midterm1 persson fall 09 - 1. (5 points) Evaluate the...

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UCB Math 1B, Fall 2009: Midterm 1 Prof. Persson, October 5, 2009 Name: SID: Section: Circle your discussion section below: Sec Time Room GSI 01 MW 8am - 9am 75 Evans G. Melvin 02 MW 8am - 9am 5 Evans T. Wilson 03 MW 10am - 11am 75 Evans D. Cristofaro-Gardiner 04 MW 10am - 11am 3113 Etcheverry E. Kim 05 MW 11am - 12pm 81 Evans G. Melvin 06 MW 12pm - 1pm 5 Evans T. Wilson 07 MW 1pm - 2pm 2 Evans A. Tilley 09 MW 2pm - 3pm 247 Dwinelle D. Cristofaro-Gardiner 10 MW 3pm - 4pm 4 Evans E. Kim 11 MW 4pm - 5pm 3113 Etcheverry A. Tilley 12 TT 11:30am - 2pm 230C Stephens L. Martirosyan Other/none, explain: Grading 1 / 5 2 / 5 3a / 3 3b / 3 3c / 4 4a / 5 4b / 5 5 / 5 /35 Instructions: One double-sided sheet of notes, no books, no calculators. Exam time 50 minutes, do all of the problems. You must justify your answers for full credit. Write your answers in the space below each problem. If you need more space, use reverse side or scratch pages. Indicate clearly where to find your answers.
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Unformatted text preview: 1. (5 points) Evaluate the integral: Z arctan xdx 2. (5 points) Determine if the integral below is convergent or divergent. If it is convergent, evaluate it. Z e 1 x (ln x ) 3 dx 2 3. Determine if the sequences { a n } below converge or diverge. If they converge, nd the limit. a) (3 points) a n = e 1 /n b) (3 points) a n = (2 n-1)! (2 n + 1)! c) (4 points) a n = (-1) n n 3 n 3 + 2 n 2 + 1 3 4. Consider the region bounded by the curves y = 0, x =-1, x = 1, and y = 1 ( x 2 + 1) 3 / 2 . a) (5 points) Find the area A of the region. Hint: Use trigonometric substitution. b) (5 points) Find the centroid of the region. 4 5. (5 points) If f is a quadratic function f ( x ) = ax 2 + bx + 1, and Z f ( x ) x 2 ( x + 1) 3 dx is a rational function, nd the value of b . 5...
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This note was uploaded on 01/02/2011 for the course MATH 1B taught by Professor Reshetiken during the Spring '08 term at University of California, Berkeley.

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midterm1 persson fall 09 - 1. (5 points) Evaluate the...

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