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Exam 4 Solutions Sp10 (1)

# Exam 4 Solutions Sp10 (1) - Math 237 Calculus II Exam 4...

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Math 237. Calculus II Exam 4, Version 1 Fall, 2011 Name: SOLUTIONS . 1. Find the indefinite integral Substitute u = ln x . This gives du = dx / x , and so 2. Find the convergence set for the series . Starting off using the Absolute Ratio Test: So the series will converge whenever |2 x 3| < 1 or, equivalently, whenever 1 < 2 x 3 < 1, which simplifies to 1 < x < 2. To finish up, we need to know whether the series converges at either endpoint. For x = 1, the series is equal to . This series, the harmonic series, is known to diverge. For x = 2, the series is equal to , which is the alternating harmonic series and is known to converge. Answer: (1, 2]. 3. Sketch the graph of the hyperbola whose equation is x 2 4 y 2 14 x 32 y 11 = 0. Include foci, vertices, and asymptotes. The first thing to do is to complete the squares. And then take it from there . . . . , or in a more standard form . So it is a vertical hyperbola with center (7, 4), a = 1, and b = 2. Adding and subtracting a = 1 to/from the y -coördinate of the center shows that the vertices are (7,

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Exam 4 Solutions Sp10 (1) - Math 237 Calculus II Exam 4...

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