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This is to be a typed report. You will be using 3 different algorithms and computer implementations of those algorithms. If you can find Suitable versions of the programs you are interested in in recipe books, the web, the disk that comes with your book, etc. you may use them. However, you will be better off writing your Own code in the long rull. 1. For each of the algorithms you will be using, bisection, Newton, and secant, write a description of the algorithm, what it is doing, and why. Write at a level in this question and, indeed, for all questions in this assignment and your other assignments in this class, so that a junior in college with the prerequisites for this class can understand what you are saying. 2. For the function / (x) = I-3 use each of the 3 methods to estimate the zero until two successive estimates have a difference of less than 10-6. For Newton's method, start with po = 2 and for the other methods use the interval [1,2]. Using p = 1.25992105, compute Pn+1 p Pn p for n = 2,3,4 4, and 5. Give your results and comment on them. 3. For the function 1 1 (x) = 2 1++2 use each of the 3 methods to estimate the zero until two successive estimates have a difference of less than 10-4 For Newton's method, start with Pr = 3 and for the other methods use the interval [0,3 Give your results and comment on them. 4. Consider the function / (x) - (2 * erf(x)) - 1 Pretend that we do not know how to differentiate / but we still want to find the zero. This is similar to trying to tune a "black box" device to a fixed output. Using [0,1], find the zero of f using the secant method. 1

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