practice_prelim1_fa05 - Math 191 Practice Prelim 1 Fall...

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Unformatted text preview: 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) b) c) -2 sec2 (x)dx d dt 2 1 cos4 (x)dx t3 x3 dx 1 + x6 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 = limit of Riemann sums. (Use uniform partitions and the right hand rule.) b) Find n n k=1 6 as a lim k7 n8 4. Evaluate a) b) c) 0 x dx 1 - x2 x2 2 - x dx 1 - sin(y) 1 - sin2 (y) dy. 1 5. Consider the region in the first quadrant bounded on the left by the yaxis, above by the line y = 2 - x, and below by the line y = x. a) Find the volume of the solid generated by revolving this region about the yaxis. b) Find the volume of the solid when rotated about the xaxis. Some formulas: cos(a + b) = cos a cos b - sin a sin b sin(a + b) = cos a sin b + sin a cos b sin(a/2) = cos(a/2) = 1-cos a 2 1+cos a 2 ...
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