O Instructions 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. You only need to find 3 of the 5 solutions! 5. Use RADIAN MODE FOR CALULATORS Upload your results using the blue "Submit Assignment" button at the top of the page. Be sure to show all of your work in making these calculations. Step 1. Write the derivative: f'(x)=(x sin (x)-5)" Step 2. Use product rule: f'(x)= (x*sin(x))'-5' Step 3. Find derivative of a function: f'(x)=x*sin'(x)+sin(x)*x' Step 4. Calculate: f'(x)=sin*x+x*cos*x 1st Problem set: Choose: x0=5 X1=x0-f(x0)/f'(x0)=5-5sin(5)-5/sin(5)+cos(5)=26.32108392 X2=x1-f(x1)/f'(x1)=26.32108392-f(26.32108/f'(26.32108)=26.32108392 2nd Problem Set: Given: f'(x)=sin*x+x*cos*x Choose:? Solve? 3rd Problem set: Given: f'(x)=sin*x+x*cos*x Choose? Solve