Show that Newton's convergence method converges to 0 quadratically, i.e show that lim of n-inf = f(xn+1)/f(xn)^2 = c

Question

Show that Newton's convergence method converges to 0 quadratically, i.e show that lim of n->inf = f(xn+1)/f(xn)^2 = c

anonymous · Answer

http://en.wikipedia.org/wiki/Newton%27s_method

anonymous · Answer

I know the basics of Newton's method but I don't know how to apply it for this precise case. And how to expand the equation above

anonymous · Answer

the link i sent has the proof that if it is convergent, then the convergence is quadratic

anonymous · Answer

yes but the proof is for root being anything. not precisely 0. and this proof we've seen in class. It wouldn't make sense for the teacher to ask us the same thing on the assignment.