M251final(fa09)

# M251final(fa09) - Name MATH 251 Student Number Final...

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MATH 251 Final Dec 16, 2009 Name: Student Number: Instructor: Section: There are 12 multiple choice questions and 5 partial credit questions. In order to obtain full credit for the partial credit problems, all work must be shown. Credit will not be given for an answer not supported by work on a partial credit prob- lem. The use of calculators is not permitted in this examination. For multiple choice problems, write the letter of your choice in the space pro- vided below. Your Answer : Points awarded 1. (5 pts) 7. (5 pts) Q. 13 (15 pts) 2. (5 pts) 8. (5 pts) Q. 14 (15 pts) 3. (5 pts) 9. (5 pts) Q. 15 (20 pts) 4. (5 pts) 10. (5 pts) Q. 16 (20 pts) 5. (5 pts) 11. (5 pts) Q. 17 (20 pts) 6. (5 pts) 12. (5 pts)

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MATH 251 -Final- 1. (5 points) Which of the following has a unique solution on the whole interval (0 , π )? (a) y + y = 0 , y (0) = 0 , y ( π ) = 0. (b) y + 4 y = 0 , y (0) = 0 , y ( π ) = 0. (c) ( t + 1) y + ty = 0 , y (1) = 1 , y (1) = 0. (d) ( t 1) y + 2 y = 0 , y (0) = 0 , y (0) = 1. 2. (5 points) Let y 1 ( t ) = 1 and y 2 ( t ) = 0. Which of the following three statements is true? 3. (5 points) For which of the following equations is it true that ALL solutions approach zero as t → ∞ ? Page 2 of 10
MATH 251 -Final- 4. (5 points) Consider the 2 π -periodic function f ( x ) = | x | , when π < x < π, and f ( x + 2 π ) = f ( x ) . Find the fourth sine coeﬃcient b 4 of the Fourier series.

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