02spr-f - FINAL EXAM Math 51 Spring 2002 You have 3 hours...

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FINAL EXAM Math 51, Spring 2002. You have 3 hours. No notes, no books, no calculators. YOU MUST SHOW ALL WORK AND EXPLAIN ALL REASONING TO RECEIVE CREDIT Good luck! Name ID number 1. (/40 points) 2. (/40 points) 3. (/40 points) 4. (/30 points) 5. (/30 points) 6. (/20 points) Bonus (/20 points) Total (/200 points) “On my honor, I have neither given nor received any aid on this examination. I have furthermore abided by all other aspects of the honor code with respect to this examination.” Signature: Circle your TA’s name: Tarn Adams (2 and 6) Mariel Saez (3 and 7) Yevgeniy Kovchegov (4 and 8) Heaseung Kwon (A02) Alex Meadows (A03) Circle your section meeting time: 11:00am 1:15pm 7pm 1
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1. Suppose that f,g : R 2 R 2 are given by f ±• x y ‚¶ = x 2 y y 2 - x 2 = u v g ±• u v ‚¶ = sin u cos u = s t (a) Evaluate J f, -→ a (where -→ a = x y ) and J g,f ( -→ a ) , in terms of x and y . (b) Without computing the composition function g f , evaluate J g f, -→ a , in terms of x and y .
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02spr-f - FINAL EXAM Math 51 Spring 2002 You have 3 hours...

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