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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 4.7, Problem 27E

To determine

**To find:** The Newton’s method fails for the given equation with any approximation

Expert Solution

**Given:**

The equation is

The initial approximation is

**Result Used:**

The Newton’s method is

**Graph:**

From the Figure 1, it is observed that the value gets doubled.

**Calculation:**

Let

Calculate the derivative of

Let

Substitute the value of

Set

Set

Similarly, proceed in the above manner.

**Observation:**

From the above calculation, each successive approximation gives the value twice than previous value.

Thus, if we consider the sequence of the Newton’s approximation fails to converge to the root