Frequently Asked Questions

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.

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.

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.

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.

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.

Yes, enter 'infinity' or '-infinity' as the approach value to evaluate the function's behavior as x grows without bound in either direction.

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.

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.

Any expression math.js can parse, including polynomials, trigonometric functions, exponentials, and rational functions.

Yes, the limit calculator is completely free with no sign-up, and all calculations run instantly in your browser.