Limits
Limits by substitution, the case by factoring, and limits at infinity.
Question types
This sitting
0 of 0
right so far
Streak
0
right on the first try, in a row
All time on Limits
First try
Free problems today
20 of 20 left
Any spelling of the right answer counts: 0.5 or 1/2, pi/2 or π/2, sine or cosine for the same graph.
Your score, on every device
Free account: your score and streak follow you to any device, and you can practice from a photo of your worksheet.
Try a sample flashcard set- Read-only with Canvas
- Free to start
- Never does your work
- Made by a student
About Limits
A limit asks what value a function is heading toward as x gets close to a number, whether or not the function actually gets there. For a polynomial or a fraction whose bottom is not 0, just put the number in.
When putting the number in gives 0/0, nothing is decided yet: factor, cancel the shared factor, and try again. As x heads to infinity, only the highest powers matter, so compare the degrees of the top and the bottom.
Keep in mind
- If the function is fine at the point, the limit is its value there.
- 0/0 means factor and cancel, then put the number in again.
- As x → ∞, same degree on top and bottom: the limit is the ratio of the leading coefficients.
- As x → ∞, bottom degree higher: the limit is 0.
The Backpack iPhone app is coming soon to the App Store