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

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Instructions
Consider the equation x sin x = 5, or in the notation above x sin x – 5 = 0.  
For this situation, what is f'(x)?
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.)
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.)
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.

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