MAT296-2007Fall

# MAT296-2007Fall - M AT 2 96 F INAL E XAM December 1 2 2 007...

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" MAT 296 FINAL EXAM - December 12, 2007 Nrune: __________________________________ _ Signature: ______________________________ ___ Instructor: (please circle one) N. MARIO A.MURPHY T. PERKINS L. SHEN D. ZAOHARIA Read before you begin: 1. This exam contains 10 problems for a total of 126 points. There are 12 pages including the cover sheet, and a blank page at the end. You are responsible Jor checking that they are all present. 2. You must show all work to completely justify your answers in order to receive any credit. Unsupported answers will receive little or no credit. I Problem , Points I 1. 10 2, 8 3. 10 4. 28 I 5. 10 6. 10 7. 10 8. 5 I 9. 18 10. 17 Total 126 1

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Math 296 FINAL EXAM - December 12,2007 1. (10 points) A solid is obtained by revolving the region bounded by the graphs of y = x 2 + 1, y 0, x = 0, and x 1 about the y-axis. (a) Set up an integral to find the volume of the solid by using the method of cross sections, but do not evaluate the integral. (b) Find the volume of the solid by using the method of cylindrical shells. 2
2. (8 points) Given a parametric curve x = 3t 2 , Y = 2t 3 , 0:::; t :::; 2.

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