Question

How do you evaluate the limit `(x^2-3x+2)/(x^2-4)` as x approaches `-2`?

Answer 1

The limit does not exist.

Explanation:

As `x rarr -2`, the numerator goes to `12` and the denominator goes to `0`.

The limit does not exist. On one side the quotient increases without bound and on the other side it decreases without bound.
The line `x=-2` is a vertical asymptote.