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408DS09assign1 - Feel free to discuss these problems with...

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M408D Spring 2009 Assignment 1 Due Thursday, January 29 Be sure that you have read and understood sections 7.8, 8.8, and 12.1 and worked the assigned text excercises before you complete this assignment. You must show sufficient work in order to receive full credit for a problem. Please write legibly and label the problems clearly. Circle your answers when appropriate. Multiple papers must be stapled together. Write your name and the time of your discussion section on each page. Homework is to be turned in at the beginning of the discussion section. You may use calculators for arithmetic. I strongly discourage you from using a calculator to do any algebraic simplification, differentiation, integration, etc., since you will not be allowed to use one on the exams.
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Unformatted text preview: Feel free to discuss these problems with your classmates. However, each student must write up his or her own solution. If you are relying heavily on help from others to complete these assignments, it is an indication that you have not suciently understood the material. For problems 1 and 2, evaluate each limit or explain clearly why it does not exist. 1. lim x xe 1 /x-x 2. lim x 1 x 3 Z x sin( t 2 ) dt 3. Evaluate Z 1 e 1 /x x 3 dx or show that it diverges. 4. For what values of a is Z e ax cos xdx convergent? Evaluate the integral for those values of a . 5. Is the sequence { ln( n + 1)-ln( n ) } monotone? Is it bounded? Find the limit of the sequence or show that it doesnt exist. 1...
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