Newton's Method Solution

Use Newton's method for approximating roots of functions to approximate $\sqrt{0.99}$

Approximate $\sqrt[4]{75}$ using the Newton Raphson method

Use the Newton Raphson method to approximate the real zero close to $x = 1$ until two successive approximations differ by less than 0.005 for the following function

$f(x) = 2x^2 - 3$

Starting with an initial value $x_1 = 1$, perform 2 iterations of Newton's Method on $f(x) = x^3 - x - 1$ to approximate the root.