# 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

Question
5 views help_outlineImage TranscriptioncloseWith 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 fullscreen
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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:

Step 2

To find the square root of 7 using newton’s method considering x be the square root of 7.
It gives: help_outlineImage Transcriptioncloselet 7 = x 7=x2 -7 0 So f(x) x-7 = 0 andfx) 2x fullscreen
Step 3

Taking the initial approximate x0=3

The first...

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### Calculus 