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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 2.7, Problem 50E

**(a)**

To determine

**To Show:** The function

Expert Solution

**Result Used:** The derivative of a function at **,**

**Proof:**

Consider the function,

Compute

Here, the function *x* tends to zero. That is,

Therefore, the derivative of the function does not exist at

Thus, the required proof is obtained.

**(b)**

To determine

**To find:** The value of

Expert Solution

The value of derivative of

**Given:**

The function

**Calculation:**

Obtain the derivative of the function

Compute

Simplify further,

Thus the value of the derivative at

**(c)**

To determine

**To Show:** The

Expert Solution

**Result Used:**

A curve has a vertical tangent line at *g* is continuous at

**Proof:**

Consider the equation

Substitute

Thus

The limit of the function

Therefore,

From part (b),

Take the limit of the function *x* approaches zero.

Since the function

By result, the curve

Thus, the curve

**(d)**

To determine

**To illustrate:** Thepart (c) by graphing

Expert Solution

**Graph:**

Use the online graphing calculator to draw the graph of the function

**Illustration:**

From Figure 1, it is clear that the *y*-axis is the vertical tangent to the curve