Calculus Homework #2
Due: 2026-04-03 (금) 23:59
For each question, please show as many details as possible.
1. Chapter 3.9, Exercise 22.
2. Chapter 3.10, Exercise 33. (Do not use a calculator.)
3. Answer the following questions:
(a) Write down the definition of the function tanh x.
1−x
1
−1
. What is the domain and the range of tanh−1 x?
(b) Show that tanh x = ln
2
1+x
(c) Chapter 3.11, Exercise 55.
4. Chapter 4.2, Exercise 35.
5. Evaluate the limits:
cos x − 1 + 12 x2
x→0
x4
1
1
(b) lim+
−
x→0
x2 x arctan x
(a) lim
1