..ooo Verizon F 8:58 PM 17% gpc.view.usg.edu 6 of 6 The following problems are t
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..ooo Verizon F 8:58 PM 17% gpc.view.usg.edu 6 of 6 The following problems are to be completed on your own paper and submitted no later than Monday, April 27 at the beginning of class. Papers submitted after this date will have a deduction applied. Papers submitted more than one class day late will not be accepted. Once again, you may work with your classmates as you complete these problems. Each student should submittheir own paper and list the names of the people that you work with. For each problem you should present atable ofthe successive iterations as shown in the examples. Keep nine decimals places and quit the process when the iterations agree to nine decimal places. Each problem is worth 5 points. 1. Estimate N3 by finding the roots of 5. Use ae-2 as your initial guess Note that we can find this value without using the square root key on the calculator. This is the method by which many square root tables were created before the use of handheld calculators. The TI-83 uses an algorithm similar to Newton's Method to give values for square roots. 2. Find the root of foe)- x 2x-s. Use the graph of the function to choose an appropriate initial guess. (Select an integer.) This is the function that Sir Isaac Newton used when he published his work. 3. Solve the equation e 4 x 10. (Hint: Rewrite the equation as a finction and find a root ofthe junction as in erample Use the graph on the calculator to choose an initialestimare. Select an integer) The function f(x) 6x +12 has no roots. ot never crosses the axis. The quadratic formula, mentioned earlier in this assignment, would retum complex numbers to indicate that the function has no real valued roots. Perform 9 terations of Newton's Method using xo as your initial guess. Describe the behavior that Newton's Method has when the functiondoes not have a 5. Obviously, the initial guess is important in the process. The closer the initial guess, the quicker the method converges. However, a poor initial guess can cause the process to fail completely. Explain why choosing a critical point of the function as the initial guess would prove to be a poor initial guess.Explanation / Answer
At critical points, f'(x)=0, therefore f(x)/f'(x) is undefined, and hence we can't apply Newton's Method. And thus, choosing critical points as initial guess is a poor choice.
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