**MATH 2431 – Summer
Session 2005**

**NAME_______________________________________________________**

**You may NOT use a calculator on this portion of the test.
Show work and write clearly.**

**For #1-3, evaluate
the limits.**

1. (10 points) _{}

2. (10 points) _{}

3. (10 points) _{}

4. (10 points) The position of an object is given by the values in the table:

t (seconds) |
0 |
1 |
2 |
3 |
4 |
5 |

s (feet) |
0 |
3 |
7 |
16 |
30 |
60 |

a. Find the average velocity for the time period beginning
when *t* = 3 and lasting

i. 1 s ii. 2 s

b. Estimate the instantaneous velocity when *t* = 3. Explain.

5. (10 points)

a. Explain what it
means to say that _{} and _{}.

b. Is it possible for
both of these statements to be true and yet _{}? Explain.

6. (10 points) Use the Intermediate Value Theorem to show
that the polynomial function _{} has a root in the
interval (3, 4). Be specific on the use of the theorem.

7. (10 points) Briefly explain the relationship between rates of change and the secant and tangent lines to a curve.

**MATH 2431 – Summer
Session 2005**

**NAME_______________________________________________________**

**You MAY use a calculator on this portion of the test.
Show work and write clearly.**

8. (20 points) Let _{} _{}

a. Locate the discontinuities of *f*(*x*).

b. For each location, determine the type of discontinuity. Explain.

c. For each location, determine if the function is continuous from the right, left or neither. Explain.

9. (10 points) Evaluate _{}, _{}, _{} and _{}. What do you notice?