MTH 201 Homework 2, Fall 2016

MTH 201. Homework II 1. Solve the following problems in the book in Chapter 8: Section 8.7: Page 487, Exercises: 17,25,29, 39, 43, 49,57,59, 59, 61,65, 76 Practice Exercises, Page 491: Exercises: 59, 61, 65, 67. 2. Is it true that the improper integral � ∞ a f(x) converges, whenever f(x) → 0. Prove or give a counterexample. 3. Evaluate the following integrals: • � ∞ e 1 x(ln x+3)2 dx • � ∞ 0 √ tan−1(x) 1+x2 dx 4. Determine whether the following integrals diverge or converge: • � ∞ 1 x (x3+2)2dx • � −3 −∞ 1 x3 dx • � ∞ −∞ x ex+e−x dx • � ∞ 2 1 √x ln x dx • � ∞ 1 x−ex x2 dx • � ∞ 0 1 x2 dx 1