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Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

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BuyFindarrow_forward

Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

Using Newton's Method In Exercises 3-6, calculate two iterations of Newton's Method to approximate a zero of the function using the given initial guess.

f ( x ) = x 3 3 , x 1 = 1.4

To determine

To calculate: Two iterations of Newton’s Method to approximate a zero of the function, f(x)=x33 where, x1=1.4.

Explanation

Given:

The function is f(x)=x33 and the initial guess is x1=1.4.

Formula used:

The general Newton’s Formula to determine an approximation is:

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

The derivative for the function, xn is:

ddx(xn)=nxn1

Calculation:

The general Newton’s Formula to determine an approximation is:

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

The function is:

f(x)=x33

Differentiate both sides of the above function with respect to x.

f(x)=ddx(x33)=ddx(x3)ddx(3)

The derivative of a constant is always zero and use the formula, ddx(xn)=nxn1 to get the above derivative:

f(x)=3x0=3x2

Thus, the derivative of the function, f(x)=x33 is:

f'(x)=3x2

The first iteration is,

x1=1

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P-36RECh-3 P-37RECh-3 P-38RECh-3 P-39RECh-3 P-40RECh-3 P-41RECh-3 P-42RECh-3 P-43RECh-3 P-44RECh-3 P-45RECh-3 P-46RECh-3 P-47RECh-3 P-48RECh-3 P-49RECh-3 P-50RECh-3 P-51RECh-3 P-52RECh-3 P-53RECh-3 P-54RECh-3 P-55RECh-3 P-56RECh-3 P-57RECh-3 P-58RECh-3 P-59RECh-3 P-60RECh-3 P-61RECh-3 P-62RECh-3 P-63RECh-3 P-64RECh-3 P-65RECh-3 P-66RECh-3 P-67RECh-3 P-68RECh-3 P-69RECh-3 P-70RECh-3 P-71RECh-3 P-72RECh-3 P-73RECh-3 P-74RECh-3 P-75RECh-3 P-76RECh-3 P-77RECh-3 P-78RECh-3 P-79RECh-3 P-80RECh-3 P-81RECh-3 P-82RECh-3 P-83RECh-3 P-84RECh-3 P-85RECh-3 P-86RECh-3 P-87RECh-3 P-88RECh-3 P-89RECh-3 P-90RECh-3 P-91RECh-3 P-92RECh-3 P-93RECh-3 P-94RECh-3 P-95RECh-3 P-96RECh-3 P-97RECh-3 P-98RECh-3 P-99RECh-3 P-100RECh-3 P-101RECh-3 P-102RECh-3 P-103RECh-3 P-104RECh-3 P-105RECh-3 P-106RECh-3 P-107RECh-3 P-108RECh-3 P-109RECh-3 P-110RECh-3 P-111RECh-3 P-112RECh-3 P-113RECh-3 P-114RECh-3 P-115RECh-3 P-116RECh-3 P-117RECh-3 P-118RECh-3 P-119RECh-3 P-120RECh-3 P-121RECh-3 P-122RECh-3 P-123RECh-3 P-124RECh-3 P-125RECh-3 P-126RECh-3 P-127RECh-3 P-128RECh-3 P-129RECh-3 P-130RECh-3 P-1PSCh-3 P-2PSCh-3 P-3PSCh-3 P-4PSCh-3 P-5PSCh-3 P-6PSCh-3 P-7PSCh-3 P-8PSCh-3 P-9PSCh-3 P-10PSCh-3 P-11PSCh-3 P-12PSCh-3 P-13PSCh-3 P-14PSCh-3 P-15PSCh-3 P-16PS

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