   Chapter 4.8, Problem 29E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# (a) Apply Newton’s method to the equation x2 − a = 0 to derive the following square-root algorithm (used by the ancient Babylonians to compute a ): x n + 1 = 1 2 ( x n + a x n ) (b) Use part (a) to compute 1000 correct to six decimal places.

(a)

To determine

To Derive: The algorithm for the square root of the given equation by Newton’s method.

Explanation

Given:

The equation is x2a=0.

Formula used:

The Newton’s method is xn+1=xnf(xn)f(xn).

Calculation:

Let f(x)=x2a and obtain the derivative of f(x).

Let the derivative of f(x)=df(x)dx.

f(x)=d(x2a)dx=d(x2)

(b)

To determine

To Compute: The root of 1000 correct to six decimal places by using part (a).

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