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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 2, Problem 38RE

(a)

To determine

**To find:** The asymptotes of the graph of

Expert Solution

The vertical asymptote is

**Calculation:**

Recall that the line

Take limit on the above.

Thus, the horizontal asymptote is

Recall that the line

*x* approaches

Thus, the vertical asymptote is

**Graph:**

Use the above information and trace the graph of

**Observation:**

*f.*

(b)

To determine

**To sketch:** The graph of

Expert Solution

**Calculation:**

From the above graph in part a,

it is cleared that *f.*

Both the two disjoint curves of *f* have negative slope.

Thus, the graph of

For the curve present below the *y-*axis,

the value of the slope decreases as the curve moves from left to right

approaching the line

Thus, the graph of

For the curve present above the *y-*axis,

the value of the slope increases as the curve moves from left to right

approaching the line

Thus, the graph of

**Graph:**

Use the information above and trace the graph of

(c)

To determine

**To find:** The derivative of

Expert Solution

The derivative is

**Formula used:**

The derivative of a function *f,* denoted by

**Calculation:**

Obtain the derivative of the function

Compute

Simplify the numerator in the above expression

Since the limit *h* approaches zero but not equal to zero, cancel the common term *h* from both the numerator and the denominator,

Thus, the value of the derivative is

(d)

To determine

**To sketch:** The graph of

Expert Solution

**Graph:**

Use an online graphing calculator to sketch the graph of

**Observation:**

From Figure 3, it has been observed that

**Comparison:**

The function in Figure 3 seems to be the same graph which was sketched in part b.