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Limit Calculator

Explore a limit by numerically sampling a supported expression near a target or toward positive or negative infinity. Compare one-sided behavior and inspect the estimates.

Use x, numbers, parentheses, + − * / ^, pi, e, and sin, cos, tan, sqrt, abs, exp, ln or log. Write multiplication explicitly, for example sin(x)/x.

Controls when nearby values count as converged; it does not guarantee mathematical accuracy.

Numerical sampling only. Supported expressions are limited to 120 characters and the parser supports real-valued arithmetic and listed functions. Near a finite target it samples progressively closer values; at infinity it samples only through |x| = 10,000. It cannot prove a limit, reliably resolve every oscillation, or certify behavior between samples.

How do you estimate a limit?

Enter an expression using x, such as sin(x)/x, then choose a finite target and direction. The calculator samples nearby values and compares both sides. This is a numerical estimate, not a symbolic proof; narrow or oscillating behavior may need a different method.

Frequently asked questions

How do you estimate a limit?

Enter an expression using x, such as sin(x)/x, then choose a finite target and direction. The calculator samples nearby values and compares both sides. This is a numerical estimate, not a symbolic proof; narrow or oscillating behavior may need a different method.

Are my expressions uploaded?

No. Expression parsing and limit sampling run locally in this browser. This tool does not upload or save your inputs.

What is the limit of sin(x)/x as x approaches zero?

In radians, this calculator samples values from both sides and estimates 1. The familiar result is a standard limit; the tool itself reports a numerical estimate, not a proof.

Can I calculate a one-sided limit?

Yes. Choose an approach from the left or right. The calculator displays only that side’s samples.

Does this prove a limit exists?

No. It compares a finite set of numerical samples. Oscillation, sharp behavior or a discontinuity between sample points can require symbolic reasoning or another method.