Project: Fixing a Hole

Section 2.3 - 10 points

Due:

Consider

1. Is f(x) defined for x = -1?

For x = 0?

For x = 1?

For x = 2?

2. What is the domain of f ?

3. Compute and . Notice that one limit exists, and

one does not.

4. Graph . There are two x-values that are not in the domain of f.

Later, we will call these “discontinuities.” Geometrically, what is the difference

between the two discontinuities?

5. We say that f(x) has one hole in it. Where do you think that the hole is? Define “hole”

in this context.

6. The function is not defined at x = 0. Sketch this function.

Does it have a hole at x = 0?