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Calculus II Exam 3, Spring 2003 Remember : You may use graphing calculators and tables of integrals, but you MUST show that you know your work. 1. Find the limits a) lim tan x x π 2 x π 2 ex 2 b) lim 2x x ∞ e 2. Does the integral converge or diverge? Give reasons. If you can, evaluate the integral. ∞ dx a) 2 3 x ln x 1 dx b) 2 0 x 1 3. Does the series converge or diverge? Give reasons. ∞ e n a) ∑ e n 0 n ∞ 3n2 5n 17 b) ∑ 3 n 0 4n 25n 1 ∞ 5n c) ∑ 2 1 2 n n 0 4. What is the radius of convergence of the power series? Show your work. ∞ a) ∑ 5n x 2 n n 0 ∞ x2n 1 b) ∑ 1 n n! n 0 5. Find the Maclaurin series for the function. DO a) OR b). a 1 x 1 4x2 b x 0 e t2 dt