Use Newton's Method

Question

Use Newton's method to approximate the positive zero of f(x) = x^2 - 5. Calculate two iterations.

Answer 1

f(x) = x² - 5

f'(x) = 2x

First guess: R₁ = 2

R₂ = R₁ -( f(R₁) / f'(R₁))

= 2 - (-1/4) = 2.25

R₃ = R₂ -( f(R₂) / f'(R₂))

= 2.25 - ( 0.0625 / 4.5) = -2.23611111111

<<the exact answer is √5 = 2.2360679775>>