Question: Consider the equation x sin x = 5, or in the notation above x sin x - 5 = 0. For this situation, what is

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 to find solutions to the above equation. (Submit this file along with your answers to the questions.)
  3. Starting with a guess of x = 6, 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.

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