Calculus I, Fall 2011 (http://www.math.nthu.edu.tw/˜ wangwc/)

Homework Assignment for Week 16-1

Assigned Dec 29, 2011.

1. Check if the improper integrals ∫_{0}^{1} x^{−p}dx and ∫_{1}^{∞} x^{−p}dx converge for the cases p > 1, p = 1 and 0 < p < 1, respectively by direct evaluation. Then memorize the results.

2. Section 8.6: Problems: 7, 13, 21, 25, 31, 33, 37, 38, 41, 51, 54, 55, 56, 58, 60, 71, 73. You may find it convenient to use Theorem 1 and Theorem 2 for almost all of the problems. Simply compare the integrand with one of the cases in Problem 1 above.