How can fear be dangerous in "Once Upon a Time"?

In Nadine Gordimer's “Once Upon a Time,” fear proves to be the family’s downfall. A family lives in a city in which there is great social unrest—modeled largely on South Africa—and fears riots and burglaries. Once further security is suggested by the husband’s mother, described as a “wise old witch,” the couple find themselves in an escalating war against their own fear. A neighborhood watch program is not enough to assuage their fears, so they get an electronically controlled fence. Having noticed a hole in one aspect of their security, they seek to mend it. Ironically, many of these measures make them more vulnerable, such as the alarms:

The alarms called to one another across the gardens in shrills and bleats and wails that everyone soon became accustomed to, so that the din roused the inhabitants of the suburb no more than the croak of frogs and musical grating of cicadas' legs. Under cover of the electronic harpies' discourse intruders sawed the iron bars and broke into homes, taking away hi-fi equipment, television sets, cassette players, cameras and radios, jewelry and clothing, and sometimes were hungry enough to devour everything in the refrigerator or paused audaciously to drink the whiskey in the cabinets or patio bars.

Quite plainly, the alarms cause more problems than they solve; however, the family does not appear to realize this fact. Their fear outweighs their common sense.
 
Near the end of the story, the family possesses an electronically-controlled fence, alarms, a seven-foot tall fence, and trusted employment: they ought to feel safe. The sight of their cat scaling the fence causes their security concerns to well up again, so they choose to arm the top of their fence with a vicious wire coil. Their child, after reading Sleeping Beauty, tries to make his way through the thorns to find a princess, but instead gets caught in the razors; he dies as a result.
 
Fear is the rationale behind the family’s actions, and look where it brought them: their only child is dead, indirectly by their hand. They do not even have the satisfaction of knowing that their efforts kept them safe, because they so clearly didn’t. Their internal desire for safety outpaced the actual threat at hand—in other words, their fear was disproportionate—and it led to the loss of their child.

How did China’s geography both help and hinder China’s development as a country?

Questions like this cannot be answered definitively.  We cannot go back and rerun China’s history, giving it different geography, to see what happens.  Instead, we can only speculate.  One famous speculation about the impact of China’s geography comes from Jared Diamond’s book Guns, Germs, and Steel.
Diamond says that China’s geography initially helped the country.  He says (on p. 414) that China’s heartland did not have many barriers to break it up.  Its two major river valleys were easily connected.  This allowed the civilization of the north to interact with the civilization of the south.  The two civilizations could share ideas and strengthen one another.  This, Diamond says, helped China become a very strong and advanced country by the early 1400s.  At that point, it was more developed than European countries were.  Thus, its geography helped it by allowing it to become a unified civilization very quickly.
However, Diamond says that this geography then caused China to lose its lead over Europe.  Because China was so geographically interconnected, it was able to become one unified country instead of being many small countries as existed in Western Europe.  In Europe, the countries competed with one another and forced each other to develop.  In China, there was only one country and there was no competition.  This meant that China did not have to keep progressing.  It could stagnate in terms of technology without being conquered by other neighboring countries.  Because China was united and unchallenged, it did not have to get stronger.  In this way, Diamond says, its geography, which had once helped it rise, also helped make it fall.
https://www.prospectmagazine.co.uk/features/geography-biology-europe-fertile-crescent

Referencing three of the following authors – Smith, Robespierre, Marx, Lenin, Marcos – define and contrast both Capitalism and Socialism. What are the core principles defining each system? What is problematic about each system? Which is better or more desirable?

Based on your question, I'll discuss Marx, Robespierre, and Smith.
History tells us that Maximilien Robespierre greatly admired the philosophies of Jean-Jacques Rousseau. Karl Marx himself was also influenced by Rousseau's socialist ideas. In fact, both Robespierre and Marx championed Rousseau's conception of democratic egalitarianism. They supported the abolition of private property and believed in Rousseau's idea of the "social contract," where the citizenry are afforded the right to replace a government that fails to secure their natural rights.
Robespierre and Marx viewed egalitarianism as the highest goal of a socialist state. In such a state, the government is (or should be) the defender of virtue and democracy. Marx believed that a socialist government should be first (and foremost) a proletariat autocracy. The proletariat or working classes would rule over the petty bourgeoisie and peasants, effectively stopping the ruling bourgeoisie elites from consolidating power in their hands.
Marx believed that wealth concentrated in the hands of a bourgeoisie elite few was morally wrong. Because the ruling elites controlled all enterprise, commerce, industry, media entities, and academic institutions in a country, the proletariat and peasantry would always be kept impoverished and disenfranchised. 
In Marx and Robespierre's socialist state, no one would own more than his neighbor. The state/government would apportion to each his need. Meanwhile, Adam Smith supported the capitalist ideals of a market economy, one that generates consumer choice, promotes economic growth, and increases production efficiency. Smith opposed the idea of mercantilism, where the government/state closely regulated industry and commerce. He believed that the government would be less efficient in apportioning economic resources than the private sector.
The core difference between a socialist and capitalist economy rests on who controls the production and distribution of goods and services. Marx and Robespierre supported the idea of a central planning entity regulating industry/commerce and then apportioning the resultant wealth to its citizenry. Meanwhile, Smith argued that an economy functioned best when market forces were allowed free rein, unshackled by burdensome government regulations and oversight. Smith believed that the best way to bring about freedom, democracy, and prosperity was to allow the inherent self-interest of human beings to flourish.
Smith maintained that self-interest and self-preservation were key motivators in facilitating economic growth. He argued that individuals would care more about their own welfare than a labyrinthine bureaucratic state. 
So, Marx, Smith, and Robespierre believed in equality, democracy, and freedom: they just disagreed on how to realize these goals. As to what is problematic about socialism and capitalism, I would argue that both share a similar weakness: the predilection of an elite few to appropriate all power and wealth towards its own purposes. You may have read Orwell's works, specifically Animal Farm and 1984, in your school/college readings. 
In Animal Farm, Napoleon ousts Snowball. While Snowball is a subtle portrayal of Trotsky, Napoleon epitomizes a composite of Lenin and Stalin. You may recall that, under the leadership of Napoleon, the pigs eventually become no different from the abusive and greedy human masters who previously ruled the farm. Snowball's Trotskyian ideals are eclipsed by Napoleon's brutality. Thus, in both capitalist and socialist economies, there is the danger of power and wealth becoming entrenched in the hands of an elite few. In such a situation, it matters little whether a central planning state or a free market economy controls industry and commerce. The populace will remain disenfranchised and marginalized.
As to which system is better or more desirable, I hope that my answer helps you to make that decision for yourself. Thanks for a thought-provoking question!
 
 
 
 
 
https://www.historytoday.com/archive/robespierre-and-terror

https://www.marxists.org/history/erol/ncm-7/lenin-socialism.htm

Where do Pyramus and Thisbe meet?

The rude mechanicals' play, The Most Lamentable Comedy and Most Cruel Death of Pyramus and Thisbe, is based on a Babylonian myth depicting separated lovers. In Shakespeare's version, Pyramus and Thisbe meet at a couple of places. First, they meet at and primarily communicate through a hole in the wall that separates them. Additionally, the lovers meet at night by Ninus' tomb to court each other in secret. It's also suggested that they meet under a mulberry tree, as Thisbe is depicted as waiting under a mulberry tree for Pyramus. This detail is consistent with the original Babylonian myth, which has the two lovers planning to meet under a mulberry tree.
The play as performed in A Midsummer Night's Dream is particularly hilarious, as it parodies the essential plot of Romeo and Juliet in addition to drawing from Babylonian myth. In that case, The Most Lamentable Comedy and Most Cruel Death of Pyramus and Thisbe is a great example of Shakespeare playfully making fun of himself.  
https://www.britannica.com/topic/Pyramus

Select a book printed in either the eighteenth or nineteenth century (like Jane Austen's Pride and Prejudice), and write out a quasi-facsimile transcription of its title page.

Austen's Pride and Prejudice was originally published in 1813 by a man named Thomas Egerton. Its title page reads, "Pride and Prejudice: A Novel. In Three Volumes." The line "In Three Volumes" is in smaller font than the first few lines. Below that, there is a line and then the following words in a smaller font: "By the Author of 'Sense and Sensibility." There is then another line and the description "Vol. 1." This is then followed by a line and, below that, the printing information, which includes, "London: Printed for T. Egerton, Military Library, Whitehall. 1813." You can see a picture of the original title page at the Jane Austen Society link below. 
To produce a facsimile of the title page of a book published in the eighteenth or nineteenth century, you could replicate this title page. Title pages, such as that for Pride and Prejudice, had a great deal of information, including their genre (such as a novel), the number of volumes they had, and any previous titles the author was known for. They also included the location of printing, the publisher, and the year.
http://www.jasna.org/austen/works/pride-prejudice/

Calculus of a Single Variable, Chapter 9, 9.9, Section 9.9, Problem 7

A power series centered at c=0 is follows the formula:
sum_(n=0)^oo a_nx^n = a_0+a_1x+a_2x^2+a_3x^3+...
The given function f(x)= 1/(1-3x) resembles the power series:
(1+x)^k = sum_(n=0)^oo (k(k-1)(k-2)...(k-n+1))/(n!) x ^n
or
(1+x)^k = 1+kx +(k(k-1))/(2!)x^2+(k(k-1)(k-2))/(3!)x^3+(k(k-1)(k-2)(k-3))/(4!)x^4+...
To evaluate the given function f(x) =1/(1-3x) centered at c=0 , we may apply Law of exponents: 1/x^n = x^(-n) .
f(x)= (1-3x) ^(-1)
Apply the aforementioned formula for power series on (1-3x) ^(-1) or (1+(-3x))^(-1) , we may replace "x " with "-3x " and "k" with "-1 ". We let:
(1+(-3x))^(-1) = sum_(n=0)^oo (-1(-1-1)(-1-2)...(-1-n+1))/(n!) (-3x) ^n
=sum_(n=0)^oo (-1(-2)(-3)...(-1-n+1))/(n!)(-3)^nx ^n
=1+(-1)(-3)^1x +(-1(-2))/(2!)(-3)^2x ^2+(-1(-2)(-3))/(3!)(-3)^3x ^3+(-1(-2)(-3)(-4))/(4!)(-3)^4x ^4+...
=1+3x +2/2*9*x ^2+(-6)/6(-27)x ^3+24/24*81*x ^4+...
=1+3x +9x ^2+27x ^3+81x ^4+...
= sum_(n=0)^oo (3x)^n
To determine the interval of convergence, we may apply geometric series test wherein the series sum_(n=0)^oo a*r^n is convergent if |r|lt1 or -1 ltrlt 1 . If |r|gt=1 then the geometric series diverges.
By comparing sum_(n=0)^oo (3x)^n or sum_(n=0)^oo 1*(3x)^n with sum_(n=0)^oo a*r^n , we determine: r =3x .
Apply the condition for convergence of geometric series: |r|lt1 .
|3x|lt1
-1 lt3xlt1
Divide each part by 3:
(-1)/3 lt(3x)/3lt1/3
-1/3ltxlt1/3
Final answer:
The power series sum_(n=0)^oo(3x)^n has an interval of convergence: -1/3 ltxlt1/3 .

What is a metaphor in Chapter 3 of Lord of the Flies?

Simon's behavior in chapter 3 has some rough correspondence with the life of Christ. When Simon pulls fruit from the trees to fill "the endless outstretched hands" of the littluns, it is as if Christ is performing a miracle of feeding the multitudes. After he feeds the others, Simon retreats, alone, to a sanctuary he has found for himself that seems lit from within with "candle-buds." His selflessness, introspection, and spirituality in this chapter and the book overall loosely parallel Christ wandering for forty days in the desert and being faced with temptations. Like Christ, Simon declines eating food (the fruit), vying for power (like Ralph and Jack), and going to the mountaintop (where the beast is thought to be). Like Christ, Simon is brutally killed. This chapter builds the elaborate metaphor of Simon's perhaps unwitting emulation of Christ and prefigures the boys' destruction of him.

In chapter 3 of Lord of the Flies, called "Huts on the Beach," we can see a metaphor in the sentence "They walked along, two continents of experience and feeling, unable to communicate." The "they" in this quote is referring to Jack and Ralph. 
First things first, we know this is a metaphor because the narrator is comparing the boys to continents and making this comparison without using "like" or "as." 
This is a particularly effective metaphor because it works on multiple levels. Continents are enormous, so the sentiment given here is that this terrible experience is causing the boys to have an enormous amount of new thoughts and feelings— enough to fill a continent. Generally speaking, continents are also separated and far apart from one another. We know from their conversations that Jack and Ralph have different priorities and aren't getting along, but this metaphor really emphasizes the idea that the two boys are on opposite wavelengths, thinking and feeling so differently from one another that trying to communicate is about as effective as trying to shout to someone from a different continent.