Chapter 4, Problem 10RCC

(a)

To determine

To explain: How the second approximation is obtained in Newton’s Method geometrically.

(b)

To determine

To write: The expression for $x_2$ in terms of $x_1,f\left(x_1\right)\text{ and }{f}^{\prime }\left(x_1\right)$.

(c)

To determine

To write: The expression for $x_{n+1}$ in terms of $x_n,f\left(x_n\right)\text{ and }{f}^{\prime }\left(x_n\right)$.

(d)

To determine

To explain: Where the Newton’s method fail or work slowly.