s251final(sp08)

# s251final(sp08) - âˆ = 2 2 2 sin dx x n x b n n = 1 2 3...

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MATH 251 Final Exam May 7, 2008 ANSWER KEY 1. A 2. C 3. A 4. D 5. B 6. C 7. B 8. (a) y ( t ) = t 2 - 1 + 5 t -2 (b) ( - , 0 ) 9. ) 2 sin( ) ( 2 1 ) 2 sin( ) 2 cos( ) ( ) 2 ( 2 2 2 2 t e t u t e t e t y t t t π - - - - + + = 10. (a) 4 X ″ + λX = 0, and T ″ + ( λ + 5) T = 0 (b) X ′(0) = 0, X (20) = 0 (c) No 11. Eigenvalues are λ = 0 and λ = n 2 , n = 1, 2, 3, … ; Eigenfunctions are X 0 ( x ) = 1, and ( ) nx x X n cos ) ( = , n = 1, 2, 3, … 12. (b) It is a sine series. (c) a m = 0, m = 0, 1, 2, …;
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Unformatted text preview: âˆ« = 2 2 2 sin dx x n x b n , n = 1, 2, 3, â€¦ (d) f (0) = 0, f (2) = 0, f (3) = -1 13. (a) -+ =---2 3 sin 10 ) sin( 4 3 sin 2 ) , ( 2 2 3 9 4 9 / 4 x e x e x e t x u t t t (b) ) , ( lim = âˆž â†’ t x u t...
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## This note was uploaded on 07/23/2008 for the course MATH 251 taught by Professor Chezhongyuan during the Spring '08 term at Penn State.

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