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 2 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: 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. The following boxes are strictly for grading purposes. Page 1 of 10: (10 points) find each of the following limits, with justi cation (show steps).
