What did a typical bedroom belonging to a Qing Dynasty princess look like?

A good example of the room of a princess during the Qing Dynasty is the Palace of Gathering Elegance, one of the six western palaces and the place where the Empress Dowager Cixi lived in the 1800s and early 1900s in the Forbidden City in Beijing. A pair of bronze deer and a pair of bronze dragons flank the entrance to the palace as signs of harmony and wealth. These dragons were only supposed to be located where emperors lived. Within the palace, Cixi had a main hall for welcoming guests, a room to the east for worshipping Buddha (as she was a devout Buddhist), and a room to the west that was her bedroom. Her bedroom (still in existence) has a large brick bed (kang), built into an alcove, and a dressing table filled with cosmetics. Around her bed are shelves that held ornaments such as jade figurines. In addition, she had several hanging lanterns that were decorated with tassels and wall hangings, likely made of silk and depicting traditional Chinese scenes. The doors to her room were draped with curtains. For more information, see the book Empress Dowager Cixi by Jung Chang.

What does Banquo think about the witches' prophecies?

At first, Banquo is a bit in awe of the Weird women.  He remarks on their appearance and actions, wondering if they are truly earthly or supernatural in nature.  After the sisters tell Macbeth what his future will hold, Banquo requests some prediction for his life too: this implies that he might put some stock in their ability to tell the future.  They then tell him that he will father kings; so, he will never rule, but his progeny will.

After they've vanished, Banquo wonders if he and Macbeth have just seen something true or if they've taken some drug that caused them to hallucinate the women and their strange words.  Once Ross and Angus arrive to tell Macbeth that he's been awarded with the title Thane of Cawdor, just as the sisters said he would be, Banquo begins to think about how strange this seems, and he grows suspicious that things may not be exactly how they seem.  He warns Macbeth that

"oftentimes, to win us to our harm, / The instruments of darkness tell us truths, / Win us with honest trifles, to betray ’s / In deepest consequence" (1.3.125-129). 

In other words, he fears that perhaps the sisters are motivated by some evil purpose and have told Macbeth one small truth in order to compel Macbeth and Banquo to believe bigger lies so that the men can be lead more easily to their own destruction. 

`int x sin^3(x) dx` Evaluate the integral

You need to use integration by parts, such that:

`int u dv = uv - int vdu`

`u = x => du = dx`

`dv = sin^3 x => v = int sin^3 x dx`

You need to solve the integral `int sin^3 x dx ` such that:

`int sin^3 x dx = int sin^2 x* sin xdx`

Replace 1` - cos^2 x` for `sin^2 x` , such that:

`int sin^2 x* sin xdx = int (1 - cos^2 x)* sin xdx`

Use substitution` cos x = t => -sin x dx = dt:`

`int (1 - cos^2 x)* sin xdx = int (1 - t^2)* (-dt)`

`int (1 - t^2)* (-dt) = int (t^2 - 1) dt`

`int (t^2 - 1) dt = int t^2 dt - int dt`

`int (t^2 - 1) dt = t^3/3 - t + c`

Replace back cos x for t:

`int (1 - cos^2 x)* sin x dx =  (cos^3 x)/3 - cos x + c`

Hence, `v = int sin^3 x dx = (cos^3 x)/3 - cos x`

Using parts, yields:

`int x sin^3 x dx = x*((cos^3 x)/3 - cos x) - int ((cos^3 x)/3 - cos x) dx`

`int x sin^3 x dx = x*((cos^3 x)/3 - cos x) - int (cos^3 x)/3 dx + int cos x dx`

You need to solve the integral `int (cos^3 x)/3dx` , such that:

`int (cos^3 x)/3dx = (1/3) int cos^2 x*cos x dx`

Replace `1 - sin^2 x ` for `cos^2 x:`

`(1/3) int (1 - sin^2 x)*cos x dx`

Use substitution `sin x = t => cos x dx = dt`

`(1/3) int (1 - sin^2 x)*cos x dx = (1/3)*int (1 - t^2) dt = (1/3) t - (1/3)(t^3)/3 + c`

`(1/3) int (1 - sin^2 x)*cos x dx = (1/3) sin x- (1/3)(sin^3 x)/3 + c`

Hence, the result of integration is: `int x sin^3 x dx = x*((cos^3 x)/3 -cos x) - ((1/3) sin x- (1/3)(sin^3 x)/3) + sin x + c`

What are the important points for Macbeth?

1. Macbeth receives a prophecy from three witches that he will be granted a new title, the Thane of Cawdor, and he will become king.  When he is named Thane of Cawdor, he immediately begins to consider how to make the second part of the prophecy come true.  Also, the witches tell Banquo that his sons will be kings.

2. Macbeth and his wife begin to plot the murder of the current king so that Macbeth can become king.  After some indecision, Macbeth stabs King Duncan, Duncan's sons flee, and Macbeth is crowned.

3. Macbeth and Lady Macbeth seem to grow apart a bit, and neither is particularly happy in their new roles as king and queen, especially because they have no children and it is Banquo's children who will, apparently, get the throne eventually.  So, Macbeth tries to have Banquo and Fleance, his son, murdered, but Fleance escapes.  People become more suspicious of Macbeth.

4. Another thane, Macduff, approaches the man who should have taken the throne, Duncan's son, Malcolm.  He convinces him to return to Scotland with an army and overthrow Macbeth.  In the meantime, Macbeth orders the murders of Macduff's family.

5. The three witches show Macbeth some apparitions that make him feel secure in his position, and then a war begins between Macbeth's army and Malcolm's army.

6. Macduff successfully kills Macbeth, bringing the apparitions' statements to fruition, and Malcolm takes the throne.

How is maternal love conveyed in the text of Romeo and Juliet?

Lady Montague expresses her maternal love by being protective of Romeo and concerned for his physical safety and emotional well-being.  When she and her husband arrive at the scene of the street fight, she asks Benvolio if he has seen Romeo today.  She says, "Right glad I am he was not at this fray" (1.1.119).  She is worried about him because, as Lord Montague says, he has been so sad lately that he just cries and shuts himself away in his bedroom, even closing the curtains so that the sunlight cannot get in. 

Lady Capulet expresses her maternal love in a somewhat less obvious way.  She speaks to Juliet about the fact that Count Paris wants to marry her, saying that many girls are made mothers by the time they are her age.  She seems to feel that getting Juliet married is her primary duty, as it is really the only topic we ever see them discuss.  Lady Capulet is the one to present Juliet with the news, after Tybalt's death, that Lord Capulet has scheduled her wedding to Paris for later that week, and when Juliet refuses this plan, her mother attempts to wash her hands of her.  After Lord Capulet promises to allow Juliet to starve in the streets should she continue to disobey him, Lady Capulet says, "Talk not to me, for I'll not speak a word. / Do as thou wilt, for I have done with thee" (3.5.214-215).  Therefore, her maternal love seems a great deal weaker than Lady Montague's. 

When does the atmosphere surrounding the ride begin to change in "Because I Could Not Stop for Death" ?

In Emily Dickinson's "Because I Could Not Stop for Death," the atmosphere surrounding the ride begins to alter and grow colder when the carriage pauses before what the speaker recognizes as a grave.

The lighthearted tone of the poem, indicated by the speaker's mention that she has put away her "labor and leisure" for an unexpected ride, changes after the driver and the speaker pass the setting sun and the speaker grows cold and quivers with a chill. Then, as the driver approaches a "House" in the ground, the roof barely apparent, the speaker must wonder.  For, it is then that the speaker begins to realize that her ride has not been spontaneous, but is ironically, gravely serious.

We paused before a House that seemed
A swelling of the Ground--
The Roof was scarcely visible--
The Cornice--in the Ground--

In the last stanza, the tone is markedly somber as the speaker narrates from the "House" in the ground that it has been ages since she first guessed that the carriage was headed to the cemetery. The repetition of the words Ground and Eternity certainly connote the serious and final destination of the carriage ride--"toward Eternity."

Why do the family members try to avoid talking of the ghost in "The Canterville Ghost"?

From their arrival at Canterville Chase, the Otis family are reluctant to talk about the ghost. In short, they do not believe in the supernatural because they are advocates of science and reason, as Mr Otis explains to Lord Canterville in Chapter One:

But there is no such thing, sir, as a ghost, and I guess the laws of Nature are not going to be suspended for the British aristocracy.

Similarly, when the family spends the day driving around the neighbourhood, they deliberately stop themselves from speaking about the ghost. According to the narrator, the family does this to prevent the "primary conditions of receptive expectation." In other words, if the family does not accept the possibility of a ghost, they are far less likely to experience any supernatural phenomena and this is crucial in safeguarding their scientific principles and beliefs.

This reluctance to talk about the ghost (so as not to accept his existence) reflects the culture clash which exists between the Otis family and the British aristocracy, one of the story's wider themes. The rational and scientific background of the Otis family acts like a barrier between these two opposing worlds and provides the story's conflict. (Please see the second reference link for more information on this theme).