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Unformatted text preview: MAD 4401 Study Guide for Test 3 Keesling Test on 12/5/11 1. Have the following programs debugged on your TI89 and ready for use on Test 3. Bisection Method Newton Method Picard Iteration Euler Method Modified Euler Heun RungeKutta Taylor Method 2. Do three iterations of the bisection method in solving the following equations. (a) sin x = cos x (b) x 5 + 3 x 4 + 2 x 5 = 3. From the intervals that you started with in the previous problem, how many steps would be necessary to have an answer accurate to 10 10 ? 4. Solve the above two problems using Newtons Method. 5. Let f ( x ) be continuous and suppose that the sequence x , f ( x ), f ( f ( x )), f ( f ( f ( x ))), converges to z . Show that f ( z ) = z . This sequence can also be defined as x n { } n = where x is arbitrary and x n + 1 = f ( x n ) for n = 0,1,2,3, . 6. State the Mean Value Theorem. 7. Let f : R R be a differentiable function. Suppose that f ( z ) = z is a fixed point for f . Suppose that for some...
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This note was uploaded on 12/27/2011 for the course MAD 4401 taught by Professor Martcheva during the Spring '08 term at University of Florida.
 Spring '08
 Martcheva

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