CALCULUS1 , TEST 1

9/23/2005

NAME:

STUDENT No:

1. Find the limits:

2. (10 points) Using the definition of limits, verify the following limit:

.

3. (50 points) Do the following to the function y = :

a) State the domain of f(x).

b) Is this function even, odd, or neither?

c) Find the limit

d) Prove (c) using the definition of a limit.

e) State the values of x at which f(x) is discontinuous.

f) Can you apply the Intermediate Value Theorem on this function? If yes – for what purposes, if no – justify your answer.

g) Sketch the graph of the function.

h) Find the inverse function if exists, otherwise justify your answer.

i) Sketch the inverse function.

j) Use transactions and the graph of (f) to sketch the graph of

4. (20 points) Find the limits as x → ∞ and as x → -∞. Use this information, together with intercepts, to give a rough sketch of the graph of the function.

y = x2