With an initial approximation of xo = 3, use Newton's Method to approximate /7, correctto at least three significant digits. Show the approximation generated by each iteration and (whenpossible) its absolute relative approximate error. How many iterations were needed?с

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Asked Sep 13, 2019
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With an initial approximation of xo = 3, use Newton's Method to approximate /7, correct
to at least three significant digits. Show the approximation generated by each iteration and (when
possible) its absolute relative approximate error. How many iterations were needed?
с
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With an initial approximation of xo = 3, use Newton's Method to approximate /7, correct to at least three significant digits. Show the approximation generated by each iteration and (when possible) its absolute relative approximate error. How many iterations were needed? с

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Expert Answer

Step 1

Concept used: Newton’s Method If xn is an approximation of a solution of f(x)=0 and if f’(xn)≠0 then the next more accurate approximation is given by:

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f(x,) f"x) n n

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Step 2

To find the square root of 7 using newton’s method considering x be the square root of 7.
It gives:

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let 7 = x 7=x2 -7 0 So f(x) x-7 = 0 andfx) 2x

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Step 3

Taking the initial approximate x0=3

The first...

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f(x) 32-7 =3 2x3 1 3 3 3 Il

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Math

Calculus