Name: ___________________________________
From Euclid to Spigotry
Assignment 15 (outline 13) 
Last modified: September 14, 2004
1. The so-called hyperbolic functions can be defined by Taylor series as

Starting from these series and proceeding as for C(x) and S(x) in class, prove the following:
a. Sh'(x) = Ch(x) and Ch'(x) = Sh(x).
b. - 
c. 

2. Find first two nonzero terms in the Taylor series expansion for f(x) = arctan x about x = 0
by computing f(0), f'(0), f''(0), and f'''(0) and using the formula presented in class.  Computing
f'''(0) is a pain, but you should conclude that
arctan x =