pracfin - answer. (a) The series ∑ ∞ n =1 (-1) n n a is...

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Practice Final Exam 1. 2.3.7. 2. 4.5.19. 3. 6.3.8. 4. 7.6.27. 5. 8.4.21. 6. 8.6.31. 7. Decide if the following statements are true or false. Explain your answer. (a) We can use the Frobenius to ±nd a power series solution for the equation x 3 y pp + 2 xy p + ( x 5 + e x ) y = 0 about x = 0. (b) It is possible to ±nd two linearly independent solutions for y p - y = e 2 x . (c) If y 1 and y 2 are two solutions for y 2 ( x ) + y ( x ) + y p ( x ) = 0, then so is y 1 + y 2 . 8. Decide if the following statements are true or false. Explain your
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Unformatted text preview: answer. (a) The series ∑ ∞ n =1 (-1) n n a is always convergent, no matter what pos-itive real number a is. (b) If in a Frobenius equation, we have q ( x ) = e x /x 2 , then 0 is a regular singular point of that equation. (c) If a function is of exponential order, then its Laplacian exists. 1...
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This note was uploaded on 01/23/2011 for the course FIN 4243 taught by Professor Dudley during the Spring '08 term at University of Florida.

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