Limits & Continuity Skills
What are Limits?
What are limits in Calculus? Learn how to identify one- & two-sided limits and when they do & do not exist.
Limits on a Graph
How do you handle limits as x goes to infinity? How do limits work when there is a break in the graph? Can a limit exist at a point if the function is undefined there?
Limits by Direct Substitution
Always your first step in investigating a limit. It’s also the simplest!
Limits by Factoring
If direct substitution doesn’t solve your limit, factoring is a simple next step that may be helpful.
More Limits by Factoring
Look at another example of limits solved by factoring. (Same Reference Page as for video above.)
Limits as x goes to ∞, End Behavior, & Horizontal Asymptotes
What does a function’s graph do at the extreme ends? Does it have a horizontal asymptote? Answer these questions by taking the limit as x goes to infinity.
Learn about the dividing technique that makes these problems super simple!
Vertical Asymptotes vs Removable Discontinuities
How do you know if a rational function has an asymptote or a hole? We’ll look at the limits necessary to figure this out.
Special Trig Limits
Learn about the two special trig limits you're expected to have memorized for AP Calculus. Try typical problems using these limits.
More Indeterminate Limit Strategies
Learn two methods you can use on an indeterminate limit if factoring isn’t possible or doesn't get you anywhere.
Continuity
How do you know if a function is continuous by looking at the graph? What about if you have just the equation? What about piecewise equations?!
Limits Flow Charts
Two flowcharts to help guide you through limits. One for when x is approaching a real number, and one for when x is approaching infinity.