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Unformatted text preview: MAC 2312 April 26, 2006 Final Exam Prof. S. Hudson Name Show all your work and reasoning for maximum credit. Especially, explain any proofs. Do not use a calculator, book, or any personal paper. You may ask about any ambiguous questions or for extra paper. 1) (20pts) Compute and simplify. Use limits on any improper integrals. Z + - 1 1 + x 2 dx Z ln(2) e 2 x dx d dx Z x 2 e t 2 dt Z / 4 tan 2 ( x ) dx Z 2 | x 2- 1 | dx 1 2a) (10pts) Find the McLaurin Series (eg the Taylor Series at 0) for f ( x ) = e- x 2 . 2b) Use your answer to 2a) to approximate R 1 e- x 2 dx to two decimal places. You do NOT have to simplify the sum, but if your answer has 7 summands (for example) explain your reasoning for including those 7. I think you do not need a calculator (eg 4! = 24 and 5! = 120 etc are pretty easy) but you can ask me for some numerical help. 3) (10pts) Find the area of the region that is inside one loop of the rose r = cos(3 )....
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This note was uploaded on 12/26/2011 for the course MAC 2312 taught by Professor Storfer during the Summer '08 term at FIU.
- Summer '08