240S09final

240S09final - NAME: PROFESSOR: (A) Donagi ; (B) Ghrist ;...

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NAME: PROFESSOR: (A) Donagi ; (B) Ghrist ; (C) Krieger 240 SPRING 2009: Calculus FINAL EXAM INSTRUCTIONS: 1. WRITE YOUR NAME at the top and indicate your professor’s name. 2. As you solve problems on the exam, FILL IN COMPLETELY the letter(s) of your solu- tion(s) ON THIS PAGE. You must mark your answer clearly to obtain credit. 3. Show your work, if possible. It might not give you partial credit, but it doesn’t hurt to be clear. 4. There is to be no cheating. No kinda-sorta-cheating. No anything that even comes close. If in doubt, don’t do it, for your honor (and perhaps more) is at stake. Play fair. 5. There are to be no calculators, no cell phones, and no books during this exam. You are permitted one hand-written sheet of paper, double-sided, as an aide. Use a pencil, an eraser, your sheet, and your head: but not in that order. 6. You have 120 minutes to complete the exam. Do the exam quickly, but read carefully! You gain nothing by doing a different problem than what is asked. 7. If you have a question, re-read carefully. If that still does not help, please raise your hand and someone will help you directly. ANSWERS: PROBLEM 1 (A) (B) (C) (D) (E) (F) (G) (H) PROBLEM 2 (A) (B) (C) (D) (E) (F) (G) (H) PROBLEM 3 (A) (B) (C) (D) (E) (F) (G) (H) PROBLEM 4 (A) (B) (C) (D) (E) (F) (G) (H) PROBLEM 5 (A) (B) (C) (D) (E) (F) (G) (H) PROBLEM 6 (A) (B) (C) (D) (E) (F) (G) (H) PROBLEM 7 (A) (B) (C) (D) (E) (F) (G) (H) PROBLEM 8 (A) (B) (C) (D) (E) (F) (G) (H) PROBLEM 9 (A) (B) (C) (D) (E) (F) (G) (H) PROBLEM 10 (A) (B) (C) (D) (E) (F) (G) (H) PROBLEM 11 (A) (B) (C) (D) (E) (F) (G) (H) PROBLEM 12 (A) (B) (C) (D) (E) (F) (G) (H) PROBLEM 13 (A) (B) (C) (D) (E) (F) (G) (H) PROBLEM 14 (A) (B) (C) (D) (E) (F) (G) (H) PROBLEM 15 (A) (B) (C) (D) (E) (F) (G) (H)
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PROBLEM 1: The portion of the plane z = 10 + 2 x + 3 y over the disc x 2 + y 2 1 has area equal to: (choose one) (A) π/ 14 (B) 14 (C) 10 + 14 (D) 14 π (E) π 14 (F) 4 π 13 (G) 4 π/ 14 (H) 14 π
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PROBLEM 2: What is det( A ) , where A is the matrix A = 1 2 4 1 4 16 1 8 64 (choose one) (A) 0 (B) 1 (C) 4 (D) 8 (E) 16 (F) 48 (G) 64 (H) None of the above.
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240S09final - NAME: PROFESSOR: (A) Donagi ; (B) Ghrist ;...

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