samplefinal - n n 2. ( 3 points ) ** Does the following...

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sample Final Exam Math 9C 7/23/2011 Name: | {z } Make sure I can read this Read all of the following information before starting the exam: NO CALCULATORS!!! Show all work, clearly and in order, if you want to get full credit. I reserve the right to take off points if I cannot see how you arrived at your answer (even if your final answer is correct). Justify your answers algebraically whenever possible to ensure full credit. Circle or otherwise indicate your final answers. Please keep your written answers brief; be clear and to the point. I will take points off for rambling and for incorrect or irrelevant statements. This test has 7 problems and is worth 25 points, Good luck! * Problem taken from notes ** Problem taken from assigned homework *** Problem taken from study guide
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1. ( 4 points ) *** Compute the following limit lim n →∞ ± 1 + 1
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Unformatted text preview: n n 2. ( 3 points ) ** Does the following series X n =1 ln( n ) n 3 converge or diverge. Justify your answer. 3. ( 4 points ) ** Does the following series X n =1 1 + 1 n n 2 converge or diverge? Justify your answer 4. ( 3 points ) ***What is the radius and interval of convergence for the following power series X k =1 (-1) k k 5. ( 4 points ) ** Find a power series expansion for the function f ( x ) = sin x centered at x = 6. ( 3 points ) ** Find a power series expansion for the function f ( x ) = 1 + x 2 1-x centered at x = 0 7. ( 3 points ) * Solve the initial value problem y + 1 x y = sin x x y ( ) = 2 8. ( 3 points ) ** Find the general solution to the ODE 2 y 00 + 3 y + 4 y = 0 9. ( 4 points ) ** Use the method of power series to solve the ODE y-2 y = 0...
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samplefinal - n n 2. ( 3 points ) ** Does the following...

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