20b_01w_fe

# 20b_01w_fe - Math 20B Section Signature Final Exam(200 points Print Name 3 PM ID Use this exam for your work Do NOT use a blue book Use the back of

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Math 20B Final Exam (200 points) 3 PM March 23, 2001 Section Print Name Signature ID # Use this exam for your work. Do NOT use a blue book . Use the back of the exam pages if you need scratch paper. The exam is CLOSED BOOK, but you may use ONE SHEET OF NOTES. Calculators are NOT allowed. You must show your work to receive credit. 1. (40 pts.) Let R be the region between the two parabolas y = x 2 and x = y 2 . Let V be the volume obtained when R is rotated about the y -axis. (a) Sketch the region R . Include in your drawing the coordinates of the point where the parabolas intersect. Set up (but do not evaluate ) integrals for the following. (b) The arc length of the boundary of R that is on the parabola y = x 2 . (c) The volume of V . (d) The surface area of V . Be careful : V has what might be called an inner and outer surface. The surface area is the sum of the areas of these two surfaces.

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## This note was uploaded on 06/17/2009 for the course MATH 20B taught by Professor Justin during the Winter '08 term at UCSD.

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20b_01w_fe - Math 20B Section Signature Final Exam(200 points Print Name 3 PM ID Use this exam for your work Do NOT use a blue book Use the back of

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