advertisement

Name: Math 2260 Exam #3 April 13, 2012 Instructions: You are welcome to use one sheet of notes, but no other references or tools are allowed (no textbooks, no calculators, etc.). This is a 50 minute exam; you may start working at 10:10 am and must stop at 11:00 am. To receive full credit for a correct answer you must demonstrate how you arrived at that answer. To receive partial credit for an incorrect answer your work must be clearly explained. 1 ∞ 1. Consider the sequence (an )n=1 where an = n2 + n 1/n . Does this sequence converge or diverge? If it converges, find its limit. 2 2. Does the series ∞ X 7n+1 n=1 (−1)n 6n−1 converge or diverge? If it converges, find its sum. If it diverges, explain why. 3 3. For what values of p does the series ∞ X np 3 + n3 n=1 converge? Explain your answer. 4 4. What is the interval of convergence of the following power series? Explain your answer. ∞ X (−1)n (x − 2)n . n3n n=1 5 5. Find the Taylor series centered at x = π for the function f (x) = sin(2x). (It suffices to write down, say, the first three non-zero terms, but it’s even better to give the general form.) 6