Math 151 WIR 4.1, 4.2 Exponential Functions and Inverse Functions

4.1 Exponential functions and their derivatives:

1. Evaluate each limit.

d) e) f) g)

2. Find for Also find if a=-1.

3. Find f'(x) for f(x) =

a) b) given that c) d)

4. Find the equation of the tangent line at the point (0, 2) for .

5. Find all values of A so that solves .

4.2 Inverse functions

6. a) Show that is one to one. b) Show that if c is nonzero, and hence is one to one.

7. Find the domain and range and any horizontal and vertical asymptotes for f and its inverse if

a) b)

8. Given that is one to one on [0, ∞], and g(x) is the inverse function to f, find

g'(3+2e) and g'(2).

9. Given that f and g are inverse functions and the tangent line to f at (1, -4) is y=3x-7, find the tangent line to g at (-4, 1).