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Solve the Problem h>0h > 0 , Applying Newton's Method To f(x)={x8,x88x,x<8f ( x ) = \left\{ \begin{array} { l l } \sqrt { x - 8 } , & x \geq 8 \\- \sqrt { 8 - x } , & x < 8\end{array} \right.

question 369

Essay

Solve the problem.
-Show that if h>0h > 0 , applying Newton's method to
f(x)={x8,x88x,x<8f ( x ) = \left\{ \begin{array} { l l } \sqrt { x - 8 } , & x \geq 8 \\- \sqrt { 8 - x } , & x < 8\end{array} \right.
leads to x2=hx _ { 2 } = h if x0=hx _ { 0 } = h and to x2=hx _ { 2 } = - h if x0=hx _ { 0 } = - h when 0<8<h0 < 8 < h .


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