1. INFINITE LIMITS

2. LIMITS What is Calculus? What are Limits? Evaluating Limits
Graphically
Numerically
Analytically
What is Continuity?
Infinite Limits
This
presentation
- When the value of the function grows without bounds
- When x approaches

3. Infinite Limits The statement means that the function
grows positively without bounds as x approaches c.
The statement means that the function
grows negatively without bounds as x approaches c.
and
One sided limits can also be infinite:
The equals signs in the statements above do not mean that the limits exist. On the contrary, it says that the limits fail by demonstrating unbounded behavior as x approaches c.
Important note:

4. Infinite Limits & Rational Functions
Infinite limits occur at vertical asymptotes.
Rational functions that cannot be fully simplified generate vertical asymptotes.
We will limit (no pun intended) our study of infinite limits to rational functions.

5. Infinite Limits: Examples1. 2. 3.
x = 1:
x = -2:
x = 2:
(Removable point
discontinuity)
Infinitely many :
For ea VA, x = c, ,
For each example,
Identify any vertical asymptotes (be sure to simplify the function first to discount any point discontinuities).
Graph the function and observe the behavior of the function as it approaches these x = c values from both directions. Does it grow without bound positively or negatively?

6. Evaluating Limits When x Approaches
is asking about the right hand behavior of the function
is asking about the left hand behavior of the function
Examples:
This is an odd polynomial with
a positive leading coefficient.
So the RH behavior
And the LH behavior
This is a rational function with a
horizontal asymptote at y = 2/3.
Therefore:
Therefore:

7. Infinite Limits: Summary
Infinite limits are written as
The equals sign is misleading since the limit does not exist.
Infinite limits generally occur at the vertical asymptotes of rational functions. The function may grow positively or negatively on either side of the asymptote.
When asking for a limit as x , i.e.,
Check the end behavior of the function.