Use Newton's method to approximate a root of the equation 3 sin ( x ) − x = 0 as follows. Let x 1 = 2 be the initial approximation.

Question

Use Newton's method to approximate a root of the equation  as follows.Let  be the initial approximation.The second approximation  is   and the third approximation 

Answer 1

Newton's method uses the following process:

x_n+1 = x_n - f(x_n)/f'(x_n)

With this problem, you are given x₁ and f(x). All you have to do is calculate f'(x) and follow the Newton rule to get all of the values.