MATH 132 Final: MATH 132 UMass Amherst math132_spring06_html final-compressed
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Math 132h spring 2006 final exam: (14 points) determine whether each of the following series is absolutely conver- gent, conditionally convergent, or divergent. Explain, in particular, which test you used and why the conditions of the test are satis ed. a) b) ( 1)n n 1. 1: (18 points) compute the following integrals algebraically. 1 x: (14 points) a) find the interval of convergence of the power series. Xn=0 x2n+1 n! (2n + 1: denote by f (x) the sum of the power series in part 4a. Show that the derivative f (x) is equal to e(x2): (14 points) a) graph the two polar curves r = 3 cos( ) and r = 2 cos( ) on the same plane. Hint: consider the length of the parametrized curve. 1: (16 points) a) use the formula for the coe cient of the taylor series, in order to determine the taylor series for f (x) = ln(x) centered at a = 1.
