On-line Math 21

1.3.1  Examples of computing limits using rules and theorems.

Problems with hints

Problem 1 Compute

lim x® 3  x2-9 x2-2x-3 .

What do I do next?

So far, we saw that we had to factor the numerator and denominator of the fraction. the next thing we do is cancel out that common factor of (x-3) from the top and bottom. At that time, we can just evaluate the limit, since we will have gotten rid of the reason why the fraction was 0/0

x2-9 x2-2x-3 = (x+3)(x-3) (x-3)(x+1) = (x+3) (x+1) ,

so

lim x® 3  x2-9 x2-2x-3 = lim x® 3  (x+3) (x+1) = (3+3) (3+1) = 3 2 .

By David L. Johnson, last modified 3/10/00.