🎯Limit Calculator
Evaluate the limit of a function as x approaches a value or infinity, with left/right limits and L'Hôpital's rule shown for indeterminate forms.
Calculations run entirely in your browser using math.js for parsing and evaluation, using numeric convergence and, when applicable, L'Hôpital's rule. No data is sent to a server.
Free Limit Calculator
Our free limit calculator evaluates the limit of a function as x approaches any finite value or infinity. It computes the left-hand and right-hand limits numerically by evaluating the function at points that converge closer and closer to the target, then checks whether both sides agree.
For indeterminate forms like 0/0, where a function such as sin(x)/x is undefined at the approach point but has a well-defined limit, the calculator detects the numerator and denominator both vanishing and applies L'Hôpital's rule — differentiating the numerator and denominator separately and evaluating the resulting ratio at the same point.
This makes the tool useful for calculus homework, verifying limit computations, and understanding one-sided limits and infinite limits. No sign-up, no downloads — everything runs instantly in your browser.
About the Limit Calculator
Features
Finite and infinite limits
Approach any finite value, or evaluate behavior as x → ∞ or x → −∞.
One-sided limits
See the left-hand and right-hand limits separately, and whether they agree.
L'Hôpital's rule
Automatic detection of 0/0 and ∞/∞ forms with the derivative-based resolution shown.
Quick-start presets
Common example limits to load with one click.
Frequently Asked Questions
What does a limit mean?
A limit describes the value a function approaches as its input gets arbitrarily close to a specific point, even if the function is undefined exactly at that point.
What are left-hand and right-hand limits?
The left-hand limit is the value the function approaches as x approaches the point from values below it; the right-hand limit approaches from values above it. If both sides agree, the two-sided limit exists.
What does 'DNE' mean?
DNE means 'does not exist'. This happens when the left-hand and right-hand limits disagree, such as with 1/x as x approaches 0.
What is an indeterminate form?
An indeterminate form, like 0/0 or ∞/∞, occurs when direct substitution gives an undefined expression, even though the limit may still exist and have a definite value.
What is L'Hôpital's rule?
L'Hôpital's rule says that for a 0/0 or ∞/∞ indeterminate form, the limit of a quotient equals the limit of the derivatives of the numerator and denominator, evaluated at the same point.
Can I find limits at infinity?
Yes, enter 'infinity' or '-infinity' as the approach value to evaluate the function's behavior as x grows without bound in either direction.
How does the calculator compute the limit numerically?
It evaluates the function at points progressively closer to the target value (or progressively larger, for infinite limits) and checks whether the results converge to a stable number.
Does this work for functions undefined at the exact point?
Yes — that's exactly the case a limit is designed for. The calculator never evaluates directly at the target point; it approaches from both sides instead.
What functions are supported?
Any expression math.js can parse, including polynomials, trigonometric functions, exponentials, and rational functions.
Is this calculator free to use?
Yes, the limit calculator is completely free with no sign-up, and all calculations run instantly in your browser.