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 PROBLEMS
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

PRACTICE PROBLEMS
More practice with limits of unbounded functions.