Question

Use Newton's method to approximate a root of the equation 3sin(x)=x as follows.
Let x1=1 be the initial approximation.
The second approximation x2 is
and the third approximation x3 is

Answer 1

f(x) = 3 sinx - x
f'(x) = 3 cosx -1
if xo = 1 is the first approximation, the second approximation is
x1 = xo - f(1)/f'(1)
= 1 - 1.524/0.621 = -1.454
x2 = x1 - f(x1)/f'(x1)
= -1.454 -1.525/1.804 = -2.299
x3 = x2 - f(x2)/f'(x2)
= -2.299 -0.0599/(-1.997)
= -2.269

Answer 2

I tried to follow the format at
http://en.wikipedia.org/wiki/Newton's_method

My xo may be your x1, etc.

Answer 3

I put -1.454 for x2 but when I put -2.299 for x3 I got it wrong