Prepared : Fri Sep 24 15:20:59 CDT 1999

MATH 1271

QUIZ II

1) Evaluate the following limits:

a)

First try plugging in x=9.

This means that we have to try cancelling out that zeros. We can't simply say that 0/0=0. That's not right. So let's work with the given quotient:

Now we can safely plug in x=9 in the limit:

b)

Again we have a similar 0/0 problem. Let's work with the quotient to cancel the zeros:

Now we can evaluate the limit.

2) Find the points where

is not continuous. For each point of discontinuity, discuss whether or not it is removable.

Rational functions are discontinuous where the denominator is zero. Factor out the denominator: . So the zeros of the denominator are 3 and -2. These are the points of discontinuity. At both of these points the denominator is zero whereas the numerator is a non-zero value, hence the limit does not exist. This means we have a nonremovable discontinuity at that point.