Use the Limit Calculator | Numerical Calculus Limit Estimator
Enter your values below. The calculator runs in your browser and shows an estimate immediately.
How the estimate is calculated
Estimate lim x→a f(x) by evaluating near a with decreasing step sizes h
Example: For f(x)=(x²−1)/(x−1) as x approaches 1, samples from either side approach 2, even though the original expression is undefined at x=1.
When this calculator is useful
One-sided samples are useful when checking a removable discontinuity, a jump or a possible vertical asymptote. The page reports left and right behavior separately because a two-sided limit exists only when both sides approach the same finite value. Use algebra or a formal argument to confirm a result.
How to use this calculator
Choose the expression and point, then select a one-sided or two-sided approach. The page samples nearby points instead of substituting directly at the point, which helps with removable discontinuities.
What to keep in mind
Numerical estimates can mislead near poles, oscillations, steep slopes and domain boundaries. If left and right values differ or grow without bound, the two-sided limit may not exist as a finite number. Use algebraic methods to confirm important results.
Frequently asked questions
How does a limit calculator work?
It evaluates the function at points increasingly close to the target and compares the values.
Can it prove a limit exists?
No. Numerical sampling suggests a limit; a proof requires mathematical reasoning.
What if the function is undefined at the target?
A limit may still exist. The tool samples nearby points rather than relying only on the value at the target.
Why are left and right results different?
The function may have a jump, a one-sided limit, an asymptote or other behavior that prevents a common two-sided limit.