MATH 131 Midterm: MATH 131 UMass Amherst 131f16 Exam 2
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Problem 1 (8 points) find the radius of convergence and the interval of convergence of the series k 1. |x 2| 3, so the radius of convergence is 3. Now, |x 2| 3 3 x 2 3 5 x 1. Check the convergence at each end point x 5, x 1 separately: x 5; . 1 k k 1 x 1; k 1. 1 2 k k 1 k3k 3k k 1 k. Hence, the interval of convergence is 5, 1 . Problem 2 (7 points) find the taylor series for f x e3x about x 0, and write out first. 5 terms. f x e3x f x 3e3x f x 32e3x f 3 x 33e3x f 4 x 34e3x f k x 3ke3x.
