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Math
CalculusSingle Variable Calculus: Early Transcendentals, Volume I8th Edition

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

8th Edition
James Stewart
ISBN: 9781305270343

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 29E
Problem 30E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
BuyFindarrow_forward

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 x2−a=0.

Formula used:

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

Calculation:

Let f(x)=x2−a and obtain the derivative of f(x).

Let the derivative of f′(x)=df(x)dx.

f′(x)=d(x2−a)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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Chapter 4.8,
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Chapter 4.8,
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