answer this please

Question

The iteration formula

                          

was obtained by applying Newton’s method to some function .

What was ?

Answer 1

Hi Shanil,

Newton method formula: x_n+1 = x_n - f(x_n) / f'(x_n)

f(x_n) / f'(x_n) = tan x_n

This looks familiar!

tan x = sin x / cos x

if f(x) = sin x, then f'(x) = cos x , then:

f(x_n) / f'(x_n) = sin x_n / cos x_n = tan x_n

Therefore, f(x) = sin x