Instructor: K.W.Nicholson

 

1. Write down the graphical definition of the derivative of y = f(x) at (x_o, f(x_o)).

2. Consider the piecewise continuous function

, Find:

a.

b.

c.

Evaluate the limits.

3.

4. a.

b.

5. Draw the graph of f ' (x).

6. Find the max's, min's, and inflection points and sketch y = 2x³ - 3x² - 72 x +4.

7. Find the equation of the line tangent to
cos (x + y) = xy at (0,p/2)

Differentiate:

8. f(x) = x² Arc tan x²

9. y = sin³ 4x

10. y = cos (p/6)

11.
12. y = ln ( tan x)

Sketch Graph without calculus:

13. y = (x+1)² (x - 3)(x + 3)³

14.

Evaluate the Integral:

15.

16.

17.

18.

19. Your worst nightmare find the area problem. If you can just graph and shade correctly I'll give you half credit. Find the area of the region bounded by x = y³ - 3y² and x - y +3 = 0

20. Related Rate Problem:
2 points Draw a picture and Label picture (if appropriate)
2 points Describe all variables involved and state clearly what you are trying to find.
2 points Find equation relating the variables
2 points Differentiate w.r.t. time
2 points Substitute in known values to solve for desired quantity

A spherical balloon filled with gas has a leak that permits the gas to escape at a rate of l.5 cubic meters per minute. How fast is the surface area of the balloon shrinking when the radius is 4 meters? (Surface Area (A) of a sphere is given by A = 4pr², and the formula for the volume (V) is V = (4/3) p r³