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Unformatted text preview: Math 116 First Exam October 10, 2007 Name: Exam Solutions Instructor: Section: 1. Do not open this exam until you are told to do so. 2. This exam has 10 pages including this cover. There are 8 problems. Note that the problems are not of equal difficulty, and it may be to your advantage to skip over and come back to a problem on which you are stuck. 3. Do not separate the pages of this exam. If they do become separated, write your name on every page and point this out to your instructor when you hand in the exam. 4. Please read the instructions for each individual problem carefully. One of the skills being tested on this exam is your ability to interpret mathematical questions, so instructors will not answer questions about exam problems during the exam. 5. Show an appropriate amount of work (including appropriate explanation) for each problem, so that graders can see not only your answer but how you obtained it. Include units in your answer where that is appropriate. 6. You may use any calculator except a TI92 (or other calculator with a full alphanumeric keypad). However, you must show work for any calculation which we have learned how to do in this course. You are also allowed two sides of a 3 00 5 00 note card. 7. If you use graphs or tables to find an answer, be sure to include an explanation and sketch of the graph, and to write out the entries of the table that you use. 8. Turn off all cell phones and pagers , and remove all headphones. 9. There is a partial table of integrals, and useful integrals for comparison of improper integrals, on the first page of the exam (after this cover page). Any integrals or comparisons other than these should be explicitly derived. Problem Points Score 1 16 2 14 3 10 4 10 5 12 6 12 7 14 8 12 Total 100 Math 116 / Exam 1 (October 10, 2007) page 2 You may find the following partial table of integrals to be useful: Z e ax sin( bx ) dx = 1 a 2 + b 2 e ax ( a sin( bx ) b cos( bx ) + C ) , Z e ax cos( bx ) dx = 1 a 2 + b 2 e ax ( a cos( bx ) + b sin( bx ) + C ) , Z sin( ax ) sin( bx ) dx = 1 b 2 a 2 ( a cos( ax ) sin( bx ) b sin( ax ) cos( bx )) + C, a 6 = b, Z cos( ax ) cos( bx ) dx = 1 b 2 a 2 ( b cos( ax ) sin( bx ) a sin( ax ) cos( bx )) + C, a 6 = b, Z sin( ax ) cos( bx ) dx = 1 b 2 a 2 ( b sin( ax ) sin( bx ) + a cos( ax ) cos( bx )) + C, a 6 = b. Z 1 x 2 + a 2 dx = 1 a arctan( x a ) + C, a 6 = 0 Z bx + c x 2 + a 2 dx = b 2 ln( x 2 + a 2 ) + c a arctan( x a ) + C, a 6 = 0 Z 1 ( x a )( x b ) dx = 1 a b (ln  x a   ln  x b  ) + C, a 6 = b Z cx + d ( x a )( x b ) dx = 1 a b (( ac + d ) ln  x a   ( bc + d ) ln  x b  ) + C, a 6 = b Z 1 a 2 x 2 dx = arcsin( x a ) + C Z 1 x 2 a 2 dx = ln  x + p x 2 a 2  + C You may use the convergence properties of the following integrals: Z 1 1 x p dx converges for p > 1 and diverges for p 1 , Z 1 1 x p dx converges for p < 1 and diverges for p 1 , Z e ax dx converges for a > . Math 116 / Exam 1 (October 10, 2007) page 3...
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This note was uploaded on 05/18/2009 for the course MATH 116 taught by Professor Staff during the Fall '08 term at University of MichiganDearborn.
 Fall '08
 Staff
 Math

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