Math 151 In Class Exam 2 Review

1. Evaluate each limit.

2. Find a formula in x for the derivative of the inverse function to f(x)= tanx

3. Find where A is a constant.

4. a) Find the tangent line to f(x) at x=1. b) Find

c) Find the tangent line to at x=f(1).

d) Is the inverse to the tangent line the tangent to the inverse?

5. A curve is parameterized by Find the tangent line to the curve at (1/4, 0).

6. Find the 59th derivative with respect to x of

a) f(x)= sinx b) c)

7. For what values of a does .

8. and L(x)= 5x - 7 is the tangent line to f (x) at x=1. Find the linear approximation to h(1.1).

9. a) Use linear approximation to approximate .

b) Using Newton's method to approximate , make a first guess and find .

10. A snowball is melting at the rate of 4 cubic cm. per hour. Find the rate of change of the surface area at the instant that the volume is 36 cubic cm.