Question

Use Newton's method to approximate a root of the equation cos(𝑥2+5)=𝑥3 as follows:

Let 𝑥1=1 be the initial approximation.

The second approximation 𝑥2 is____

Answer 1

f(x) = cos(x^2+5)-x^3
f'(x) = -2x sin(x^2+5)-3x^2
x_n+1 = x_n - f(x_n)/f'(x_n)
x0 = 1
n...........x_n
1 0.98368
2 0.98315
3 0.98315