1. Visualization and interpretation of the limit

2. The limit has a finite value L
The limit is at infinity

3. In the next slide we present the visual representation of this limit
the values of f approach L
x increases without bound
In the next slide we present the visual representation of this limit

4. f (x) x x x L
from the right as

5. This limit is telling us that the function f (x) has a horizontal asymptote y = L in the positive direction
We show in the next slides other sketches of possible functions whose limit at infinity is L.

6. L
f (x) x x x
from the left as

7. f (x) L
f (x)
from right and left as

8. It is not true that when a function has a horizontal asymptote its graph does not touch the horizontal asymptote for large values of x, they may or may not.
We give next some examples of different interpretations of this limit

9. If T is the temperature in degrees centigrade and t is time in minutes, then the interpretation of the limit is
The temperature stabilizes around L degrees centigrade
After a long time

10. If P is the price of a commodity in dollars and s is the supply, then the interpretation of the limit is
its price stabilizes around 0 dollars
As supply of the commodity increases without bound
If the commodity is abundant then it becomes worthless