Compare the theoretical number of iterations required under the bisection method against the actual number of iterations for each part of the solution to Example 13.2.

Example 13.2

Use the bisection method to obtain the roots required of the following functions to an error tolerance of ϵ = 0.01.

a. The single real positive root of f (x) = x² + 2.011x − 5.04795.

b. The single real negative root of f (x) in part a.

c. The single positive root of g(x) = sin(x²) − x + 1.