Solve the Problem $f ( x ) = \sqrt [ a ] { x } , a > 0$

question 242

Essay

Solve the problem.
-Apply Newton's method to $f ( x ) = \sqrt [ a ] { x } , a > 0$ , and write an expression for $x _ { n } + 1$ . If the initial guess $x _ { 0 }$ is greater than or equal to 1 , what happens to $\left| x _ { n } + 1 \right|$ as $n \rightarrow \infty$ ?

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Definitions:

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