s251final(su10)

s251final(su10) - MATH 251 Final Exam August 13, 2010...

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Unformatted text preview: MATH 251 Final Exam August 13, 2010 ANSWER KEY C C A B D B D B B C C D C , = 1, 2, 3, … ¡ ¡ ¢ £ ∞ ¦ ¤ (−1 / 2) → −1, ¦ ¦ ( , ) = 2cos(2 )sin( ) – 3cos(4 )sin(2 ) ¨ ¨ ¤ ¨ ¤ © ¤ © © § ◦ ◦ (a) The left and right ends are kept at, respectively, constant −1 and 1 . 2 −1 (b) lim ( , ) =      π →∞ (a) Both ends are perfectly insulated. (b) lim ( , ) = 1   →∞   18. © 17. ¥ 16. (2 − 1)π 4 sin 2 = 1 ( 2 − 1)π (−2) → 0 ( )=∑ ¢ (c) (b) ¢ (a) -- 15. ¤ ¢ = sin ¤ = − 2, 14. ¢ 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. ...
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