For Wallace, is the garden just a mere retreat from mundane life? What makes the reader sympathize with the character?

Wallace confides in the narrator, Redmond, that he is a haunted man. He says that he is haunted by a “beauty and happiness that fills his heart with insatiable longings that makes all the interests and spectacle of worldly life seem dull and tedious and vain.” However, this does not prevent him from achieving success in life, for he excels in school and in his professional life, and especially when he is able to concentrate on these things.
Wallace talks to the narrator about the door in the wall two times: once when the two are still students in school; and later when they are all grown up—actually just a month before his death. He says that he first saw the door when he was only five years old. Upon seeing the door, he had been overwhelmed by feelings of curiosity: “an attraction, a desire to get to the Door and open it and walk in.” However, these strong feelings were accompanied by great hesitation on his part to yield to the need to get through the door. In the end, he had submitted to the attraction he felt for the door, pushed it open and walked into the most amazing garden. He gives the following description of the garden to the narrator:

There was something in the very air of it that exhilarated, that gave one a sense of lightness and good happening and wellbeing; there was something in the sight of it that made all its color clean and perfect and subtly luminous.

Further, he adds that

in the very moment the door swung to behind me, I forgot the road with its fallen chestnut leaves, its cabs and tradesmen’s carts, I forgot the sort of gravitational pull back to the discipline and obedience of home. I forgot all hesitations and fear, forgot discretion, forgot all the intimate realities of this life.

He explains to the narrator that his return back to earth had been a harsh reality; he had been grief-stricken, disconsolate.
Wallace sees the door about four times as a young man but does not walk through the door to experience the garden. In his adult life, he sees the door more frequently, especially when overwhelmed by the struggles of life.
Thus for Wallace, the garden is more than “just a mere retreat from mundane life.” The garden represents the ultimate ideal life for Wallace. He dreams of it, yearns for the chance to revisit it. The garden encapsulates all those good things that Wallace desires but cannot have. The reader sympathizes with Wallace, for the garden almost ruins all the goodness that he could have experienced in everyday life. One wishes that the younger Wallace never had a chance to walk through that door the first time. Also, the fact that the door finally kills Wallace is saddening. Yet, the reader is not surprised by this event. The paradise that exists beyond the door is unworldly, thus unattainable except, maybe, in death.

Why does Claudia plan on returning home in From the Mixed-Up Files of Mrs. Basil E. Frankweiler by E. L. Konigsburg?

Claudia is not running away from home for good.  The whole purpose of running away from home is to show her parents how important she is.  Claudia is the oldest, and she is feeling unappreciated.  Her life is boring, and she always has to do the chores while her brothers don’t.  This is why she saves up her money to run away.  It will accomplish both purposes.  Her parents will realize how valuable she is, and she will get some excitement.

Since she intended to return home after everyone had learned a lesson in Claudia appreciation, she had to save money for her return trip, too, which was like full fare one way. (Ch. 1)

Claudia wants her parents to know what happened, so she mails her parents a letter, telling them she ran away and not to contact the FBI. She doesn't seem to think they will panic.  That is still probably more practical than sending the letter with the Corn Flakes box tops to get twenty-five cents.  Yes, she may need the money, but how does she expect to get it?  Jamie points this out.
Claudia chose Jamie to accompany her in running away mostly because he had money.  Even though he was nine, he earned money cheating at cards, and he also saved his money.  Claudia had been saving for three weeks and still did not have as much money as he did.  He wasn't thrilled with her idea to run away to the Metropolitan Museum of Art in New York City at first, but she was older.

Is the subject of history considered a narrative?

History is definitely a narrative, or story. In fact the word story is incorporated into this word history; interestingly, the word for history and for story are exactly the same word in French: histoire. 
Napoleon declared history as "a story retold"; that is, the history of events are retold usually by the victorious country or the country which holds power. Therefore, this history does become a story, a tale told according to the power in control. That this definition is true can be verified by an examination of history books that have a narrative in them about World War II, for instance. Certainly, the presentation of historical accounts differ greatly depending upon which side--Allies or Axis--that the account is written.
When Napoleon conquered a country during his drive for empire, one of his first actions was to gain control of the newspapers. In this way, he controlled history since the written word was essentially the only source of information. While documents are used to record history, many of them are written by those whose ideology matches that of the power in control. In Hitler's Germany, of course, the media was certainly controlled by the Nazi regime, so the record of historical events was altered greatly. Therefore, even historical writings of a later date must be, at least, somewhat affected by what has been omitted in such writings. In American history, for instance, an examination of older history books and certain social issues of years ago and the modern record of these issues provides support for the argument of Napoleon that the "story" of a country is retold.
https://www.thefreedictionary.com/historical+record

The Merriam Webster Dictionary defines a narrative as a story that is told or written. Because all events of history have happened in the past, we have to rely on individuals’ stories and accounts of what occurred when considering an historic event. When reading a history textbook, we are only getting one viewpoint or account of that moment in time. For example, a quick review of history textbooks from the United States, Japan, France, and Germany regarding World War II would result in an immediate understanding of the narrative nature of history. Although each text could be considered an accurate account of that period in history, the historian’s biased viewpoint and perspective on the event cannot reasonably be denied. As the presidential campaign heats up in the United States, we see the same events described differently on a daily basis. Therefore, the answer to your question is yes, history is a narrative of events occurring in the past. 
https://www.merriam-webster.com/dictionary/narrative

What is the nature of political science?

Political science has been a field of study going back as far as the 5th Century BCE when Aristotle defined the term as the study of examining the function of the state. Aristotle considered political science to be of utmost importance since it affects nearly every other human endeavor. Much of what we understand as modern political science was first posited during the European Enlightenment by philosophers such as Thomas Hobbes, Voltaire, and John Locke. They wanted to know exactly what the relationships and obligations between citizens and governments was and ought to be.
The current study of political science fits under the broader category of social sciences. It is specifically related to the study of laws, government, and politics. Political scientists examine the connections between the functions of the state and the conditions that it creates. They take into account human behavior and political thinking. Political science also must take into consideration many other subjects such as economics, sociology, behaviorism, and history, as these fields all affect the role and function of the state in contemporary society.
Political science also examines trends in politics and the function of the state across geography and over time. As such, people in this field are often sought after to make predictions by collecting and studying relevant data. The hope is that political scientists can predict a crisis before it occurs and lay out the actions needed to avoid one.
There are five commonly recognized sub-disciplines of political science. These are public administration, comparative politics, political theory, public law, and international relations. Each examines the role of politics and government within these particular fields.
Many people who study political science find employment as career politicians, campaign managers, lobbyists, and political consultants. Many can also apply it to a legal profession or in business since there is a lot of cross-over in these fields as well.
https://www.ru.nl/politicalscience/profile/what-political-0/

Political science is an academic discipline. Its focus is the theory and practice of politics at every level of governance. This involves so many different facets that it is difficult to characterize the essential nature of the discipline. Generally, however, political science focuses on a few key areas. One is political theory. Since the ancient Greeks, philosophers have thought hard about the best ways to organize societies, the nature of political behavior, and other important questions. These issues still occupy political scientists. Another aspect of political science is comparative politics, the comparison of different aspects of varying political systems and cultures and their counterparts. However, political science is also a quantitative discipline that attempts to measure political trends, behaviors, and practices through hard data. This means that political science has close relationships with other disciplines, including communications, psychology, sociology, and history. The best way to characterize the nature of political science is to say that it is a very wide-ranging and diverse discipline.
https://www.polisci.washington.edu/what-political-science

What is a detailed summary of The Passion?

The Passion is a British novel written by author Jeannette Winterson in 1987. The novel revolves around a French man named Henri who is sent off to fight for Napoleon in the Napoleonic wars. When the novel begins, Henri mentions his dreams of becoming a drummer, but he soon finds out he will instead be helping in the kitchen. Despite his disappointment, Henri makes the most of his role, primarily because he gets to spend time with Napoleon.
While in the grand armee, Henri forms friendships with two men. Patrick is an ex-priest who tells Henri a lot of false stories, and Domino is a impulsive horse keeper. They all live together at Napoleon's base camp as France devises a plan to invade England; however, Henri soon becomes discouraged over the sheer amount of death and destruction taking place in the army. Many of his fellow soldiers and friends have died, and he begins to question whether or not the military is the place for him.
While all of his is happening, the novel shifts focus to Villanelle, a beautiful red-haired Italian woman from Venice who is living in Russia. She is in love with another woman whom she refers to as the "Queen of Spades," but she knows it will never go anywhere, because the woman is already married to a man.
Years pass and Napoleon's army arrives in Moscow, where Henri and Villanelle's fates intertwine. Villanelle is currently working as a prostitute, and Henri learns that her husband sold her into the prostitution ring through Napoleon's army. By this point, Henri has had enough, so he convinces both Villanelle and Patrick to desert the army. Despite Villanelle's broken heart over the Queen of Spades, she pretends to be Henri's wife. Henri falls in love with her, but she tells him that she cannot commit to him, because her heart still belongs to the Queen.
The troupe decides to flee to Venice, but Patrick unfortunately falls ill and does not finish the trip alive. Henri and Villanelle escape to Villanelle's childhood home, where her parents urge her to marry Henri. She tells them that she cannot marry him because she is not in love with him. He feels more like family than a lover. Despite Villanelle's rejection, Henri still loves and cares for her. He ends up killing her husband by cutting his heart out, but he confesses to his crime and is soon imprisoned for the murder.
While in prison, Henri awaits frequent visits from Villanelle. She eventually becomes pregnant with their child but still refuses to marry him, which makes Henri incredibly upset. He eventually cuts all ties with Villanelle because it hurts him too much to imagine a life without her as his wife.
As time goes on, Villanelle has the child and realizes that she will never spend her life with the Queen of Spades, no matter how madly she loves her. Meanwhile, Henri loses his grip on reality in the jail cell. He still sees Villanelle walking with their daughter, and the two often wave at him, but he now understands that they will never be together. He continues to write about his feelings for Villanelle until the end of the novel, mentioning that he does not wish anything bad upon Villanelle even though they cannot be together.

Calculus of a Single Variable, Chapter 5, 5.6, Section 5.6, Problem 59

Equation of a tangent line to the graph of function f at point (x_0,y_0) is given by y=y_0+f'(x_0)(x-x_0).
The first step to finding equation of tangent line is to calculate the derivative of the given function.
y'=2cdot1/sqrt(1-x^2)
Now we calculate the value of the derivative at the given point.
y'(1/2)=2/sqrt(1-(1/2)^2)=2/sqrt(1-1/4)=2/sqrt(3/4)=2/(sqrt3/2)=4/sqrt3=(4sqrt3)/3
We now have everything needed to write the equation of the tangent line.
y=pi/3+(4sqrt3)/3(x-1/2)
y=(4sqrt3)/3x+(pi-2sqrt3)/3
Graph of the function along with the tangent line can be seen in the image below.

The diary was Anne’s best friend with whom she could share all her secrets. Justify this statement by stating evidence from the text.

In Anne Frank's diary, written while she was in hiding between the dates of June 12, 1942, and August 4, 1944, she clearly states that the diary is her best friend and confidante. In fact, at the very onset of the diary, she writes, "I hope I will be able to confide everything to you, as I have never been able to confide in anyone, and I hope you will be a great source of comfort and support" (June 12, 1942).
Further on in her diary, Anne confides that she really has no friends and that the diary will be her best friend. She personifies the diary, naming her Kitty: "I want the diary to be my friend, and I'm going to call this friend Kitty" (June 20, 1942). In this way, the diary takes on an almost human quality as Anne shares her deepest thoughts and emotions with her friend, 'Kitty.'
Throughout the years that Anne wrote in her diary from the ages of thirteen to fifteen, she depended on the diary to "listen" to her. She wrote about her fears, her hopes, and her life in hiding. She wrote about becoming a woman: "It's such a momentous event" (Nov. 2, 1942). All that a young girl would share with her friends, Anne shared with Kitty.
Toward the end of the diary Anne confides to Kitty that she has two sides to her personality: "I'm split in two. One side contains my exuberant cheerfulness, my flippancy, my joy in life . . . [the other side] is much purer, deeper and finer" (Aug. 1, 1944). Anne goes on to state that other people have not seen her 'better' side. In this way, Anne's diary, Kitty, has become her best friend, the only friend who has seen the real Anne.