Question

Newton-Raphson/Iteration help. *Question attached below* Will give medal

Answer 1

So I have already done part a to this question and I believe I can do part c once I get some help on part b. Can someone guide me, please?

Answer 2

HI!!

Answer 3

it is algebra to turn newton's method for square roots in to mechanics rule known by the babylonians

Answer 4

Hmm, I've never actually heard of that xD

Answer 5

that is the one that says
\[x_{n+1}=\frac{1}{2}\left(x_n+\frac{N}{x_n}\right)\]

Answer 6

which makes perfect sense
if you want the square root of a number make a guess
say i guess the square root of five is two
then 2 is too small, \(\frac{5}{2}\) is too big, so i get closer by taking the average
that is what it says to do

Answer 7

in any case you have
\[f(x)=x^2-N\\
f'(x)=2x\] and
\[x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}\] substitute and do the algebra to make it look like you want

Answer 8

How should I go about turning xn+1 into xn ?

Answer 9

that is actually a typo in your question

Answer 10

this \[x_{n+1}=\frac{1}{2}\left(x_n+\frac{N}{x_n}\right)\] is the iterative formula
it gives the next number in terms of the previous one
it was written incorrectly in your worksheet

Answer 11

Thank you! Because I was wondering how come the one we did in class had xn+1 and our assignment had xn :S Thank you so much!