Math 125 Test 1 4 points each Jan 26, 2005

Circle answers where appropriate.

Use the function in the graph below for problems 1 & 2:

1. At which value(s) of x does the limit not exist ?

2. Find .

Use the piecewise continuous function below for problems 3 - 5

, Find:

3.

4.

5.

Use the Rules for Limits to evaluate:

If and ,

6.

7.

8.

Evaluate the limits.

9.

10.

Find the Vertical Asymptote(s) for:

11.

12.

13.

Find the Horizontal Asymptotes for :

14.

15.

16.

17. If D represents the number of deer amd W represents the number of wolves in the forest as a function of time, what sign would you expect dD/dW to have?

18. Give the graphical definition of the derivative of y = f(x) at the point (a, f(a)). You must use a complete sentences to get any credit at all.

19. Find the equation of the line tangent to f(x) = 4x² - 3x - 1 at x = 1.

20. If the position of a rabbit is given by the function

x(t) = 2t² - 4t +5, find her speed and when t = 4 s.

What is her acceleration at this same instant?

Differentiate the function:

(means find f ' (x) ).

21. f(x) = 3sin x

22.

23. f(x) = cos (π)

24. f(x) = 5cos (x)

25. f(x) = x² + tan x
5 Points Bonus:

Does this function have a vertical asymptote? If so, find it, if not, explain why not.

5 Points Bonus:

Draw the f(x) vs x and f’’(x) vs x (assume the object starts at the origin ) graphs for the given f’(x) vs x graph.