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ReviewTest3Spr08

# ReviewTest3Spr08 - Solve on the interval[0,1 using h =.1...

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MAC 3473 Honors Calculus 2 Keesling Review Test #3 Test Date 4/4/08 1. Determine a numerical estimate of the following integrals using Romberg Integration using 2 6 = 64 intervals. For each answer the following questions: (a) Give the numbers in the matrix for the Romberg method to three digits. (b) What is the best estimate of the integral. For this number give all the digits that are carried by the calculator in your answer (c) Circle the digits in answer (b) that you are confident are correct and explain (a) x ! e x ! sin( x ) dx 1 2 " (b) sin 3 ( x ) dx 0 ! " 2. Solve the following differential equations. (a) dy dx = y ! sin x (b) dy dx + 3 y = e x 3. Solve the differential equations numerically using the Euler method.

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Unformatted text preview: Solve on the interval [0,1] using h = .1 . Give twelve digits. Show the formulas used. (a) dy dx = y ! sin x y (0) = 2 (b) dy dx = e x ! y y (1) = 2 4. Do three iterations of the Picard Method. Let y ! 2 . dy dx = x ! y 2 y (0) = 2 5. Do four iterations of the Picard Method. Let y ! 3 . dy dx = x 2 + x ! y y (0) = 3 6. Determine the exact solution of the following differential equations. (a) dy dx = x ! y 2 y (0) = 2 (b) dy dx + 3 y = e x (c) dy dx = x ! 1 " y 2 7. Solve the following differential equation numerically using the Taylor Method of order two. Solve on the interval [0,1] using h = .1 . dy dx = sin( x ! y ) y (0) = 2...
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ReviewTest3Spr08 - Solve on the interval[0,1 using h =.1...

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