Chapter 6, Problem 30P

To determine

(a)

A MATLAB program that calculates the cubic root of a number such that, the program uses $x_1=P$ for the first estimate of the solution, then, by using the general equation in a loop, new, more accurate values can be calculated. (Stop the looping when the estimated relative error $E$ defined by $E=\left|\frac{x_{i+1}-x_i}{x_i}\right|$ is smaller than 0.00001.); the cube root of $\sqrt[3]{100}$.

To determine

(b)

The cube root of $\sqrt[3]{53701}$.

To determine

(c)

The cube root of $\sqrt[3]{19.35}$.