Calculus 1: Newton Raphson Method

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.

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

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

Use Newton's Method to approximate a solution to $2\cos{(x)} = 3x$ (Let $x_0 = \frac{\pi}{6}$ and find $x_2$)