Solved: In Section 4.8 we considered Newtons method for approximating a root of the
Chapter 11, Problem 39(choose chapter or problem)
In Section 4.8 we considered Newtons method for approximating a root of the equation , and from an initial approximation we obtained successive approximations , , . . . , where Use Taylors Inequality with , , and to show that if exists on an interval containing , , and , and , for all , then [This means that if is accurate to decimal places, then is accurate to about decimal places. More precisely, if the error at stage is at most , then the error at stage is at most .]
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