Calculus I, Fall 2015 (http://www.math.nthu.edu.tw/˜ wangwc/)

Brief answer to selected problems in HW15

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. Chap 7, Additional and Advanced Exercises: problems 6: (a): Put x = 0, y = 0 in (i). (b): g′(x) = lim_{y→0} \frac{g(x+y)−g(x)}{y}. (c): Use method introduced in section 7.2 and g(0) = 0. Answer: g(x) = tan x.