You may use any result from class you like, but if you cite a theorem be sure to verify the hypotheses are satis ed: this is a closed-book exam. No calculators or other electronic aids will be permitted. You are allowed to have one 8. 5 by 11 sheet of paper containing handwritten notes on both sides: in order to receive full credit, you must show all of your work and justify your answers. Your answer should be clearly labeled: if you need extra room, use the back sides of each page. Staple any scratch paper to your 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. Please leave the following table blank for the grader. 6. (/10 points) (/35 points) (/10 points) (/10 points) (/10 points) (/10 points)
