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 4.7, Problem 4E

(a)

To determine

To sketch: The graph of a tangent line at x1=0.

Expert Solution

Explanation of Solution

At first draw the tangent line at the point x1=0 and the tangent line intercept the x -axis.

Let the intercept point is x2 and the value of that point is negative.

Similarly draw the tangent line at the point x2 and the tangent line intercept the x-axis.

Let that intercept point is x3 and value of that point more negative than previous one.

Graph:

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 4.7, Problem 4E , additional homework tip  1

Observation:

From Figure 1, observed that the point x1=0 is Newton’s method fail.

(b)

To determine

To sketch: The graph of a tangent line at x1 = 1.

Expert Solution

Explanation of Solution

At first draw the graph of tangent line at the point x1=1 and the tangent line intercept x-axis.

Let the intercept point is x2 and that is parallel to x-axis.

Graph:

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 4.7, Problem 4E , additional homework tip  2

Observation:

From Figure 2 observed that the Newton’s method fail.

(c)

To determine

To sketch: The graph of a tangent line at x1 = 3.

Expert Solution

Explanation of Solution

At first draw the tangent line at the point x1=4 and the tangent line intercept the x -axis.

Let the intercept point is x2.

Graph:

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 4.7, Problem 4E , additional homework tip  3

Observation:

From Figure 3, observed that the point x2=1 The Newton’s method fail.

(d)

To determine

To sketch: The graph of a tangent line at x1 = 4.

Expert Solution

Explanation of Solution

At first draw the graph of tangent line at the point x1=1 and the tangent line intercept x-axis.

Let the intercept point is x2 and that is parallel to x-axis.

Graph:

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 4.7, Problem 4E , additional homework tip  4

Observation:

From Figure 4 observed that the Newton’s method fail.

(e)

To determine

To sketch: The graph of a tangent line at x1 = 5.

Expert Solution

Explanation of Solution

At first draw the tangent line at the point x1=5 and the tangent line intercept the x -axis.

Let the intercept point is x2.

Similarly draw the tangent line at the point x2 and the tangent line intercept the x-axis.

Let that intercept point x3.

Graph:

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 4.7, Problem 4E , additional homework tip  5

Observation:

From Figure 5, observed that the point x1=5 is Newton’s method work.

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