MATH 41 Final: MATH 41 Stanford 11Final

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Math 41 final exam december 12, 2011. In order to receive full credit, please show all of your work and justify your answers: you do not need to simplify your answers unless speci cally instructed to do so. You may use any result from class that you like, but if you cite a theorem be sure to verify the hypotheses are satis ed: you have 3 hours. No calculators or other electronic aids will be permitted. 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: the last page of this exam contains information that may be. Needed in some of the problems: summation formulas, geomet- Ric formulas and some values of trigonometric functions. Ok to detach that page from the exam for your convenience: please sign the following: