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Unformatted text preview: Name: TA: Math 20B. Midterm Exam 2 February 27, 2009 Sec. No: PID: Sec. Time: Turn oﬀ and put away your cell phone. You may use one page of notes, but no books, calculators, or other assistance during this exam. Read each question carefully, and answer each question completely. Show all of your work; no credit will be given for unsupported answers. Write your solutions clearly and legibly; no credit will be given for illegible solutions. If any question is not clear, ask for clariﬁcation. ln(x) dx. x4 1. (4 points) Evaluate the integral # 1 2 3 4 5 Σ Points 4 4 6 4 6 24 Score 2. (4 points) Evaluate the integral exponentials in your answer. e3ix cos(2x) sin(5x) dx. You may leave complex 3. (a) (3 points) Find the partial fraction expansion (PFE) of 3x2 + x + 9 . x3 + 3x (b) (3 points) Use the partial fraction expansion from part (a) to evaluate the integral 3x2 + x + 9 dx . Please be sure to show all of your work. x3 + 3x 4. (4 points) Let R be the region in the ﬁrst quadrant below the graph of y = √ 2 x−3 and between the vertical lines x = 3 and x = 5. Is the area of R ﬁnite? If so, ﬁnd its value. 5. Determine whether the given series converges or diverges. If the series converges, ﬁnd its sum. Be sure to justify your conclusions by stating relevant theorems and/or convergence tests.
∞ (a) (3 points)
n=2 n2 n3 − 2 (b) (3 points) 4 − 1 + 1 1 1 − + −··· 4 16 64 ...
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 Winter '20
 lindblad
 Math, Derivative, Partial fractions in complex analysis, partial fraction expansion

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