Each of the equations in Table 2.8 has one solution. Select an equation, and then do the following:
(a) Sketch the functions to determine the approximate location of the solution.
(b) For the bisection method, provide an initial interval that can be used to find the solution, and provide an explanation why it works. With this calculate, by hand,
0
and
1.
(c) What is Newton’s iteration formula (2.10) for this equation? Also, provide a starting point
0
for the solution, providing an explanation of why it is a good choice. With this calculate, by hand,
1.
(d) What is the secant iteration formula (2.24) for this equation? Also, provide starting points
0
and
1
for the solution, providing an explanation of why they are a good choice. With this calculate, by hand,
2.
(e) Compute the solution of the equation. Your answer should be correct to at least four significant digits. Make sure to state which numerical method was used, why you made this choice, and what error condition you used to stop the calculation.