8 Questions of Calculus II - Exam 3 | Math 172, Exams of Calculus

Download 8 Questions of Calculus II - Exam 3 | Math 172 and more Exams Calculus in PDF only on Docsity! Math 172-01 Exam 3 Summer 2007 Name: ID: Date: Directions: Show all work. No work equals no credit. You may use a basic scientific calculator, but no graphing calculators. Use proper notation. 1.(18 pts) Which of the following converge and which diverge? Please state the test used for each. (a) ∞∑ n=1 (−2)n 3n (b) ∞∑ n=1 (ln n)n nn (c) ∞∑ n=1 (n + 3)! 3!n!3n 2.(4 pts) If a Taylor polynomial of order 1 is a linearization, what do we call a Taylor polynomial of order 2? 3.(18 pts) Determine which of the following converge absolutely, conditional, or diverge. State the appropriate test and conditions. (a) ∞∑ n=1 (−1)(n+1) n n3 + 1 (b) ∞∑ n=0 (−1)n 1 n + 3 (c) ∞∑ n=1 (−5)−n 4.(8 pts) The series tan x = x + x3 3 + 2x5 15 + 17x7 315 + 62x9 2835 + · · · converges for −π/2 < x < π/2. Find the series for sec2 x. Five terms is fine. Where does the series for sec2 x converge?