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MAD 4401 Study Guide for Test 3

MAD 4401 Study Guide for Test 3 - MAD 4401 Study Guide for...

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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 TI-89 and ready for use on Test 3. Bisection Method Newton Method Picard Iteration Euler Method Modified Euler Heun Runge-Kutta 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 Newton’s 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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MAD 4401 Study Guide for Test 3 - MAD 4401 Study Guide for...

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