# midterm2 - 1. (4 points) Evaluate Z . 5 x 2 cos( x 2 ) dx...

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UCB Math 1B, Spring 2010: Midterm 2 Prof. Persson, April 7, 2010 Name: SID: Section: Circle your discussion section below: Sec Time Room GSI 01 MW 8am - 9am 75 Evans C. Raicu 02 MW 9am - 10am 110 Barker M. Daub 03 MW 10am - 11am 3105 Etcheverry M. Daub 04 MW 12pm - 1pm 3105 Etcheverry M. Daub 05 MW 12pm - 1pm 7 Evans C. Raicu 06 MW 12pm - 1pm B51 Hildebrand H. Tran 07 MW 9am - 10am 47 Evans A. Boocher 08 MW 8am - 9am 81 Evans A. Boocher 09 MW 4pm - 5pm 110 Barker H. Chaperon 10 MW 5pm - 6pm 70 Evans H. Tran Other/none, explain: Grading 1 / 4 2 / 4 3a / 3 3b / 4 4a / 3 4b / 4 5 / 4 /26 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. (4 points) Evaluate Z . 5 x 2 cos( x 2 ) dx as an innite series, and estimate the error if the series is approximated by the rst two terms. 2 2. (4 points) Find the Taylor series for f ( x ) = 1 x centered at a =-3, and nd its radius of convergence. 3 3. Determine if the series below are absolutely convergent (AC), condition-ally convergent (CC), or divergent (D). a) (3 points) X n =1 (-1) n ( n + 1)3 n 2 2 n +1 b) (4 points) X n =1 (-1) n tan-1 1 n 4 4. Find the sum of the series below. a) (3 points) X n =1 (ln 2) n + 4 2 n b) (4 points) X n =1 (-1) n +1 n 2 n +1 5 5. (4 points) Find the Maclaurin series for f ( x ) = e-x 2 and evaluate f (99) (0) and f (100) (0). 6...
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## This note was uploaded on 03/25/2011 for the course MATH 1B taught by Professor Reshetiken during the Fall '08 term at University of California, Berkeley.

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midterm2 - 1. (4 points) Evaluate Z . 5 x 2 cos( x 2 ) dx...

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