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 3E
To determine

To find: The second approximation x2.

Expert Solution

Answer to Problem 3E

The second approximation is x2=92.

Explanation of Solution

Given:

The tangent line to the curve y=f(x) at the point (2,5) is y=92x.

Initial approximations are x1=2,f(x1)=5.

Calculation:

Calculate the derivative of y.

dydx=d(92x)dx=2

Calculate x2 by using Newton’s method.

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

Substitute n=1, we get x2=x1f(x1)f'(x1).

x2=(2)5(2)=2+52=4+52=92

Thus, the second approximation is x2=92.

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