Newton-Raphson Method is a numerical method for finding solutions to f(x)=0 . We start with a suitable intial value x_0 and find a sequence by x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)} . With right conditions the sequence x_n will converge to a solution of f(x)=0 .
We are going to use this method to find the value of \sqrt{2} , which is the positive solution of f(x)=x^2-2=0 . Which of the following statements are True with x_0=1 ?

Question

Newton-Raphson Method is a numerical method for finding solutions to   f(x)=0 . We start with a suitable intial value   x_0  and find a sequence by   x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)} . With right conditions the sequence   x_n  will converge to a solution of   f(x)=0 . 
 We are going to use this method to find the value of   \sqrt{2} , which is the positive solution of   f(x)=x^2-2=0 . Which of the following statements are True with   x_0=1 ?

Accepted Answer

x_n  is decreasing for all   n\geq 1  and bounded below by   \sqrt{2} .

Accepted Answer

\lim_{n	o\infty}x_n=\sqrt{2}

Accepted Answer

x_{n+1}=\frac{1}{2}(x_n+\frac{2}{x_n})

Answer

x_n  is decreasing for all odd   n\geq 1  and bounded below by   \sqrt{2} .

Answer

x_n  is increasing for all   n\geq 1  and bounded above by   \sqrt{2} .

Answer

\lim_{n	o\infty}x_n=\sqrt{2}^+

Answer

x_n  is increasing for all even   n\geq 1  and bounded above by   \sqrt{2} .

Answer

\lim_{n	o\infty}x_n=\sqrt{2}^-

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Newton-Raphson Method is a numerical method for finding solutions to f(x)=0 . ...

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