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samplefinal - n ² n 2 3 points Does the following series...

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1. ( 4 points ) *** Compute the following limit lim n →∞ ± 1 + 1

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Unformatted text preview: n ² 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 ² 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 = π 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 ( π ) = 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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This note was uploaded on 02/22/2012 for the course MATH 9c taught by Professor C during the Fall '11 term at UC Riverside.

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samplefinal - n ² n 2 3 points Does the following series...

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