Limit Calculator
Find the limit of a function as x approaches a number or infinity — checks the left- and right-hand limits and spots infinite limits and limits that don't exist.
How to use
- 1Type the function, e.g. sin(x)/x or (x^2-1)/(x-1).
- 2Enter the value x approaches (a number, inf or -inf).
How it's calculated
The function is evaluated ever closer to the point from both sides, and the sequence is extrapolated (Richardson) to the limit. Nice values (integers, simple fractions, π, e) are recognized.
Frequently asked questions
Is this symbolic like L'Hôpital's rule?
No — it's a high-precision numerical estimate, which agrees with the exact limit for ordinary functions. Always show your own working for homework.
When does a limit not exist?
When the left- and right-hand limits differ (e.g. |x|/x at 0) or the function oscillates (sin(1/x) at 0).
How do I enter infinity?
Type inf or -inf in the 'x approaches' box.