Why isn't Salerio present in the Act III, Scene iii of The Merchant of Venice by Shakespeare? Where is he?

In Act 3, Scene 3, Shylock stands in his doorway alongside Antonio, Solanio, and a Jailer. Antonio tries his best to reason with Shylock, but Shylock refuses to listen to him. Shylock insists that he will have his bond, and Solanio comments that he is an obstinate dog. Antonio then mentions that he only wishes that Bassanio will come see him pay his debt before leaving with the Jailer. The reason Salerio is not present in the Act 3, Scene 3 is because he traveled to Belmont to give Bassanio a letter from Antonio. In Act 3, Scene 2, Salerio arrives at Belmont with the terrible news that Antonio has lost all of his merchant ships at sea and Shylock plans to collect Antonio's flesh. Bassanio becomes extremely upset and explains the situation to Portia before leaving for Venice. During Act 3, Scene 3, Salerio is traveling with Bassanio to return to Venice before Antonio is forced to pay his bond.

What is the characterization of Tessie Hutchinson?

Tessie Hutchinson is an ordinary housewife who accepts life as it comes to her without questioning its values until it is too late.
She arrives late at the annual lottery and chats easily with her neighbors, saying she had almost forgotten it. This suggests it is not an event she wants to think about. Nevertheless, it is a tradition in her village, and she apparently goes along with it every year without raising any problems. She doesn't seem to feel the least bit of fear that she might be the chosen sacrifice.
Tessie Hutchinson is an "everyman," a conventional person willing to put up with evil or barbarism and not rock the boat until the evil touches her. Then, it is another story. When her family's name and then her name is drawn in the lottery, suddenly the procedure, and her fate, are "unfair." She apparently has lacked the empathy to understand how others might feel as the victims of an arbitrary stoning. By the time it is her turn, she has participated too long to expect any mercy.
Jackson's story suggests that we speak up against injustice rather than assume, like Tessie, that it will never happen to us.

In Shirley Jackson's "The Lottery," Tessie Hutchinson is first characterized as a harried housewife who has simply forgotten that it is lottery day until she notices her husband and children are gone. It is possible that her forgetfulness is either intentional or a subconscious effort to avoid the lottery. She hurries to the gathering, greets her neighbors, and makes a lighthearted joke about her tardiness. She urges her husband to quickly take his slip of paper, cracking another joke that amuses those standing near. Her levity quickly comes to an end, however, once she sees that the lottery will claim one of her family members. She adopts a protesting, defensive tone. Getting no support from her husband or any of the crowd, she becomes quieter, yet insistent that the proceedings aren't being conducted fairly. Her defiance intensifies, and her husband has to pry her paper from her hand. Tessie Hutchinson does not accept her fate uncomplainingly, which makes her death by stoning all the more unsettling at the story's conclusion.

Calculus of a Single Variable, Chapter 9, 9.6, Section 9.6, Problem 20

To determine the convergence or divergence of a series sum a_n using Root test, we evaluate a limit as:
lim_(n-gtoo) root(n)(|a_n|)= L
or
lim_(n-gtoo) |a_n|^(1/n)= L
Then, we follow the conditions:
a) Llt1 then the series is absolutely convergent.
b) Lgt1 then the series is divergent.
c) L=1 or does not exist then the test is inconclusive. The series may be divergent, conditionally convergent, or absolutely convergent.
We may apply Root test on the given series sum_(n=1)^oo 5^n/n^4 when we let: a_n =5^n/n^4 .
Applying the Root test, we set-up the limit as:
lim_(n-gtoo) |5^n/n^4|^(1/n) =lim_(n-gtoo) (5^n/n^4)^(1/n)
Apply Law of Exponent: (x/y)^n = x^n/y^n and (x^n)^m= x^(n*m) .
lim_(n-gtoo) (5^n/n^4)^(1/n) =lim_(n-gtoo) (5^n)^(1/n)/(n^4)^(1/n)
=lim_(n-gtoo)5^(n*1/n)/n^(4*1/n)
=lim_(n-gtoo)5^(n/n)/n^(4/n)
=lim_(n-gtoo)5^1/n^(4/n)
=lim_(n-gtoo)5/n^(4/n)
Evaluate the limit.
lim_(n-gtoo) 5/n^(4/n)=5 lim_(n-gtoo) 1/n^(4/n)
=5 *1/oo^(4/oo)
=5 *1/oo^(0)
=5 *1/1
= 5*1
=5
The limit value L =5 satisfies the condition: Lgt1 since 5gt1 .
Conclusion: The series sum_(n=1)^oo 5^n/n^4 is divergent.

Why did Western nations use appeasement with the Axis powers?

One reason the Allied powers pursued a policy of appeasement is that they were weary of war after the bloodletting of the First World War and were reluctant to pursue any policy that seemed likely to bring about another conflict. Having lost vast swaths of their male populations, they were understandably fearful about entering into any new war.
Another reason was that Hitler, while repugnant to many Westerners, was seen by many as the lesser of two evils when compared to Joseph Stalin in the Soviet Union. Communists advocated global revolution in a way that Hitler did not, and many saw Hitler as a valuable if dangerous bulwark against the Soviets. This is why they were so horrified at the announcement of the Nazi-Soviet non-aggression pact in 1939. In fact, many British, American, and Frenchmen shared Hitler's views on race and anti-Semitism.
In 1938, with the crisis over the Sudetenland breaking out, the British army was not seen as capable of dealing with the threat posed by the Nazis. The Sudetenland was not worth going to war over, but without it Czechoslovakia was seen as impossible to defend. So essentially, the Munich Conference, where the much-reviled Neville Chamberlain claimed to have achieved "peace in our time," was held over a territory seen as a lost cause by many strategists.
Another reason that Europeans pursued appeasement is that they underestimated Hitler's capacity for boldness and dishonesty. When he promised no further aggressions at Munich, some believed him, if only because, as mentioned above, they had little choice.
Finally, the United States, which, as a massive industrial and financial power, was essential to any war against the Germans, adopted an isolationist stance in the 1930s. "America First" advocates, many of whom were genuinely sympathetic to the Nazis, were vocal and prominent in the United States. Others in Congress attempted to restrain President Franklin Roosevelt, whose instincts were always toward involvement in global affairs. Without the backing of the United States, the European powers played with a weaker hand in dealing with Hitler's aggression.
https://www.iwm.org.uk/history/how-britain-hoped-to-avoid-war-with-germany-in-the-1930s

https://www.spiegel.de/international/europe/the-road-to-world-war-ii-how-appeasement-failed-to-stop-hitler-a-646481.html

To what extent is Christopher's condition responsible for these three types of conflict that arise in the book? Identify and analyze the following: character versus character, character versus self, character versus nature.

To a great extent, Christopher's condition is responsible for three main conflicts in the book: character versus character, character versus self, and character versus nature.
In the story, 15-year-old Christopher is mildly autistic, and his symptoms are typical of someone with this condition. The first indication of Christopher's autism is shown in his preoccupation with numbers, specifically prime numbers. In fact, the chapters of his book are ordered accordingly. For example, we begin with Chapter 2, progress to Chapter 3, and proceed accordingly. In chapter 19, Christopher explains why he likes prime numbers (they are logical) and how he calculates subsequent numbers (beginning from 2).
Christopher's conflicts with his father, Mrs. Shears, and, later, Mr. Shears and his mother (in London) are often precipitated by his condition. A large part of Christopher's challenges derive from his inability to correctly interpret nonverbal forms of communication such as facial expressions, gestures, and body language. His difficulties are briefly alluded to in chapter 3. Here, Christopher explains that he can tell when a person is sad or happy. However, he runs into problems deciphering other types of facial expressions.
In chapter 11, Christopher is approached by the police. During their interaction, he becomes confused by an officer's rapid questions. At this point, it is clear that Christopher is overwhelmed, and he protects himself in the only way he knows how: he begins groaning heavily. Alarmed by Christopher's behavior, the officer takes hold of the teenager in an attempt to bring him to his feet. Because many autistic individuals are hypersensitive to touch (especially during a stressful situation), Christopher hits back at the officer. Additionally, Christopher's inability to correctly interpret the officer's body language also contributes to his outburst.
In chapter 17, we learn that Christopher has been arrested for assaulting an officer. However, he shows little indication of being distressed by his arrest. In fact, Christopher's mind continues to focus on what he likes best: numbers. He happily notes that his jail cell is a perfect cube and contains exactly 8 cubic meters of air. Like many autistic individuals, Christopher harbors intense obsessions; in Christopher's case, prime numbers and scientific facts give him a feeling of control and normalcy.
It can be seen that Christopher's struggles with himself and others largely stem from his condition. In chapter 67, Christopher admits that he does not like strangers, as he has a difficult time understanding them. We learn more about Christopher's condition in chapter 73, where he describes some of his "behavioral problems." In chapter 97, Christopher learns from Mrs. Alexander (a neighbor) the real reason for his father's explosive dislike of Mr. Shear.
Despite Mrs. Alexander's careful and empathetic manner, Christopher is distrustful of her. Again, his difficulties arise from his condition. Throughout the novel, Christopher has difficulty relating to others, and he struggles to process his experiences. When overwhelmed, he falls back to reciting facts and statistics.
Later, in the book, we learn that Christopher also has unconventional feelings about nature. In chapter 103, he describes his impression of clouds. He tells us that sometimes clouds are boring: they are grey or blue and have little personality. At other times, a big, grey cloud may be a rain cloud, and it may take the shape of an alien spaceship "hundreds of kilometers long." In the same chapter, we learn that Christopher smells "nothing" when he sniffs the air in the garden. Again, Christopher's conflict with nature stems from his condition; many autistic individuals have difficulty processing sensory information, such as sights, sounds, and smells.
In all, Christopher's condition is directly responsible for the three types of conflict in the book.
https://www.autismspeaks.org/what-are-symptoms-autism

https://www.autismspectrum.org.au/about-autism/what-is-autism

Is there a quote to show how the littlun with the birthmark dies? Thanks.

In chapter 2, one of the littluns with a mulberry-colored birthmark on his face tells the group of boys during an assembly that he saw a snakelike "beastie" the previous night, and the older boys assure the littluns that he was simply experiencing a nightmare. Later on, Ralph proposes that the boys climb to the top of the mountain and create a signal fire so that passing ships will stop to rescue them. The boys get excited and gather a large bundle of dead wood for the signal fire. They then use a lens from Piggy's glasses to magnify the sun and start the fire. Suddenly the fire bursts into flames, and the wind carries the flames down the side of the mountain, causing a small forest fire. Piggy immediately begins criticizing the older boys for their lack of responsibility and asks if anyone thought to take count of how many littluns are in the group. Piggy then mentions that some of the littluns were playing in the location of the forest fire by saying,

and them little 'uns was wandering about down there where the fire is. How d'you know they aren't still there? (Golding, 36).

One of the boys then says, "Him that talked about the snakes. He was down there," and Golding writes,

A tree exploded in the fire like a bomb. Tall swathes of creepers rose for a moment into view, agonized, and went down again. The little boys screamed at them (36).

When the boys continue to ask if they saw the littlun with the mulberry-colored birthmark, Golding writes,

Ralph muttered the reply as if in shame. "Perhaps he went back to the, the—" Beneath them, on the unfriendly side of the mountain, the drum-roll continued (36).

While Golding does not explicitly describe what happens to the littlun with the mulberry-colored birthmark, he implies that the littlun dies in the forest fire, which is created when the boys initially attempt to create a signal fire.

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

a.) Determine the slope of the tangent line to the parabola $y = 4x - x^2$ at the point $(1, 3)$

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

$\displaystyle \lim \limits_{x \to a} \frac{f(x) - f(a)} {x - a}$

Here, we have $a = 1$ and $f(x) = 4x - x^2$, so the slope is


$
\begin{equation}
\begin{aligned}

\displaystyle m =& \lim \limits_{x \to 1} \frac{f(x) - f(a)}{x - 1}\\
\\
\displaystyle m =& \lim \limits_{x \to 1} \frac{4x - x^2 - [4(1) - (1)^2]}{x - 1}
&& \text{ Substituting value of $a$ and $x$}\\
\\
\displaystyle m =& \lim \limits_{x \to 1} \frac{4x - x^2 - 3}{x - 1}
&& \text{ Factor the numerator}\\
\\
\displaystyle m =& \lim \limits_{x \to 1} \frac{-1(x - 3) \cancel{(x - 1)}}{\cancel{x - 1}}
&& \text{ Cancel out like terms and simplify}\\
\\
\displaystyle m =& \lim \limits_{x \to 1} (-x+3) = -1+3= 2
&& \text{ Evaluate the limit }\\

\end{aligned}
\end{equation}
$

Therefore,
The slope of the tangent line is $m=2$
$(ii)$ Using the equation

$\displaystyle m = \lim \limits_{h \to 0} \frac{f (a + h) - f(a)}{h}$

Let $f(x) = 4x - x^2$. So the slope of the tangent line at $(1, 3)$ is


$
\begin{equation}
\begin{aligned}

\displaystyle m =& \lim \limits_{h \to 0} \frac{f(1 + h) - f(1)}{h}\\
\\
\displaystyle m =& \lim \limits_{h \to 0} \frac{4(1 + h) - ( 1 + h)^2 - [4(1) - (1)^2]}{h}
&& \text{ Subsitute value of $a$} \\
\\
\displaystyle m =& \lim \limits_{h \to 0} \frac{4 + 4h - ( 1 + 2h + h^2) - 3}{h}
&& \text{ Expand and simplify }\\
\\
\displaystyle m =& \lim \limits_{h \to 0} \frac{2h - h^2}{h}
&& \text{ Factor the numerator}\\
\\
\displaystyle m =& \lim \limits_{h \to 0} \frac{\cancel{h} ( 2 - h)}{\cancel{h}}
&& \text{ Cancel out like terms }\\
\\
\displaystyle m =& \lim \limits_{h \to 0} (2 - h) = 2 - 0 = 2
&& \text{ Evaluate the limit}\\
\end{aligned}
\end{equation}
$

Therefore,
The slope of the tangent line is $m=2$
b.) Write an expression of the tangent line in part (a).

Using the point slope form


$
\begin{equation}
\begin{aligned}

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

Therefore,
The equation of the tangent line at $(1,3)$ is $y = 2x + 1$
c.) Illustrate the graph of the parabola and the tangent line. As a check on your work, zoom in toward the point $(1,3)$ until
the parabola and the tangent line are indistinguishable.