Consider the equation x sin x = 5, or in the notation above x sin x - 5 = 0.

1. For this situation, what is f'(x)?
2. Set up an Excel spreadsheet, or a program in your favorite programming language, to find solutions to the above equation. (Submit this file along with your answers to the questions.)
3. Starting with a guess of x = 5, what solution does Newton's method converge to? (Run the method until the x values don't change in the first five decimal places.)
4. There are five solutions to x sin x = 5 between x = 0 and x = 20 (it is at heart a sine wave, after all). By varying your initial guess, find them all to within five decimal places.