As described by Comic Book Nation, how did Wolverine reflect the cultural and political sensibilities of the 1980s?

Wolverine was a popular 1980s antihero, as he reflected the anti-government sentiment of the era.
According to Wright, 1980s anti-government sentiment resulted from the Watergate scandal and the Vietnam War in the 1960s. In that same decade, the Civil Rights movement became connected to the anti-war movement. Both African Americans and anti-war activists disapproved of Lyndon B. Johnson's handling of the Vietnam War. African American activists particularly disliked what they considered a racially biased draft system. They also worried that the costs of the mounting war would affect spending levels on President Johnson's Great Society programs.
The anti-government sentiment which began in the 1960s spilled over into the 1980s. People were wary about domestic and foreign federal policies that they felt did not represent their interests.
According to Wright, Wolverine was an invincible anti-hero, the kind who was unencumbered by "bureaucratic technicalities" and sentimental inclinations. Like the Punisher, Wolverine represented vigilante justice. His adamantium skeleton, mutant healing powers, and retractable claws made him indestructible. In short, Wolverine represented an omnipotent 1980s Dirty Harry, the kind that helped the oppressed when the government was the enemy.
https://www.h-net.org/reviews/showrev.php?id=11852

Calculus: Early Transcendentals, Chapter 6, 6.2, Section 6.2, Problem 11

The volume of the solid obtained by rotating the region bounded by the curves y^2=x and y=x^2 about y = 1, can be evaluated using the washer method, such that:
V = int_a^b pi*(f^2(x) - g^2(x))dx
You need to find the endpoint of interval, hence, you need to solve for x the following equation, such that:
sqrt x = x^2 => x - x^4 = 0 => x(1 - x^3) = 0 => x = 0 and x = 1
You need to notice that x^2 < sqrt x on [0,1], such that:
V = int_0^1 pi*(((sqrt x) - 1)^2 - (x^2 - 1)^2)dx
V = pi*int_0^1 (x- 2sqrt x + 1)dx - pi*int_0^1 (x^4-2x^2 + 1)dx
V = (pi*x^2/2 - (4/3)pi*x^(3/2) + pi*x - pi*x^5/5 + 2pi*x^3/3 - pi*x)|_0^1
V = pi*1^2/2 - (4/3)pi*1^(3/2) - pi*1^5/5 + 2pi*1^3/3 - 0
V = pi/2 + (4pi)/3 - pi/5 - (2pi)/3
V = pi/2 + (2pi)/3 - pi/5
V = (15pi + 20pi - 6pi)/30
V = (29pi)/30
Hence, evaluating the volume of the solid obtained by rotating the region bounded by the curves y^2=x , y=x^2 about y = 1 , using the washer method, yields V = (29pi)/30.

How do you find the y-intercept of a function?

Hello!
The y-intercept of a function is the point of intersection of the graph of this function and the y-axis. So such a point belongs both to y-axis and to the graph of a function.
All points on the y-axis have an x-coordinate of 0, they are of the form (0, y), where y may be any number.
All points on the graph of a function f(x) have the form (x, f(x)), where x is any number from the domain of f.
If both conditions are met, we have x = 0 and the second coordinate is f(0), hence the y-intercept of f is the point (0, f(0)), it is unique if function is one-valued. Of course this requires that 0 is in the domain of f, otherwise f has no y-intercept.
For example, f(x)= x^2+1 has the y-intercept (0, 1), and g(x) = 1/x has no y-intercept.
More general curves, not graphs of (one-valued) functions, may have more than one y-intercept, for example the circle x^2+y^2=1 has two (find them yourself using x=0 ).
 

What was Winston’s age when his mother died?

Winston was a child when his mother disappeared. He is not sure how old he was, but he thinks he was 10 or 11.
At one point, Winston also thinks:

His mother’s death, nearly thirty years ago, had been tragic and sorrowful in a way that was no longer possible.

Later, having fallen in love with Julia, he more clearly remembers the circumstances surrounding his mother's disappearance. He recalls he was at least 10 but no more than 12 when he last saw her. He was hungry all the time and stole a piece of chocolate from his starving little sister—then ran out of the room where they lived. When he came back, his mother and sister were gone. At this point, he backtracks on the idea that his mother is dead, thinking:

To this day he did not know with any certainty that his mother was dead. It was perfectly possible that she had merely been sent to a forced-labour camp.

After his arrest, he meets a drunken old woman in detention who says her name is Smith, and he notes that she might be his mother. While unlikely, it is not impossible:

She might, thought Winston, be his mother. She was about the right age and physique, and it was probable that people changed somewhat after twenty years in a forced-labour camp.

The key points are as follows: first, he sees his mother for the last time when he is about the 11. Second, while he does not know if she is dead or alive, she is gone from his life thereafter. Third, she is woven deeply into the fabric of his soul, especially in her love him. This is the most important point of all. O'Brien can get to Julia—he knows Winston loves her—but he never penetrates fully to Winston's mother. It is significant that at the end of the book, Winston is thinking of a very happy moment playing Snakes and Ladders with his mother shortly before he dies. Did the state get full control of him, or did a part of him elude its grasp?

What ideas at the end of the chapter 11 does the author want to emphasize?

The most important idea conveyed in this chapter is the true meaning of courage. Scout and Jem are regularly subjected to vicious tongue-lashings by Mrs. Dubose, a mean old lady who lives in the neighborhood. It's bad enough when she starts yelling at the children about running wild, or accuses them of playing hooky, but it's even worse when she trash-talks Atticus about representing Tom Robinson in court. Jem always tries really hard to stay calm in the face of Mrs. Dubose's abuse, but the insult against Atticus is just too much, and one day he snaps and goes on the rampage in her garden, ripping off the heads of her camellias. As a punishment, Jem is ordered by Atticus to go and read to the old lady.
Shortly afterwards, Mrs. Dubose passes away. Scout is shocked to hear Atticus describe her as the bravest person he ever knew. This puzzles Scout. Not only does she think that Atticus is the bravest person around but she cannot understand how someone as ornery and downright unpleasant as Mrs. Dubose could ever be thought of as being brave. Atticus tells her that Mrs. Dubose had been a morphine addict for a number of years but was determined to beat her addiction before she died. She failed, of course, but her heroic struggle against the evils of drug dependency displayed exemplary courage and earned her the undying admiration of Atticus. Scout learns not just about putting yourself in other folks' shoes but about the many different ways it's possible to show courage.

Single Variable Calculus, Chapter 5, 5.2, Section 5.2, Problem 46

Evaluate $\displaystyle \int^{\pi/2}_0 (2 \cos x - 5x) dx$ using the properties of integrals and the fact that $\displaystyle \int^{\pi/2}_0 \cos x dx = 1$ and $\displaystyle \int^a_b x dx = \frac{b^2 - a^2}{2}$

Applying the properties of integrals

$
\begin{equation}
\begin{aligned}
\int^a_b [f(x) - g(x)] dx &= \int^a_b f(x)dx - \int^a_b g(x) dx \\
\\
\int^{\pi/2}_0 ( 2 \cos x - 5x) dx &= \int^{\pi/2}_0 2 \cos x dx - \int^{\pi/2}_0 5x dx
\end{aligned}
\end{equation}
$


Then apply $\displaystyle \int^a_b c f(x) dx = c \int^a_b f(x) dx$, where $c$ is any constant then
$\displaystyle \int^{\pi/2}_0 2\cos x dx - \int^{\pi/2}_0 2 5 x dx = 2 \int^{\pi/2}_0 2 \cos x dx - 5 \int^{\pi/2}_0 2 x dx$
Since $\displaystyle \int^{\pi/2}_0 2 \cos x dx 1$ and $\displaystyle \int^b_a x dx = \frac{b^2 - a^2}{2}$, we have

$
\begin{equation}
\begin{aligned}
2 \int^{\pi/2}_0 2 \cos dx - 5 \int^{\pi/2}_0 2 x dx &= 2 (1) - 5 \left[ \frac{\left(\frac{\pi}{2} \right)^2 - (0)^2}{2} \right]\\
\\
2 \int^{\pi/2}_0 2 \cos dx - 5 \int^{\pi/2}_0 2 x dx &= 2 2 - 5 \left( \frac{\frac{\pi^2}{4}}{2}\right)\\
\\
2 \int^{\pi/2}_0 2 \cos dx - 5 \int^{\pi/2}_0 2 x dx &= 2 2 - \frac{5\pi^2}{8}
\end{aligned}
\end{equation}
$

Why is watching release forbidden to children, but not to Jonas

Jonas is allowed to watch the release of a child because he is the Receiver.
In the society in which Jonas lives, pain and suffering have been eliminated. Because people are not permitted to be in situations in which there is suffering, they are not made aware of what "release" actually entails. In chapter nineteen, Jonas mentions to the Giver that his father is going to release one of the identical twins recently born because such twins are not allowed in his society. "I wish I could watch," Jonas adds after he tells the Giver that his father, whom he considers "such a gentle man," performs the ceremony and makes the little twin "clean and comfy."
The Giver explains that Jonas can watch because he is allowed to "ask anyone anything." Since the ceremony has already been performed, Jonas decides that he will view the tape which the Giver tells him is available. The Giver has Jonas himself ask for the tape on the speaker. The video screen then comes on, and Jonas is surprised to see a small room because he believes that release involves a ceremony. As the video continues, Jonas is shocked when he witnesses his father inject a needle into the smaller twin's head. Jonas sees the baby die as his father calmly speaks in his "special voice" for babies.

He killed it! My father killed it! Jonas said to himself, stunned at what he was realizing. He continued to stare at the screen numbly. (Ch. 19)

After a short time, Jonas feels a "terrible pain" as he is made aware of one of the harsh realities of his society.