1. 2.2B Limits Involving Infinite Heights
Created by Greg Kelly, Hanford High School, Richland, Washington
Revised by Terry Luskin, Dover-Sherborn HS, Dover, Massachusetts

2. Limits that are infinite in height
As the denominator approaches zero,
the magnitude of the fraction gets
very large.
vertical asymptote at x=0.
If the denominator is positive, then the fraction’s overall sign is positive.
If the denominator is negative, then the fraction’s overall sign is negative.
The overall limit as x approaches zero does not exist,
since the left-hand and right-hand limits don’t match.

3. The overall limit as x approaches zero is
Example 4:
The denominator is positive after squaring x, so the limit has the same overall sign from left and right.
The overall limit as x approaches zero is
“positive without bound,” since the left-hand and right-hand
limits both trend toward positive infinity.