Show that the iterates x,, defined by (4) will converge to f

Chapter 1, Problem 1

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QUESTION:

Show that the iterates x,, defined by (4) will converge to f

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QUESTION:

Show that the iterates x,, defined by (4) will converge to f

ANSWER:

Step 1 of 4

The square root of 2 is the solution of the equation .

In order for Newton’s method to converge, it should be  on the interval, where the iterations will converge to a unique root.

The equation  has a unique root  at an interval    

                                                       

if the function  is monotonic and continuous in the same interval.

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