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s251final(fa07)

s251final(fa07) - X ′(4 = 0 14(a ∑ ∞ =-= 1 1 2 sin 1...

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MATH 251 Final Exam December 20, 2007 ANSWER KEY 1. C 2. B 3. B 4. C 5. B 6. B 7. B 8. C 9. A 10. B 11. (a) S ′ = 0.1 S - k (b) S ( t ) = (5000 - 10 k ) e t /10 + 10 k (c) 1 500 500 1 500 2 / 1 2 / 1 2 / 1 - + = - = e e e k 12. The eigenvalues are λ n = 4 n 2 , n = 1, 2, 3, … ; the corresponding eigenfunctions are (any nonzero multiple of) X n = sin(2 nx ), n = 1, 2, 3, … 13. (a) = + + = + 0 2 0 T T T X X λ λ (b) X

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Unformatted text preview: X ′(4) = 0 14. (a) ∑ ∞ =---= 1 ) ) 1 2 sin(( ) 1 2 ( 8 ) ( n x n n x f π (b) It converges to 0. 15. (a) - + =--3 4 cos 2 3 2 cos 4 10 ) , ( 9 / 80 9 / 20 2 2 x e x e t x u t t (b) 10 ) , ( lim = ∞ → t x u t...
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s251final(fa07) - X ′(4 = 0 14(a ∑ ∞ =-= 1 1 2 sin 1...

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