Calculus I, Fall 2013 (http://www.math.nthu.edu.tw/˜ wangwc/)

Brief answer to selected problems in Homework 14

1. Section 7.4 Problem 8: Note that ln 2 < 1. Answer (from slow to fast growth): (ln 2)^{x}, x^{2}, 2^{x} ≈ e^{x}. Problem 10: a. True, b. True, c. False, d. True, e. True, f. True, g. True, h. False. Problem 24: Answer (from slow to fast growth): (log_{2} n)^{2}, \sqrt{n} log_{2} n, n. The slower growth rate, the more efficient.

2. Section 8.1: Problem 65: Define F (x) = ∫_{x}^{b} f(t)dt. It follows that F (b) = 0, F′(x) = −f(x). Then apply integration by parts to ∫_{a}^{b} F (x)dx.