The Newton’s method of obtaining the second approximation by using a graph.

Single Variable Calculus: Concepts...

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

Single Variable Calculus: Concepts...

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

Solutions

Chapter 4, Problem 9RCC

a.

To determine

The Newton’s method of obtaining the second approximation by using a graph.

Expert Solution

Explanation of Solution

Given information:

The initial approximation is x1 to a root of the equation f(x)=0 .

Calculations:

Newton’s method of obtaining the second approximation is done by using the formula,

xn+1=xnf(xn)f'(xn)x2=x1f(x1)f'(x1)

For getting the third root the same formula is followed. The process is kept on repeating and it finally converges to a desired root.

b.

To determine

Expert Solution

Explanation of Solution

Given information:

The initial approximation is x1 to a root of the equation f(x)=0 .

Calculations:

Newton’s method of obtaining the second approximation is done by using the formula,

xn+1=xnf(xn)f'(xn)x2=x1f(x1)f'(x1)

For getting the third root the same formula is followed. The process is kept on repeating and it finally converges to a desired root.

c.

To determine

Expert Solution

Explanation of Solution

Given information:

The initial approximation is x1 to a root of the equation f(x)=0 .

Calculations:

Newton’s method of obtaining the second approximation is done by using the formula,

xn+1=xnf(xn)f'(xn)x2=x1f(x1)f'(x1)

For getting the third root the same formula is followed. The process is kept on repeating and it finally converges to a desired root.

d.

To determine

Expert Solution

Explanation of Solution

Given information:

The initial approximation is x1 to a root of the equation f(x)=0 .

Calculations:

Newton’s method of obtaining the approximation is done by using the formula,

xn+1=xnf(xn)f'(xn)

Several approximations are taken and the process is kept on repeating until it finally converges to a desired root. Under certain circumstances the method fails or works very slowly. This happens when f'(x1) is close to zero. Also there can be certain situation when the approximation is outside the domain of f . In such cases the method will fail.

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