1. Given that f (x) = ex + e-x/2 and g (x) = ex - e-x/2 show that [f (x)]2 - [g (x)]2 = 1.
2. Use a graphing utility to compare the graph of the function y = ex with the graph of each function.[n! (read "n factorial") is defined as n! = 1.2.3. . . (n - 1) =. n.]
(a) y1 = 1 + x/1!
(b) y2 = 1 + x/1! + x2/2!
(c) y3 = 1 + x/1! + x2/2! + x3/3!