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practice_prelim1_fa05 - Math 191 Practice Prelim 1 Fall...

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Math 191 Practice Prelim 1 Fall 2005 No calculators, notes or books allowed. To improve the chance for partial credit and also generally ease the work of grading, please: write clearly and be well organized; use the page backs for ungraded scrap work and for checking your answers; box in your answers; and reduce your answers as much as possible. None of the calculations are long and none of the answers are long. 1. Evaluate the following expressions: a) integraldisplay sec 2 ( x ) dx b) d dt integraldisplay 1 t 3 cos 4 ( x ) dx c) integraldisplay 2 - 2 x 3 1 + x 6 dx 2. Consider the region bounded on the left by the y -axis and on the right by the curves y = sin( x ) and y = cos( x ). Find the area of the region. 3. a) Express the area under the curve y = sin( x ) between x = 0 and x = π 6 as a limit of Riemann sums. (Use uniform partitions and the right hand rule.)
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