Use Newton’s method to estimate a solution for x^2 - 2x + 1=sinx and use x0=0

Answer 1

f(x) = x²-2x+1-sin(x)

f'(x) = 2x-2-cos(x)

x_i = x_i-1 - f(x_-1)/f'(x_x-1)

x₀ = 0

x₁ = 1/3

x₂ = 0.3848

x₃ = 0.3862

x₄ = 0.3862