Question #263131

Let f(x) =x²-a. Show that the Newton-raphson method leads to the recurrent

1
Expert's answer
2021-11-09T16:29:44-0500

A recurrence relation is an equation that expresses each element of a sequence as a function of the preceding ones.


by the Newton-Raphson method:


xn+1=xnf(xn)f(xn)x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}


f(x)=2xf'(x)=2x


recurrence relation:


xn+1=xnxn2a2xnx_{n+1}=x_n-\frac{x_n^2-a}{2x_n}


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