as a) sardonic b)reverent c) didactic d)solemn What is a literacy foil? Which characters serve as foils in The Awakening and how does their relationship illuminate the text? Protagonist Edna Pontellier is said to possess “that outward existence which conforms, the inward life that questions.” Identify a character who outwardly conforms while questioning inwardly. Analyze how this tension between outward conformity and inward questioning contributes to the meaning of the work. Avoid mere plot summary.

You ask what a literary foil is, which characters serve as foils in the text, and what their relationships with Edna might illuminate.  To begin, a foil is a character who possesses traits that contrast the traits of another character, often the protagonist, in order to illuminate the qualities possessed by that other character.  We might consider both Adele Ratignolle as well as Mademoiselle Reisz foils to Edna, each accomplishing something different. 
The contrast with Adele shows us how short Edna falls when it comes to doing her duty to her husband, Leonce, and behaving in accordance with her Creole community's mores.  Adele is quite feminine, a "sensuous Madonna," and a "mother-woman," who spends her time ministering to her children and performing her wifely duties as though they were a divine calling.  She keeps up her music to beautify her home and to bring joy to her husband.  She would do nothing that might embarrass him or subject him to ridicule by his peers.  
Mademoiselle Reisz, on the other hand, shows us how very far short Edna falls when it comes to becoming an artist and giving up the need to be accepted by society.  Reisz is invited to parties in order to be the entertainment, not because she is accepted as an equal.  However, Edna is unwilling to give up ties to society completely, and she still craves acceptance and praise, especially from Adele.  Reisz says Edna must have strong wings to soar above the plain of tradition, but Edna is not strong enough to do so alone.  
Both of these characters illuminate Edna's inability to choose a role.  Initially, she chooses to be a Creole wife and mother, but she finds that unfulfilling.  Then, she wishes to be an artist. She dabbles without any real, serious talent, but she finds that unfulfilling as well.  She must be willing to give something up in order to have each one, but neither option is, in the end, sufficient to satisfy her.  
To address your next open-ended question, the tension between Edna's outward conformity and inward questioning illuminates the theme that the individual is almost always at odds with society in some way.  Further, the tension conveys the idea that the price of total freedom from society's rules is alienation from that society.  Edna cannot break the rules of society and still be accepted by that society.  No person can.

Is the Commander sterile in The Handmaid's Tale?

The short answer is yes, probably, the Commander is sterile. When Offred goes for her routine appointment at the gynecologist, he says as much to her and offers to get her pregnant himself. She is horrified by the doctor's suggestion and is sure that he could be an Eye (a spy for the government) or that he might report her as disloyal and disobedient if she declines his offer—but the fact is that Offred has had a child before, and so we know it is most likely possible for her to become pregnant again. However, the Commander has never fathered a child, and, because of his age, it is extremely likely that he cannot do so. The doctor implies that this is the case himself.

The reader is never explicitly told whether or not the Commander is sterile, but it can be inferred that he is. The Commander is an older officer of the “Sons of Jacob,” so because he is in a respectable position in this dystopian society, it is forbidden to even insinuate that he is sterile. Actually, it is forbidden to insinuate that any man in power is sterile, even though it is a fact that most of the civilization has become sterile from toxicity in the environment. Sterility is publicly blamed only on the women because of the patriarchal nature of Gilead.
The handmaids, then, are a group of women that are forced to reproduce by these men in power because they have been proven to have healthy reproductive systems, which is difficult to find. Childbirth has become so rare that any single healthy child is revered and celebrated while the handmaids continue to live a life of reproductive slavery. In this society, however, even being in this position is a “blessing” because there are many other worse positions to be in, such as cleaning up toxic waste until eventual death.
Offred, having not produced a child for the Commander yet, is in grave danger of being sent to the toxic wastelands because the handmaids have a “deadline” that they must produce a child within. The reader can assume that the Commander’s wife, Serena Joy, is aware that her husband is most likely sterile. It is difficult for her to watch the monthly “ritual” between the Commander and Offred (essentially a ritual of rape), so she arranges for Offred to sleep with her husband’s chauffeur, Nick, in secret. This is a risky move that could get all three of them in trouble, but both Nick and Offred are afraid of what Serena Joy may do should they not follow her instructions so they oblige.

While we never know for sure, the text strongly suggests that the Commander is sterile. The reason handmaids exist at all is that pollution has rendered much of the population sterile. The Commander is an older man who has never fathered a child. Given the high levels of infertility in the culture, the Commander's age, and his lack of other children, the odds are very high that he can't procreate.
However, in this dystopia, a fundamentalist Christian world, a man can never be considered sterile. The myth that protects the men is that it is always the woman's fault if a pregnancy doesn't occur. If a handmaid doesn't eventually get pregnant, she is blamed, even if every likelihood is that the problem is with the man.
Serena and Offred both know this. Serena, a pragmatist, understands that her husband is most likely sterile. (Her thoughts on the subject help convince us that he is sterile.) Therefore, she arranges for Offred to have sex with the younger, very possibly fertile Nick. Although this is a risky move, Offred agrees to it, knowing that if she doesn't get pregnant, she will be sent to die cleaning up toxic waste.

In what ways are the current problems facing the United States similar to and/or different from the problems identified during the founding ?

The founders of the American constitution were challenged with an immensely bold undertaking: to address the problems faced by the colonies but do so in such a way that their solutions would pave the path for "a more perfect union" for centuries to come. Therefore they had to build a rigid but flexible structure, able to handle both the crises of the day and those of the future. In many ways they created a framework that has done just that—in other ways, at best, there were obstacles no one could have foreseen.
The largest of the discrepancies have stemmed from three main things: technology, political norms, and geography. Technology may be the largest unforeseeable factor: today our communication, governance, social glue, journalism, news reporting, and, therefore, democracy are all fundamentally changed by technology. New questions about the second amendment and gun rights are raised by entirely new forms of weapons in civilian hands. The internet has brought us self-publishing, which has shaken trust in established central news outlets, and instantaneous transmission, whereas communication in late-18th century America was done via horseback or stagecoach. Drones, missiles, and AI are changing our warfare and national security. The existence of smart phones and big data affect our privacy and central intelligence. When drafting both the protections of individuals under the Bill of Rights and the powers of the three branches of government, we have seen how simple wording in the Constitution can have profound consequences. Take, by example, how the wording "right to assemble" can be interpreted in an online context or how "a well regulated Militia" can be understood in the context of assault weapons, bombs, and gases designed to kill crowds. Granted, the Bill of Rights followed the founding of America in 1791, but the examples still stand as disparities in problems faced across time.
The second difference, political norms, is one that has changed in part because of the US constitution. The founders were responding to the central power of a king, whereas today we have presidents, prime ministers, and congresses whose powers are more distributed than monarchs of old. The difference, more broadly, is due to a general shift in regional powers from colonialism to tighter nation states and the constraining realities of nuclear power, economic warfare, cyber warfare, and global alliances such as the UN, EU, and NATO that shape global hegemonies.
The third major difference is a simple matter of geography. Some argue it was easier for Americans to fight for independence as colonial entities in America because they were separated from their oppressors by an ocean and had at their disposal a wealth of resources and land (after they had committed terrible genocide against the many indigenous populations existing before them). Any separatists and secessionists of today's America will find it much harder, as the South discovered in the mid-19th century.
I chose to end with the similarities between the problems the founders faced and those that exist now because I find them far more compelling. Of the similarities of great significance are the troubles imposed by a tyranny of the majority, the danger of factions to democracy, the power of money to corrupt, the threats misinformation and alienation of news sources bring to the people's right to free press and sharing of information, the damage to national security caused by degradation of trust in intelligence agencies, and the conflicts of interest held by a governing entity having lasting consequences. Many of the beliefs held by the founding fathers were to thwart these various threats against democracy and to create institutions that could withstand them. By drafting checks and balances between the executive, judicial, and legislative branches of government and by preserving freedom of speech and the press as a fourth check on the government, the founders hoped that the nation would continue to build on its good assets while fortifying against the corruption that has so often toppled former regimes. They also hoped to eventually purge the country's inherited habits of oppression, as was the case with institutionalized slavery (a slow process). The current dilemmas we face today that we share with the colonies are more important than ever.

What are some quotations from A Separate Peace that show peace and conflict in the scene where Gene visits Finny in the infirmary?

In chapter 5, the closest quotes that show peace and conflict during Gene's visit to Finny are below:

"I don't know; I must have just lost my balance. It must have been that. I did have this idea, this feeling that when you were standing there beside me, y—I don't know. I had a kind of feeling. But you can't say anything for sure from just feelings. And this feeling doesn't make any sense. It was a crazy idea. I must have been delirious. So I just have to forget it. I just fell . . . that's all . . . I'm sorry about that feeling I had."
He was never going to accuse me. It was only a feeling he had, and at this moment, he must have been formulating a new commandment in his personal decalogue: never accuse a friend of a crime if you only have a feeling he did it. And I thought we were competitors. It was so ludicrous I wanted to cry.

In the first quote, Finny hints that he had suspicions about Gene's involvement in his accident. However, since he only has his feelings to go by, he refuses to make accusations. 
In the second quote, Gene comes to the grim realization that he's been mistaken about Finny, and he becomes ashamed of the way he's treated him.The conflict first originated in Gene's mind. However, the tension between the two is clear in the two quotes above.
Gene visits Finny again later in the book, and we find them reconciled in chapter 12. Here, your best bet for quotes about peace and conflict are:

. . . I've gotten awfully mad sometimes and almost forgotten what I was doing. I think I believe you . . . Something just seized you. It wasn't anything you really felt against me, it wasn't some kind of hate you've felt all along. It wasn't anything personal.
. . . Tell me how to show you. It was just some ignorance inside me,some crazy thing inside me, something blind, that's all it was.
. . . I believe you. It's okay because I understand and I believe you. You've already shown me and I believe you.

In Americanah by Chimamanda Ngozi Adichie, who are Curt and Blaine?

Curt and Blaine are both past lovers of the main character Ifemelu.Curt becomes Ifemelu’s boyfriend for a couple years when Ifemelu is living in the United States. In her blogs, Ifemelu refers to Curt as the “Hot White Ex.” Curt and Ifemelu meet through Curt’s cousin Kimberly. Kimberly hires Ifemelu to be a babysitter in her home. While Curt is compassionate and kind to Ifemelu, he is also a Caucasian male who comes from a wealthy family and he doesn’t completely understand the racism and culture shock that Ifemelu regularly endures. Blaine is an African American professor at Yale University who later becomes Ifemelu’s boyfriend after she has been in the United States for several years. Ifemelu was immediately able to conclude that Blaine was African American, not African. Blaine is highly intelligent and intellectual, but he can also come across as snobbish and close-minded. For these reasons, Ifemelu becomes dissatisfied with the relationship.

In Chimamanda Ngozi Adichie's Americanah, a deeply exploratory and engaging novel on race and identity Curt and Blaine are minor characters. The reader is introduced to Curt who becomes Ifemelu's (main character) first boyfriend since she came to America for work and study. Ifemelu meets Curt while babysitting for his cousin Kimberly. A rich, handsome white man, Curt is enchanted and immediately drawn to Ifemelu and they soon start dating. Curt is a happy go lucky, optimistic and spontaneous man and everything always seems to fall into place for him. Despite their relationship appearing to be happy and solid on the surface, they are unable to have any serious conversations pertaining to race. This culminates to the disintegration of their relationship when Ifemelu cheats on Curt. Following their breakup, Ifemelu starts a blog called Raceteenth or Various Observations About American Blacks (Those Formerly Known as Negroes) by a Non-American Black.
Though not chronologically her first boyfriend, the reader is first introduced to Blaine before Curt. Ifemelu meets Blaine on a train and she is immediately drawn to his sharp wit and charm. An African-American professor at Yale and a fellow blogger, their shared interests in race and it's role in America heralds the beginning of a romance. However over time it becomes clear that Ifemelu doesn't quite fit in with Blaine, his friends, their intellectual discussions and political correctness. This puts a strain on their relationship and eventually Ifemelu decides to move back home to Nigeria.

Curt and Blaine are American men with whom the main character, Ifemelu, has significant relationships in Chimamanda Ngozi Adichie’s novel Americanah. Curt is the well-to-do cousin of Ifemelu’s boss, Kimberly. In Part II of Americanah, Ifemelu and Curt start dating, and he helps her find a job. At the beginning of Part IV, Ifemelu has just broken up with him. Although Curt—who is white—loved Ifemelu, he never really understood her experiences as a Nigerian woman dealing with racism in the US, nor did he realize that he could sometimes be subtly racist himself. After their breakup, Ifemelu starts a blog called Raceteenth or Various Observations About American Blacks (Those Formerly Known as Negroes) by a Non-American Black. When she blogs about Curt, she refers to him as “The Hot White Ex.”
Blaine, who is African American, is a fellow blogger and teaches at Yale. He and Ifemelu met years ago on a train and reconnect at one of the lectures Ifemelu is invited to give after the unexpected success of Raceteenth. Ifemelu moves to New Haven to be with him. While Blaine is supportive of Ifemelu’s writing, he sometimes disagrees with her on political issues. After Ifemelu doesn’t come to a demonstration Blaine organizes, he refuses to speak to her, and Ifemelu goes to stay with her Aunty Uju until Blaine arrives to make amends. Reunited, the two of them look for an apartment in Princeton, where Ifemelu has received a fellowship at the university. She and Blaine grow closer when she decides to join him in supporting Barack Obama as a presidential candidate, but before long Ifemelu grows unhappy and decides to move back to Nigeria.

What is the writer telling us about human nature and the world?

Yukio Mishima's retelling of Takeyama's suicide gives the reader a glimpse into the lengths that people will go to for the sake of preserving traditional values. In Mishima's eyes, Japan's growing materialism was a cause for concern. It seemed like Japan was focusing more on economic success instead of maintaining the values of the past. Takeyama's desire for transcendence outweighs any temporal reward he would gain if he complied with Japan's interest for profit during the 1960s.
Takeyama's decision to commit suicide calls back to a feudal tradition in which the losing hero would kill himself as an act of bravery. Once all other options are exhausted and he is put in a predicament where he can't win, Takeyama chooses to hold on to his honor. While most readers may be put off by Mishima's inclusion of the preparation prior to the suicide, it shows a level of admiration for a culture that he grew up in.

Single Variable Calculus, Chapter 3, 3.5, Section 3.5, Problem 36

Determine the derivative of the function $\displaystyle f(t) = \sqrt{\frac{t}{t^2+4}}$


$
\begin{equation}
\begin{aligned}
f'(t) &= \frac{d}{dt} \left(\frac{t}{t^2+4} \right)^{\frac{1}{2}}\\
\\
f'(t) &= \frac{1}{2} \left(\frac{t}{t^2+4} \right)^{\frac{-1}{2}} \frac{d}{dt} \left(\frac{t}{t^2+4} \right)\\
\\
f'(t) &= \frac{1}{2} \left(\frac{t}{t^2+4} \right)^{\frac{-1}{2}} \left[ \frac{(t^2+4)\frac{d}{dt} (t) - (t) \frac{d}{dt} (t^2+4)}{(t^2+4)^2}\right]\\
\\
f'(t) &= \frac{1}{2} \left(\frac{t}{t^2+4} \right)^{\frac{-1}{2}} \left[ \frac{(t^2+4)(1) - (t)(2t)}{(t^2+4)^2} \right]\\
\\
f'(t) &= \frac{1}{2} \left(\frac{t}{t^2+4} \right)^{\frac{-1}{2}} \left[ \frac{t^2 + 4 - 2t^2}{(t^2+4)^2} \right]\\
\\
f'(t) &= \frac{1}{2} \left(\frac{t}{t^2+4} \right)^{\frac{-1}{2}} \left[ \frac{-t^2+4}{(t^2+4)^2} \right]\\
\\
f'(t) &= \frac{1}{2} \frac{(t)^{\frac{-1}{2}}(4-t^2)}{(t^2+4)^{\frac{-1}{2}}(t^2+4)^2}\\
\\
f'(t) &= \frac{4-t^2}{2(t)^{\frac{1}{2}}(t^2+4)^{\frac{3}{2}}}
\end{aligned}
\end{equation}
$

What is Edward Bloom's vision of success and greatness from Big Fish by Daniel Wallace?

Edward Bloom's vision of greatness takes one form when he is younger and changes over time into another vision when he matures and becomes a father. According to William, Edward's son, Edward the child and young man, sees successful accomplishment of many different goals and challenges as a vision of greatness, but later in life, he wants to be remembered as a great man who did great things.
Daniel Wallace, the author of Big Fish, uses many mythological allusions to emphasize Edward's greatness when he encounters challenges as a child and a young man. Hyperbole works with these allusions to emphasize Edward's larger-than-life ability and personality; for example, when Edward is bedridden, he reads to pass the time, and over several months, he reads a thousand books. The weather changes dramatically in response to Edward's birth and milestones. Later in life, Edward somehow avoids being attacked by a particularly aggressive dog when he tries to walk through a town, suggesting he has a unique power over animals. Edward's powers of observation and persuasion are prodigious, powers that better suit a young god , rather than a mere mortal. In his own eyes, Edward sees himself as great thanks to his ability to take on difficult tasks successfully.
Of course, the reader learns about these stories through William, Edward's son, and William heard them all from Edward, his father. Through William's telling, the reader can gather that Edward wants to be remembered as a great man of many successes. The emotional depth and the significance of Edward's desire, later in life, to be remembered well is poignant when it is understood within the context of the family problems that afflict the Blooms. Edward turns out to be a cheating husband, which calls into question his other promises and claims, and by the end of the novel, Edward's vision of success is tempered. If, after all the hurt and disappointment, he can be remembered by his son as a great man, perhaps that will be enough.

When does Atticus show courage in the book To Kill a Mockingbird?

After the death of Mrs. Dubose and Atticus's disclosure that she died free of any drugs by withdrawing from morphine, Atticus defines courage for his son: 

It's when you know you're licked before you begin but you begin anyway and you see it through no matter what. You rarely win, but sometimes you do (Ch.11).

This definition serves Atticus when he is asked by Judge Taylor to be the defense attorney for Tom Robinson, a black man who has been accused of the crime of rape. Before the trial begins, the town of Maycomb is filled with tense, hostile, and excited public feeling. On the day of the trial, there is a virtual parade of people from both the county and the town who cram the courtroom. Certainly, Atticus is aware that Tom Robinson has only the truth on his side. He is a black man accused of raping a white woman, Jim Crow laws are in existence, and the jury is made of twelve white men from the area. (True to his definition, Atticus "begins anyway.")
Even in spite of the fact that there is no medical evidence proving that any rape occurred, that Bob Ewell is a known reprobate, and that there are contradictions in the testimonies of the Ewells, Atticus does not count out any evidence in support of the defense. He very wisely disproves that Tom could have choked and struck Mayella: she testifies that she was injured on both sides of her neck and struck on the right side of her face—all indications that a left-handed man inflicted her injuries. Tom Robinson has a useless left arm, which was injured years ago.
In other instances, Atticus has the courage to follow his code of ethics, morals, and child-rearing. He holds to his convictions by not engaging in gossip about Boo Radley and by insisting that the children "leave that man alone." On the night of the pageant when his children are attacked, Atticus bravely accepts that Jem may have killed Bob Ewell. He refuses to lie to protect Jem from the consequences. (Later, Sheriff Tate informs Atticus that his son was not the one who killed Ewell; Boo Radley saved both Scout and Jem.)

In Gulliver's Travels by Jonathan Swift, what makes Gulliver leave his house?

Gulliver leaves his childhood home in Nottinghamshire in order to acquire an education.  He attends a school in Cambridge called Emanuel College from age fourteen to seventeen.  After this, as the third of five sons, he is sent to be an apprentice to a doctor in London.  He studies as much as possible, but he eventually leaves this home in order to continue his formal education in medicine at Leyden.  When he returns to London, he leaves home again, at the suggestion of the man he had formerly apprenticed, in order to be the doctor on board the Swallow, a ship on which Gulliver travels for over three years. 
Later, after Gulliver marries and sees his medical practice fail, he leaves home to go to sea again and travels for six years more.  At this time, he determines to remain at home, but when he cannot make another business work, he goes, again, to sea, and thus begins his journey to Lilliput.

Based on the myth "The Wrath of Achilles," what are four reasons why the Greeks won the war against the Trojans?

The student's question does not specify any particular text, although one could logically presume that Homer's The Iliad provides the basis of the inquiry. The classic text tells the story of the ten-year war between a coalition of Greek kingdoms and the Kingdom of Troy, lead by King Priam. Priam's son, Paris, of course, takes Helen, the beautiful wife of King Menalaus, for himself. The Greeks retaliate by attacking and laying siege to Troy. During the course of the ten-year conflict, many well-known figures from Greek mythology appear and play prominent roles, including mortals and immortals alike. The Iliad, alone, however, may be insufficient to provide a full response on the Greek victory over Troy. Other sources of Greek mythology must also be consulted.
The question asks for four reasons the Greeks prevailed over Troy. The most direct answer as to why, or how the Greeks prevailed is the successful use of deception involving a giant wooden horse. As students of the Trojan war know, the Greeks, despite their long siege of Troy, had been unable to penetrate the king's fortress walls. The giant wooden horse was the brainchild of Odysseus (the hero of Homer's other well-known classic The Odyssey) and was constructed with the aid of Athena and Epeius, a respected carpenter. It was hollow inside, allowing for the concealment of a number of Greek soldiers. The horse was inscribed to the Trojans as a monument to Athena and is presented as a gift. Despite the misgivings of some Trojans, the wooden horse was wheeled inside the fortress walls. The Greek soldiers sneak out of the horse in the darkness of night and proceed to slaughter and/or rape all those within the fortress walls.
The "Trojan Horse," in effect, is the main reason for the Greek victory. It does not, however, answer the student's question. That answer, perhaps, can best be formulated by drawing on the recommendations of Helenus, brother of Paris and a seer who Odysseus and other Greeks interrogated in an effort at attaining valuable intelligence on the Trojan enemy. The lessons taken away from this interrogation are that, in order to defeat Troy, the Greeks must meet several conditions: they must enlist the son of Achilles, Neoptolemus, in their fight; they must retrieve and transport to Troy the bones of Pelops, whose grandson, Agamemnon, was among the most powerful of the Greek leaders; they need to bring into the battle Philoctetes, a master archer who would use the the weapons of Hercules in the battle against the Trojans and who had been abandoned by the rest of the Greeks on the island of Lemnos; and the Greeks would have to capture the Palladium, a wooden statue crafted by Athena in the image of Pallus, the god of war. 
The four tasks prophesied by Helenus were executed by Odysseus and Diomedes. It was the wooden horse, however, that sealed Troy's fate while revolting all those upset by the vengeful slaughter carried out by the Greek soldiers who had been hidden in the hollow structure.
https://ryanfb.github.io/loebolus-data/L170N.pdf

What ghost has the best effect on Scrooge?

No single ghost has a "best" effect on Scrooge.  In fact, the messages of all of the spirits, including Marley's ghost, are essential in helping Scrooge become a better person.  Looking at what Scrooge gains from each of them will help illuminate their joint effect.Marley's ghost not only shocks Scrooge, he also gives him a direct warning regarding his chains and the connection to the chains that Scrooge is forming in life.  By starting with Marley's ghost, Scrooge is given a touchstone and a level of familiarity with the ensuing events in his journey.  While the spirits do wish to shock him, their entire goal is to help him change.  As terrible as his afterlife is, Marley's  afterlife is significantly better than the afterlife that awaits Scrooge if he does not change.The Ghost of Christmas Past is essential to reminding Scrooge of where he came from and of the kindness that Scrooge experienced earlier in his life.  Through a glimpse of Scrooge's childhood at the boarding school, the spirit reminds Scrooge of what it is like to be lonely and abandoned. However, the spirit also shows Scrooge what it is like to feel love through Scrooge's sister.  This scene also reminds Scrooge to love Fred, the only family he has left.  Through Fezziwig, the spirit shows Scrooge how a boss should act.  Through Scrooge's breakup with Belle and the view into her life on the eve of Marley's death, the spirit shows Scrooge what he could have had.The Ghost of Christmas Present shows Scrooge a number of important scenes that help him to change.  By showing Scrooge Cratchit's meager home and Fred's dinner party, the spirit shows Scrooge the kindness, love, and forgiveness of the holiday season.  Though Scrooge has mistreated all of them, they all toast him and wish him the best.  Further, the spirit also introduces Scrooge to Ignorance and Want, the manifestation of humankind's worst traits.  Finally, the spirit also throws Scrooge's own words in his face to show him how calloused Scrooge has become.Finally, the Ghost of Christmas Yet to Come reveals the future that lies ahead if Scrooge fails to change.  Rather than hint at Scrooge's afterlife, as Marley did, the spirit shows Scrooge the world without him.  Tiny Tim dies, and Scrooge dies cold and alone; his possessions are stripped from him and pawned off.  The only good that comes from his death is the relief of those who owe him money.Each spirit is essential to Scrooge's movement from greedy to giving.  Without the combination of past, present, and future, Scrooge would not have been able to change.  This reflects Dickens's own belief in the importance of experience.  Experience is important;  it comprises who we are and who we will become.

How does Jack London use the literary element of flashbacks to impact his audience in "A Piece of Steak"?

Jack London uses flashbacks in "A Piece of Steak" to help the reader see exactly where Tom King had once been in his life. The flashbacks simply help the reader compare and contrast Tom King's former status with his current one.
As Tom King is making his way to his next fight, on foot, he remembers what it was like when he was considered the best in the world.

Big money--sharp, glorious fights--periods of rest and loafing in between--a following of eager flatterers, the slaps on the back, the shakes of the hand, the toffs glad to buy him a drink for the privilege of five minutes' talk--and the glory of it, the yelling houses, the whirlwind finish, the referee's "King wins!" and his name in the sporting columns next day.

This lets the audience know that Tom King was, at one point, used to glory and fame and all of the privileges that came along with it. The flashback shows Tom King once had people fawning over him, buying him food, and practically throwing money at him. When compared to what Tom King is going through currently in the story, it's a sharp contrast. 

The secretary of the Gayety Club had advanced him three pounds--the loser's end of the purse--and beyond that had refused to go. Now and again he had managed to borrow a few shillings from old pals, who would have lent more only that it was a drought year and they were hard put themselves.

This quote shows Tom King's current status in life: penniless and borrowing money from any source he could. Tom King fell from grace, and he had to learn how to reconcile that fact within himself. 

How, in Animal Farm, does Napoleon's use of of obedience tactics help the farm?

In a general sense, Napoleon's tactics lead to greater productivity on the farm. His insistence that the animals follow instructions and remain loyal guarantees that the animals remain committed and unquestioning. In such a system, more focused and productive labor ensures greater returns and bigger profits. Furthermore, the tactic guarantees a servile attitude and minimizes the risk of recalcitrance and rebellion.
Napoleon ensures that the animals remain obedient not only through propaganda, misinformation, and deceit, but also brutally enforces control by slaughtering those who dare rebel against him. The best example of this occurs in chapter seven, when the three hens who resisted his instruction to sacrifice their eggs are executed by his dogs. Animals who supposedly plotted against him also suffer the same fate. In this manner, Napoleon establishes a merciless tyranny. He becomes supreme leader and his authority cannot not be questioned.
The success of this strategy is proven by the successful completion of the windmill after it had been destroyed, the lack of wastage on the farm, and the general air of commitment, although enforced, that exists. This is best encapsulated by Boxer's two maxims: "I will work harder" and "Napoleon is always right." These statements reflect the overall sentiment on the farm, with the exclusion, to a certain extent, of Benjamin. Although he is quite cynical and recalcitrant, Benjamin does what is asked of him.
Although Napoleon's strategy leads to the successful running of the farm, it is, sadly and ironically, only the pigs and Napoleon's dogs who truly benefit. They live lives of luxury whilst the other animals are always tired, hungry, cold, and miserable.
The greatest irony lies in the fact that the gullible general animal populace believe they have achieved utopia when, in fact, their dream has resulted in a dystopian reality that is worse than the one they experienced under Jones's rule.

How is Pip rescued from Orlick?

In chapter 53 of Charles Dickens's Great Expectations (1861), Philip Pirrip (nickname: Pip) is lured by an anonymous letter to a sluice house. Once he arrives, he is ambushed by Dolge Orlick. A noose is put around Pip's neck, and he is tied to a ladder.
Orlick was first introduced in chapter 15 and resents Pip for a variety of reasons. At this time, he reveals some of them to Pip. He believes Pip is the reason that Biddy did not fall in love with him, and he hates that Pip was preferred over him as an apprentice. On this occasion, Orlick also confesses to the attack on Mrs. Joe.
Just as Orlick grabs a hammer to kill Pip, the latter is rescued by Herbert, Startop and Trabb's lad. Herbert later reveals that they managed to arrive just in time because he had found the anonymous letter at Pip's apartment and—worried for his safety—had decided to chase after him. The three men attack Orlick (who escapes) and then take Pip away to the town.

In the chapter titled "Signlight and Moonlight" there is this paragraph: “I want some gum-drops,” she said, humorously apologetic; “you can’t guess what for this time. It’s just that I want to bite my finger-nails, and I will if I don’t get some gum-drops.” She sighed, and resumed as they stepped into the empty elevator: “I’ve been biting ‘em all day. A bit nervous, you see. Excuse the pun." I am not a native English speaker and I do not understand the pun in here. In Chapter II (Symposium) what's the meaning of "unpleasantly undergraduate" in the phrase "the best of the men not unpleasantly undergraduate"? Further on when Maury speaks of himself he says "I read Smith, who laughed at charity and insisted that the sneer was the highest form of self-expression–but Smith himself replaced charity as an obscurer of the light." What exactly does the author mean by obscurer of the light?

In terms of the pun in the first quotation, I cannot be entirely certain without seeing the full context, but I would interpret this to be a joke on the part of the author—that is, there is not actually a pun at all. A phrase like "Excuse the pun" might be dropped into conversation by a nervous person almost as a figure of speech, without this person having actually made a pun. The joke is therefore that, whatever pun the speaker is thinking of, it was not evident to the listener. It is entirely possible that the pun could be on "gum-drops" and nail-biting—with "gum" here referring both to the gums in the mouth and the gum that the drops themselves are made of—but this is extremely tenuous and not truly a pun.
"Unpleasantly undergraduate" is an interesting one; "undergraduate" is here being used as an adjective, but it is typically used as a noun. If someone is "unpleasantly undergraduate" that means that they are behaving unpleasantly like an undergraduate (a student who has not yet graduated from university). As a result, an "unpleasantly undergraduate" person is immature in the manner of someone aged between 18 and 21 and probably has some mannerisms particular to a college student (pretentiousness, an inflated sense of self, and so on).
In the third example, "obscurer of the light" would literally mean someone who gets in the way of the light. In this case, it is probably being used metaphorically: an "obscurer of the light" is someone who makes it difficult to see or understand things clearly, or, alternatively, it could refer to someone who makes it difficult for goodness to shine through.