Calculus of a Single Variable, Chapter 7, 7.3, Section 7.3, Problem 9

To be able to use the Shell method, a rectangular strip from the bounded plane region should be parallel to the axis of revolution. By revolving multiple rectangular strip, it forms infinite numbers of this hollow pipes or representative cylinders.
In this method, we follow the formula: V = int_a^b (length * height * thickness)
or V = int_a^b 2pi * radius*height*thickness
where:
radius (r)= distance of the rectangular strip to the axis of revolution
height (h) = length of the rectangular strip
thickness = width of the rectangular strip as dx or dy .
For the bounded region, as shown on the attached image, the rectangular strip is parallel to y-axis (axis of rotation). We can let:
r=x
h=f(x) or h=y_(above)-y_(below)
h =4-(4x-x^2) = 4-4x+x^2
thickness = dx
Boundary values of x from a=0 to b =2 .
Plug-in the values on V = int_a^b 2pi * radius*height*thickness, we get:
V = int_0^2 pi*x*(4 -4x+x^2)*dx
Simplify: V = int_0^2 pi(4x -4x^2+x^3)dx
Apply basic integration property: int c*f(x) dx = c int f(x) dx
V = 2pi[ int_0^2(4x -4x^2+x^3)dx]
Apply basic integration property:int (u+-v+-w)dy = int (u)dy+-int (v)dy+-int(w)dy to be able to integrate them separately using Power rule for integration: int x^n dx = x^(n+1)/(n+1).
V = 2pi[ int_0^2(4x) dx -int_0^2(4x^2)dx+int_0^2(x^3)dx]
V = 2pi[ 4*x^2/2 -4*x^3/3+x^4/4]|_0^2
V = 2pi[ 2x^2 -(4x^3)/3+x^4/4]|_0^2
Apply the definite integral formula: int _a^b f(x) dx = F(b) - F(a) .
V =2 pi[ 2(2)^2 -(4(2)^3)/3+(2)^4/4]-2pi[ 2(0)^2 -(4(0)^3)/3+(0)^4/4]
V = 2pi[ 8-32/3+4] - 2pi[0-0+0]
V = 2pi[ 4/3] -0
V = (8pi)/3 or 8.38 (approximated value)

Some people say that Hitler was Jewish. Is that true?

There have been reports that Adolf Hitler may have had some connections to Judaism, and therefore he was Jewish. The irony in this is that Hitler wanted to destroy the Jewish people in Europe and attempted to accomplish this by creating the extermination camps throughout Europe.
The question about Hitler’s Jewish connections is centered on Hitler’s grandfather. Hitler’s father was born to an unknown man. His father's mother did work in the home of a wealthy Jewish person. As a result, there is a remote possibility that Hitler's grandmother might have somehow become pregnant by a son of this Jewish person.
There also is a question about Hitler’s DNA. He apparently had a gene that was uncommon in Western Europe and has been found in some Jewish people.
Both of these theories, however, are not strong enough to support the claim that Hitler was Jewish. It is generally accepted that Hitler was not Jewish.
https://www.history.com/news/study-suggests-adolf-hitler-had-jewish-and-african-ancestors

https://www.jewishvirtuallibrary.org/was-hitler-jewish

Calculus: Early Transcendentals, Chapter 4, 4.6, Section 4.6, Problem 14

f(x)=((2x+3)^2(x-2)^5)/(x^3(x-5)^2)
Vertical asymptotes are the undefined points, also known as zeros of denominator.
Let's find the zeros of denominator of the function,
x^3(x-5)^2=0
x^3=0 ,(x-5)^2=0
x=0, x=5
Vertical Asymptotes are x=0 , x=5
For Horizontal Asymptotes
Degree of Numerator of the function=7
Degree of Denominator of the function=5
Degree of Numerator> 1+Degree of Denominator
:. There is no Horizontal Asymptote
Now let's find intercepts
x intercepts can be found when f(x)=0
(2x+3)^2(x-2)^5=0
2x+3=0 , x-2=0
x=-3/2 , x=2
So x intercepts are -1.5 and 2.
Since x is undefined at x=0 , there are no y intercepts.
See the attached graph and link.
From the graph,
Local Minimum
f(-1.5)=0
f(8) ~~ 600
No Local Maximum

How does Victor's passion drive him to negative things?

Victor's passion for knowledge and for immortality (in the form of his reputation in the scientific community) leads to the destruction of his family and his entire life. In a quest for the "philosopher's stone," or an answer to his questions about the fine line between life and death, Victor comes up with a project in which he builds a human out of an assemblage of body parts from dead people. He brings his creation to life and is immediately horrified. He was only concerned about the scientific developments and how his name would be remembered forever for his accomplishments; he did not think about the real consequences of his actions.
Victor's creation results in tragedy after tragedy in Victor's life. For one, he loses a number of family members as a result: his brother is killed by the creature, his wife is killed by the creature on their wedding night, his best friend is also presumably murdered by the creature, and finally, his father basically dies of stress and grief after all of the other tragedies. Victor's obsession with the creature dominates his life and leads eventually to his own death. While he's building the creature, he is isolated and withdrawn, and after, he is ashamed and hiding from the consequences of his actions. At the end of the novel, Victor is wasting away in the Arctic, basically in a chase to the death between himself and the creature. The negative effects of Victor's passion are clearly depicted in the novel and result in complete tragedy for Victor and those around him.

What does "guns never shoot" mean?

It sounds like the phrase in your question is related to the aphorism, "Guns don't shoot people; people do." Both this phrase and the simpler, "Guns never shoot," may be used in discussions about laws regulating the ownership, handling, and use of guns. The argument that "guns don't shoot people" is championed by organizations like the National Rifle Association in the United States as a means of emphasizing responsible gun ownership.
You see, a gun on its own is an inanimate object. A gun cannot shoot anyone or anything without intentional manipulation by a person. Of course, there are accidents where people do not mean to fire, or even drop their weapon and cause a misfire, which may result in injury or death. The act of shooting, most often, comes from a person who is handling the firearm. Phrases like those mentioned above are intended to draw a distinction between the gun itself, which is not an inherently bad thing, and the actions of people who own or use guns. 

How is pride featured in "The Scarlet Ibis"?

The brother's pride is the driving force for what occurs in the narrative of James Hurst's "The Scarlet Ibis."
The narrator/ brother initially describes his little brother, to whom he gives the nickname Doodle, as a "disappointment" and "a burden." Clearly, the little brother is an affront to the narrator's pride. At first, Doodle just lies on a rubber sheet and does not seem to be "all there." Later, he does develop some, but he still cannot walk. As a result, the proud brother, who is embarrassed to do so, must pull Doodle in a go-cart his father made for him. Because of this perceived affront to his pride, the brother insists Doodle learn to walk. They practice secretly because the brother knows he should not strain Doodle, whose heart is weak. Nevertheless, he pressures Doodle to practice for weeks until he can finally walk. The boys decide not to reveal this learned skill until a special occasion occurs; they choose Doodle's sixth birthday. After bringing Doodle to the doorway of the dining room in the cart, the brother tells all the other family members to turn their backs and not to peek around. He helps his brother up. While Doodle stands, his brother tells the family they can now look.

There wasn't a sound as Doodle walked slowly across that room and sat down at his place at the table.

When the adults see Doodle walk slowly across the room and sit down at the table, they are overjoyed. When they congratulate the brother, who Doodle credits with his accomplishment, the brother suddenly begins to cry in shame. 

They did not know that I did it for myself; that pride, whose slave I was, spoke to me louder than all their voices; and that Doodle walked only because I was ashamed of having a crippled brother.

Later on, in the summer, the brother gives Doodle swimming lessons and tries to teach his brother to row a boat because he does not want to be embarrassed by Doodle before school begins. The stress upon Doodle is apparent, as he looks feverish and does not sleep well. Nevertheless, in his blind pride, the brother pushes Doodle to keep working.

I should have already admitted defeat, but my pride would not let me. . . It was too late to turn back, for we had wandered too far into a net of expectations and had left no crumbs behind.

Even the appearance of the omen of the scarlet ibis, a delicate and beautiful bird who wanders too far out of its element and dies, does not arrest the brother in his selfish drive to make Doodle normal. Shortly before school begins, the brother takes Doodle out on the water and makes him row back against the tide and the approach of a storm. When they finally reach shore, Doodle is exhausted, and as the rain begins to pelt them, Doodle falls behind his brother in their rush to get home. "Brother, Brother, don't leave me! Don't leave me!" he cries, but the pride and the "streak of cruelty" in the brother emerges as he is its "slave," and he runs as fast as he can. When he finally turns back for Doodle, the narrator finds his piteous brother limply seated with his face buried in his arms. When his brother moves Doodle, he falls backward onto the earth, dead. Just as the beautiful and fragile scarlet ibis has died, both the ibis and Doodle are victims of a certain pride that has pushed too far.

a

We are given a+b+c=395, b+c+d=1001 and aAs stated, d can take on a range of values.
Subtract the two equations:
   b+c+d=1001a+b+c   =395-----------------a      +d=606   or
d=606+a
This isn't the whole story as we also know that aAssuming that a,b,c,d are integers there is a clear upper bound on a: a<130. (If a=131, then b+c=264 ==> b=c=132 but bThere is also a lower bound on a. (Unless a,b,c,d are natural numbers, in which case the lower bound is a>0.) If a<-271 then d becomes too small. e.g. if a=-272, then b+c=667 and the smallest that c can be is 334, but d=334 which contradicts c---------------------------------------------------------------------------
Assuming a,b,c,d are integers then the value of d depends on a ; d=606+a where -272If a,b,c,d are natural numbers then d=606+a where 0---------------------------------------------------------------------------