Chapter 12.2, Problem 39E

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

Each of Problems 41 and 42 has the form

dx.

(a) Evaluate each integral to obtain a family of functions.

**(b) Find and graph the family member that passes through the point (0,2). Call that function**

**(c) Find any x-values where**

is.

**(d) At the x-values found in part (c), what kind of tangent line does**

have?

**(a)**

To determine

**To calculate:** The value of integral

Explanation

**Given Information:**

The provided integral is,

**Formula used:**

According to the power formula of integrals, if

**Calculation:**

Consider the provided integral:

Rewrite the provided integral by multiplying and dividing by

Consider the power rule of integrals:

Now, to use the power rule, the integrand should have the function

Here,

Then, on obtaining differentials,

Thus,

All required parts are present, so the integral is of the form,

**(b)**

To determine

**To graph:** The family member of the solution to part (a) which passes through point

**(c)**

To determine

The values of *x* where the function

**(d)**

To determine

The nature of tangent line of

Sect-12.1 P-1CPSect-12.1 P-2CPSect-12.1 P-1ESect-12.1 P-2ESect-12.1 P-3ESect-12.1 P-4ESect-12.1 P-5ESect-12.1 P-6ESect-12.1 P-7ESect-12.1 P-8E

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