1) The complete table is shown in the attachment .
2) The direction field is shown in attachment.
3) The given differential equation is:

We separate variable to get:

We integrate both sides wrt x to get:

This implies that:


Or

We apply the initial condition:



The particular solution is:

4) See attachment
Answer:
The discussion suggests that the narrator understands the reasons that make Shamengwa pay so much attention to appearance.
Explanation:
The discussion in the second paragraph suggests that the narrator is very empathetic and understandable, he understands Shamengwa, analyzes him and manages to develop sympathy, understanding and acceptance of Shamengwa to the point of being able to accept and understand the reasons that lead Shamengwa to pay so much attention to appearance, even neglecting other elements of his life.
(1) The integral is straightforward; <em>x</em> ranges between two constants, and <em>y</em> ranges between two functions of <em>x</em> that don't intersect.

(2) First find where the two curves intersect:
<em>y</em> ² - 4 = -3<em>y</em>
<em>y</em> ² + 3<em>y</em> - 4 = 0
(<em>y</em> + 4) (<em>y</em> - 1) = 0
<em>y</em> = -4, <em>y</em> = 1 → <em>x</em> = 12, <em>x</em> = -3
That is, they intersect at the points (-3, 1) and (12, -4). Since <em>x</em> ranges between two explicit functions of <em>y</em>, you can capture the area with one integral if you integrate with respect to <em>x</em> first:

(3) No special tricks here, <em>x</em> is again bounded between two constants and <em>y</em> between two explicit functions of <em>x</em>.

Taste (gustation) and smell (olfaction) are called chemical senses because both have sensory receptors that respond to molecules in the food we eat or in the air we breathe.