fall 05

fall 05 - MATH 126 FINAL EXAM You should do all ten...

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MATH 126 FINAL EXAM December 14, 2005 You should do all ten problems. Read the problems carefully and answer the questions asked. Write neatly and indicate clearly your answer to each problem. If you need more space, use the backs of these pages and clearly indicate where the continuation may be found. You must show your work to obtain full credit. Points may be deducted if you do not justify your final answer. Calculators, notes, books, or collaboration with others are not allowed. If you have any questions about any of the problems ask the proctor, but no one else! 1 . [16 points] (a) Sketch the region R in the first quadrant below the curve y = 6 + x - x 2 . (b) Find the volume of the solid V obtained by rotating the region R about the y -axis. 2. [24 points] Evaluate the integrals (i) Z x sin xdx (ii) Z 3 x 2 - 3 x + 4 ( x - 2)( x 2 + 1) dx (iii) Z x 3 1 - x 2 dx 3 . [24 points] Determine whether or not the limit exists. If the limit exists find it, and indicate clearly how you obtained your answer. If the limit does not exist give reasons why.
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fall 05 - MATH 126 FINAL EXAM You should do all ten...

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