31b_ThirdMidterm_solutions - UCLA ID NAME(First Last...

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UCLA ID:NAME (First, Last) :SECTION:Math 31b Spring 2014Third MidtermProblemPointsGrade120220330415515615TOTAL:NOTE:You only need to dotwoof the problems marked with a “*”, which adds to30 points. If you obtained full credit for the integral problem then you do not need todo any of them (you already have those 30 points secured), if you obtained half creditfor the integral problem then you need to do justONEof them (you already have 15of the 30 points secured).Write as neatly and clearly as possible. Feel free to write down the name of a lemmaor a theorem that you are using, it could get you partial credit in case you make acomputational error (but also:don’tmake computational errors).Cheat sheets, cell phones, calculators and abaci arenotallowed.You do not need to simplify the final expression of your solution, except in the caseswhere it is explicitly noted. For each question, place your final answer inside a box.Good luck!.

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