Calculus I, Fall 2021 (http://www.math.nthu.edu.tw/˜ wangwc/)

Brief solutions to selected problems in homework week 07

1. Section 3.8, problem 8:

\frac{df^{−1}(y)}{dy}|_{y=0} = \frac{1}{\frac{df(x)}{dx}|_{x=5}} = \frac{1}{6}

2. Section 3.8, problem 98: Use

(a) the identity (⋯)^{n} = ((⋯)^{\frac{n}{x}} )^{x}

(b) Theorem 4

(c) Theorem 10 of section 2.5

(d) The function f(a) = a^{x} is continuous at a = e to get the answer = e^{x}.