BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 2.2, Problem 30E

a.

To determine

To evaluate the given function for given values.

Expert Solution

Answer to Problem 30E

  h(1)=0.557408h(0.5)=0.37042h(0.1)=0.334672h(0.05)=0.333667h(0.01)=0.333347h(0.05)=0.333337

Explanation of Solution

Given:

The given function is h(x)=tanxxx3

Calculation:

Substituting the following values in the given function as follows-

  h(x)=tanxxx3h(1)=0.557408h(0.5)=0.37042h(0.1)=0.334672h(0.05)=0.333667h(0.01)=0.333347h(0.05)=0.333337

b.

To determine

To guess the value of given function.

Expert Solution

Answer to Problem 30E

  13

Explanation of Solution

Given:

The given function is limx0tanxxx3

Calculation:

  limx0tanxxx3limx0tanxxx3=0.33333=13

c.

To determine

To evaluate h(x) for successively smaller values of x and to explain whether your guess is correct.

Expert Solution

Answer to Problem 30E

No.

Explanation of Solution

Given:

The given function is limx0tanxxx3

Calculation:

The following is the table of all smaller values-

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 2.2, Problem 30E , additional homework tip  1

The guess in part (b) does not seem to be correct.

d.

To determine

To graph the function h in the viewing rectangle [1,1] by [0,1] and continue to zoom until distortions are observed and then compare the results.

Expert Solution

Explanation of Solution

Given:

The given function is limx0tanxxx3

Calculation:

The following are the graphs-

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 2.2, Problem 30E , additional homework tip  2

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 2.2, Problem 30E , additional homework tip  3

In part (C), it was observed that limx0tanxxx3=0

From the above graphs the limit does not approach to a specific value, hence the limit does not exist.

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