How are the ways people view gender roles in Maycomb different from the way we view gender roles today? How are they similar?

Gender roles in Maycomb are, for the most part, radically different from how they are today. To Kill a Mockingbird is set in the Deep South during the 1930s, when the respective roles of men and women were clearly fixed, and almost immovable. Generally speaking, women were expected to stay at home and raise the children, while the men went out to work. To be even more specific, African-American women were expected to help raise white women's children, or at least those who could afford to hire help. Respectable white ladies were put on a pedestal in Southern society. They were expected to be gracious, demure, and dignified at all times. This is the ideal of womanhood that Aunt Alexandra tries so hard to instill in Scout.
The elevated notion of Southern womanhood also extends to those from less privileged backgrounds. Even though Mayella Ewell is widely despised throughout the town as a member of a notorious "white trash" family, she still has the privilege of being a white woman, and as such her honor must be protected against the depredations of an alleged black sexual predator. Mayella gives her evidence on the witness stand in court, but women are excluded from serving on the jury, as their delicate sensibilities are thought too fragile to withstand the sordid details of a rape case.
There aren't too many similarities between gender roles then and now. But Scout very much points towards a more modern, more enlightened approach to women's roles. Scout is an unashamed tomboy, and her rough and tough behavior is far removed from prevailing standards of female conduct. She mixes with Jem and the other boys on a more or less equal basis and always gives as good as she gets. Aunt Alexandra wants to turn her into a fine, upstanding Southern lady, but it's pretty much a losing battle. Although gender roles remain largely fixed throughout the book, in the character of Scout we see the possibility of their transcendence. Scout represents a link between gender roles as they operated in the 1930s and how they operate today.

Calculus of a Single Variable, Chapter 9, 9.2, Section 9.2, Problem 11

sum_(n=1)^oo n^2/(n^2+1)
To verify if the series diverges, apply the nth-Term Test for Divergence.
It states that if the limit of a_n is not zero, or does not exist, then the sum diverges.

lim_(n->oo) a_n != 0 or lim_(n->oo) = DNE
:. sum a_n diverges

Applying this, the limit of the term of the series as n approaches infinity is:
lim_(n->oo) a_n
=lim_(n->oo) n^2/(n^2+1)
= lim_(n->oo) n^2/(n^2(1+1/n^2))
=lim_(n->oo)1/(1+1/n^2)
=1/1+0
=1
The limit of the series is not zero. Therefore, by the nth-Term Test for Divergence, the series diverges.

What caused Opal to forget about Winn-Dixie

Opal forgets about Winn-Dixie because she's so preoccupied with saving her outdoor party from a sudden thunderstorm. She and Gloria Dump threw the party together, and the impromptu downpour threatens to destroy everything. When the rain hits, Opal snatches the egg salad sandwiches and runs them into Gloria's kitchen. Then she tries to take Gloria by the arm and lead her inside. She spots Otis by the garden, gazing at his feet, and beckons him to come inside, too.
It's not until Gertrude squawks "Dog" that Opal realizes Winn-Dixie is missing. In all the commotion, Opal simply forgot about Winn-Dixie who, like most dogs, is terrified by thunder and ran away. Though she's happy that she helped ferry the party-goers (and the food) to safety, Opal feels guilt over not protecting Winn-Dixie and holding tight to him when the storm began.

What aspects of the German tribes' way of life does Tacitus admire? What aspects does he criticize?

Tacitus admires the German people's ability to fight as infantry or foot soldiers and their ability to withstand being cold and hungry:

Cold and hunger they are accustomed by their climate and soil to endure.

In warfare, he admires that a German leader is supposed to show greater courage in battle than his men or is held in disgrace. Tacitus commends the Germans for expecting military leaders to command by example and character, rather than simply because they are appointed to a position. He also praises the fact that the common people have a say in who becomes their civilian leader and also have input in decision making in the community.
Tacitus praises the Germans for their easy hospitality. He very much admires their marital arrangements, which are monogamous and equal:

The matrimonial bond is, nevertheless, strict and severe among them; nor is there anything in their manners more commendable than this. ... she comes to her husband as a partner in toils and dangers; to suffer and to dare equally with him, in peace and in war ...

However, he criticizes the German men for being:

impatient of toil and labor, least of all capable of sustaining thirst and heat.

Tacitus also notes that although the German men are brave warriors, they are lazy in civilian life and want to do nothing, leaving the women and old people to manage all the day-to-day work of keeping the community functioning:

All the bravest of the warriors, committing the care of the house, the family affairs, and the lands, to the women, old men, and weaker part of the domestics, stupefy themselves in inaction: so wonderful is the contrast presented by nature, that the same persons love indolence, and hate tranquillity!

The Roman orator and public official Publius Cornelius Tacitus was a historian who took it upon himself to not only record but critique other cultures outside of the Roman Empire during the first century.  His historical writing, Germania, gives his overall impression of the ways of the Germanic tribes, but his subtle wording suggests that while he admires some structured aspects of their culture, he is less impressed with their physical and behavioral natures.
Tacitus has much good to say of the Germanic government system.  He seems impressed that their kings’ powers are somewhat limited; they discuss important matters with the tribe rather than dictating, and they do not have the right to exact corporal punishments.  The people listen to their leaders out of respect and admiration, not out of fear of their power. Although the tribes have scheduled meetings, Tacitus makes the point that they will sit down to council “[w]hen the multitude think proper.”  He also spends much time explaining how young men of the tribe are guided to adulthood by men of rank, which provides honor not only for the youths but for the men, who acquire many followers.  Ultimately, Tacitus says, “such a man is courted by embassies… and the very prestige of his name often settles a war.” It makes sense that Tacitus would be impressed with these aspects of the Germanic government system, since they are in many ways similar to those of the Romans.  However, Tacitus also seems to admire the Germanic marriage philosophy, so different from that of the Romans, calling it a praiseworthy part of their manners.  The men are “content with one wife,” who plays a more active role in her husband’s life than does a Roman woman, even accompanying him to war so that she might tend his wounds. Tacitus finds it practical that both partners bring gifts to the marriage—practical gifts that can support their lives together.
Tacitus mentions several times that the Germanic tribes are racially “pure,” which seems a compliment, but he says this is because no other people would subject themselves to the violent lifestyle and “sullen manners and aspect” of the Germans.  Their manner of dress seems to almost offend the Roman historian, as he comments that their cloaks are handmade from “the skins of wild beasts” and often fastened merely by a thorn.  More so, he is appalled that the women dress much like the men, with their arms uncovered, exposing the lower part of their bosoms.  To a Roman, whose station in life is proclaimed by his manner of dress, the Germans’ clothing must seem crude indeed.  Tacitus also criticizes their idleness when not at war.  Even the best warriors simply eat and sleep, leaving the women and the elderly to run the household and land.  The lack of beautiful, organized cities is also odd to Tacitus, who points out that rather than creating community through public buildings, each family lives quite away from the others in “rude [dwellings] without ornament or attractiveness.” 
It seems that the overall lack of refinement and culture cinch the Roman historian’s view of Germanic tribes.  Although he finds honor in some of their ways, their lack of refinement is simply a huge cultural gap between the Germans and the Romans.
http://www.pbs.org/empires/romans/empire/life.html

Calculus of a Single Variable, Chapter 6, 6.4, Section 6.4, Problem 59

y'+3x^2y=x^2y^3
Multiply the above equation by y^(-3)
y^(-3)dy/dx+3x^2y(y^(-3))=x^2
y^-3dy/dx+3x^2y^(-2)=x^2
Taking the transformation v=y^(-2)
(dv)/dx=d/dy(y^(-2))*dy/dx
(dv)/dx=-2y^(-3)dy/dx
-1/2(dv)/dx=y^(-3)dy/dx
Now the Bernoulli equation is transformed as ,
-1/2(dv)/dx+3x^2v=x^2
(dv)/dx-6x^2v=-2x^2
Now the above is a linear equation in the dependent variable v and independent variable y.
The integrating factor is n(x)=e^(int(-6x^2dx))
=e^(-6x^3/3)
=e^(-2x^3)
Then,
e^(-2x^3)*(dv)/dx-6e^(-2x^3)*x^2v=-2e^(-2x^3)*x^2
d/dx(e^(-2x^3)*v)=e^(-2x^3)(dv)/dx+ve^(-2x^3)(-6x^2)
=e^(-2x^3)(dv)/dx-6e^(-2x^3)*x^2v
=-2e^(-2x^3)*x^2
intd/dx(e^(-2x^3)*v)dx=int-2e^(-2x^3)x^2dx
e^(-2x^3)*v=-2inte^(-2x^3)*x^2dx
Let t=x^3
dt=3x^2dx
e^(-2x^3)*v=-2inte^(-2t)*dt/3
=-2/3(e^(-2t)/(-2))+C
=e^(-2t)/3+C
Substitute back t=x^3
e^(-2x^3)*v=1/3e^(-2x^3)+C
Substitute back v=y^(-2)
e^(-2x^3)*y^(-2)=1/3e^(-2x^3)+C
y^-2=1/3+C/e^(-2x^3)
1/y^2=1/3+Ce^(2x^3)
y^2 = 1 / (1/3+Ce^(2x^3))
y = +-sqrt(3)/(Ce^(2x^3) + 1)

What is the double meaning in the use of the word "game" in the title of "The Most Dangerous Game"?

"The Most Dangerous Game" is certainly a title that has multiple levels of meaning. Ultimately, the word "game" here can be interpreted according to two separate definitions. It be used both in reference to a contest (in the way we might say baseball is a game), as well as to wild animals pursued in a hunt.
Thus, if we apply the first definition, "The Most Dangerous Game" refers to the hunt itself, by which Rainsford is being hunted by Zaroff. Meanwhile, the second definition can be applied to human beings. This is a point expressed by Zaroff himself, who has grown disillusioned with hunting big game animals, viewing them as insufficient challenges to his skills; thus, he hunts people instead.
Furthermore, however, there is actually a third layer of meaning: rather than it being the human species in aggregate, the term might also be in reference to Rainsford himself. After all, what could be a more dangerous opponent for an experienced big game hunter than another experienced big game hunter?
Thus, from these two definitions of the word "game," there arise three distinct layers of meaning. Each represents an entirely valid interpretation, in resonance with the story's themes and plot. But each, on its own, is also incomplete. It is only when all these various layers are brought together that the title's full significance and thematic meaning can be ascertained.

The double meaning of the word game in Richard Connell's short story entitled "The Most Dangerous Game" pertains to both animals that are hunted and to a type of activity that involves challenges and winners and losers—"a sporting proposition," as General Zaroff describes it.
In the exposition of this story, Sanger Rainsford and his friend Whitney are aboard a steamer because they are going hunting "up the Amazon." As they anticipate their arrival in a few days, Whitney wonders how the jaguar will feel as it is hunted, but Rainsford has no sympathy for this animal: "Who cares how a jaguar feels?" For Rainsford, the jaguar is merely a game animal that is hunted. The irony of this insensitive remark is that he later becomes the game that is tracked by General Zaroff, so he experiences for himself the terror of a prey animal.
When Rainsford falls from the rail of the ship upon which he stood in the night after trying to determine the direction of the gunshots that he heard, he swims to the shore of what he later learns is Ship-Trap Island. The next day Rainsford follows the "print of hunting boots" to a huge chateau on a high bluff. There he is welcomed by General Zaroff and served an exquisite dinner. The general, who is a big game hunter and has hunted all over the world, tells Rainsford that he lives to hunt and, to keep his interest, he now hunts "more dangerous game." Later, Rainsford learns that this "game" hunted by Zaroff is men. The general tells Rainsford,

"Hunting had ceased to be what you call 'a sporting proposition.' It had become too easy."

Zaroff goes on to tell his dinner guest about his new "sporting proposition," or game: He now hunts men. Further, Zaroff informs Rainsford that the next day Rainsford himself will become this "game"/prey in a "most dangerous game"/Zaroff's sporting proposition.

How does the life experience of Frank Kafka affect how he wrote the narrative "The Metamorphosis"?

Kafka himself experienced the loneliness and isolation that he ascribes to Gregor in The Metamorphosis. His parents, busy running their fashion business, were too occupied to devote much time to Kafka, who was the oldest of six children (two of whom died in infancy). His three sisters would die in the Holocaust after his death (which occurred before World War II). His relationship with his father was particularly distant.
Kafka felt distanced from those around him. He considered himself repulsive, as reflected in Gregor's metamorphosis into a grotesque beetle, and he never married before dying at age 40 from tuberculosis. He was a German-speaking Jew in Prague, isolating him linguistically and religiously from the mainstream Czech population. Much of his life was drawn from inner sources, and he spent his time writing, even when employed as a lawyer at an insurance company. Like his character, Gregor, Kafka withdrew into his room, and he felt alone and isolated from the world around him.

Franz Kafka's and Gregor Samsa's lives have several similarities. In this story among others, he drew extensively on his own experience, including family, work, and creativity.


Both men have conflicted relationships with their fathers; both have sisters. Both men work in tedious, unfulfilling jobs.


Kafka stayed in his job and wrote in his off-work hours. His father was very hostile to the idea of his writing. He often wrote about father-son conflicts, both in his published fiction and his unpublished diaries.


In the story, Gregor is forced out of his job by his transformation and his boss. His father is both angry that Gregor cannot work to support the family and repulsed by his new physical appearance. The injury caused when his father throws and hits him with apples is one cause of his death.


Gregor mentions some advantages of not working, such as appreciating his sister play music. While not a musician himself, whereas Kafka was a writer, he is a sensitive person with creative interests.

Franz Kafka's "The Metamorphosis" tells the story of a young salesman, Gregor Samsa, who wakes up one morning to find he has been fully transformed into a large insect. The themes of alienation, isolation and familial sacrifice that develop as Samsa begins to face his day as an insect can certainly be traced to Kafka's life experiences.
Kafka grew up in Prague, son of an upper middle class Jewish family in the late 1800s. He lost two brothers in their infancy, leaving him the only boy in a family that included three daughters (all of whom later die as a result of the Nazi rise to power). This places all of his parents hopes on him and his success. This is much the same pressure we see placed on Samsa in "The Metamorphosis." His parents and his sister depend on him as the sole breadwinner. It is implied in his parents' cold interactions with him in this new reality that their love is somewhat conditional.
We know Kafka had difficulty relating to his own parents: his mother was a homemaker who did not understand the depths of his thinking, and his father has been described as a tyrant who had little understanding of his son's desire to become a writer. Again, the isolation and alienation Samsa feels as an insect could be connected to Kafka's own sense of loneliness in his own home. Samsa's father's instinct is to attack the insect—almost becoming a monster himself. It is Samsa's mother who flings herself on her husband to stop him from hurting their son, though she does it almost ambivalently, not wanting necessarily to face her son or offer consolation herself.
Kafka's life experience seems to be, in some ways, dramatized in his novella, "The Metamorphosis." While the alienation, isolation, and family pressures that Samsa feels in the story can be seen in Kafka's own childhood, they can more generally be seen as products of modern life.