Let f(x) =x²-a. Show that the Newton-raphson method leads to the recurrent
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=xn−f(xn)f′(xn)x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}xn+1=xn−f′(xn)f(xn)
f′(x)=2xf'(x)=2xf′(x)=2x
recurrence relation:
xn+1=xn−xn2−a2xnx_{n+1}=x_n-\frac{x_n^2-a}{2x_n}xn+1=xn−2xnxn2−a
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