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**Unformatted text preview: **Math 41: Calculus Final Exam December 11, 2006 Name : Section Leader (Circle one) : Chang Ivanov Mathews Requeijo Segerman Section Time (Circle one): 11:00 1:15 This is a closed-book, closed-notes exam. No calculators or other electronic aids will be permitted. In order to receive full credit, please show all of your work and justify your answer. You do not need to simplify your answers unless specifically instructed to do so. If you need extra room, use the back sides of each page. If you must use extra paper, make sure to write your name on it and attach it to this exam. Do not unstaple or detach pages from this exam. Please sign the following: 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: The following boxes are strictly for grading purposes. Please do not mark. 1 15 8 7 2 15 9 10 3 24 10 5 4 8 11 15 5 8 12 8 6 15 13 5 7 15 Total 150 GOOD LUCK ON THE REST OF YOUR EXAMS, AND HAVE A GREAT WINTER BREAK! 1. (15 points) Evaluate each of the following limits, showing all reasoning. (a) lim h e 5+2 h- e 5 h (b) lim x 2 + x 2- 1 x 2- 5 x + 6 (c) lim x R x sin 2 t dt R x tan t dt 2. (15 points) Differentiate, using any method you choose. You do not have to simplify your answers. (a) y = (cos x ) x (b) f ( z ) = e sec 2 z ln z (c) g ( x ) = Z sin x 1 ( t 2 + 1) 2006 dt 3. (24 points) Evaluate each of the following integrals, showing all reasoning. (a) Z 3 2 3 x 2 + 2 x + 1 x dx (b) Z tan x dx (c) Z 1- 1 xe x dx (d) Z x 2 x- 1 dx (e) Z arctan x x dx 4. (8 points) The rate at which the worlds oil is being consumed, measured in billions of barrels4....

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