Newtons Method Approximate Real Zeros of a Function

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

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

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.

Use Newton's Method to approximate the solution to the following equation

$\cos{(x)} = \frac{x}{5}$