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MATH 101 HOMEWORK 6 Due on Wednesday, October 22 Covers sections 6.5 and 6.6. For full credit, show all work. 1. (12 marks, 4 for each part) For each of the following integrals, use the comparison test to determine whether it is convergent of divergent. (Do not try to compute the integrals: this could be either very hard or impossible.) Z ∞ (a) 1 Z ∞ (b) √ x3 − 1 dx, x2 + 1 (x2 + 1)e−x dx, 2 0 Z (c) 0 ∞ dx . + x3 x1/3 Z 1 2 ex dx. 2. (8 marks) We want to evaluate numerically the integral 0 (a) Write out (but do not try to evaluate) the midpoint and trapezoid approximations M4 and T4 . (b) How large should n be, if we want the error for the midpoint approximation Mn to be no greater than .001? (Feel free to use a calculator.) 1