Limits and infinity

7 videos
2 skills
You have a basic understanding of what a limit is. Now, in this tutorial, we can explore situation where we take the limit as x approaches negative or positive infinity (and situations where the limit itself could be unbounded).

Limits and infinity

VIDEO 7:41 minutes
Here we consider the limit of the function f(x)=1/x as x approaches 0, and as x approaches infinity.

Vertical asymptote of natural log

VIDEO 7:00 minutes
What happens to ln(x) as x approaches 0?

Visually determining vertical asymptotes

VIDEO 1:46 minutes
You can often tell if a function has a vertical asymptote just by looking at its graph.

Limits at infinity where f(x) is unbounded

Practice reasoning about limits of unbounded functions.

Limits at positive and negative infinity

VIDEO 4:07 minutes
When taking a limit at infinity, you can either go right to positive infinity or left to negative infinity.

More limits at infinity

VIDEO 4:33 minutes
A few more examples of limits as x goes to infinity.

Limits with two horizontal asymptotes

VIDEO 5:14 minutes
Here we look at a function with distinct horizontal assymptotes: One for the limit as x goes to infinity, and one for the limit as x goes to negative infinity.

Limits at infinity using algebra

VIDEO 5:26 minutes
Just like other limits, limits as x goes to infinity can be simplified and solved by manipulating things algebraically.

Limits at infinity where x is unbounded

More practice with limits of unbounded functions.