# midterm2 persson fall 09 - 1. (5 points) Find the interval...

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UCB Math 1B, Fall 2009: Midterm 2 Prof. Persson, November 9, 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 / 5 3b / 5 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) Find the interval of convergence, including determination of the convergence at the end points, for the power series below. ∞ X n =1 (-1) n x n n · 3 2 n 2 2. (5 points) Show that the series y = ∞ X n =0 x 2 n +1 1 · 3 · 5 ····· (2 n + 1) is a solution of the diﬀerential equation y = 1 + xy. 3 3. Determine if the series below are absolutely convergent (AC), condition-ally convergent (CC), or divergent (D). a) (5 points) ∞ X n =0 ± 2-3 sin n 6 ² n b) (5 points) ∞ X n =1 (-1) n ³ sin(1 /n 2 ) ´ 1 / 3 4 4. Find the sum of the series below. a) (5 points) ∞ X n =1 2 n ( n + 2) b) (5 points) ∞ X n =0 ± 1 1 + 3 · (-1) n ² n 5 5. (5 points) Find all x that satisfy the equation ∞ X n =0 (-1) n ( n + 1) x 2 n +2 = 2 9 . 6...
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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 Berkeley.

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midterm2 persson fall 09 - 1. (5 points) Find the interval...

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