HW5_2384f10 - I within 0.01 of the true value. Round your...

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MAT 2384-Fall 2010-Homework #5 To be submitted in class on Friday, November 19 Question 1. In each case, find the solution to the linear homogeneous system of differential equa- tions: ~ y 0 = A~ y satisfying the given initial condition: ( i ) A = " - 1 3 3 - 1 # , ~ y (0) = " 2 - 4 # ( ii ) A = " - 1 5 - 1 3 # , ~ y (0) = " 1 3 # ( iii ) A = " 1 - 9 1 7 # , ~ y (0) = " 2 - 3 # Question 2. Solve the following nonhomogeneous systems: ( i ) ~ y 0 = " 2 - 3 0 - 2 # ~ y + " 2 e - x 3 e 4 x # ( ii ) ~ y 0 = " 1 3 - 2 - 4 # ~ y + " e - 2 x 2 x + 3 # Question 3. Let I = Z 1 0 1 1 + 2 x dx. 1. Use the Trapezoidal Rule to approximate the value of
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Unformatted text preview: I within 0.01 of the true value. Round your answers to 6 decimal places. 2. Use the Simpsons Rule with n = 8 to approximate the value of I . Round your answers to 6 decimal places. Give bounds for your Error using the error bounds for Simpsons Rule. 3. Compute the true value of I . Give the exact errors in your estimates of parts (1) and (2). 1...
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