Limit Calculator
Estimate limits numerically for x approaching a point or infinity. Supports two-sided, left-hand, and right-hand checks with a convergence table and chart.
Limit calculator for two-sided and one-sided checks
English SERPs for limit calculators expect a solver that accepts f(x), an approach value, direction, and infinity notation. This page is intentionally transparent: it gives a numerical convergence check rather than claiming a full CAS proof.
The limit describes the value f(x) approaches as x gets close to a, even if f(a) itself is undefined.
- Enter a function of x, such as sin(x)/x or (x^2-1)/(x-1).
- Use a number, pi, e, inf, or -inf as the approach value.
- Compare left-hand and right-hand behavior before trusting the two-sided result.
How to read the numerical result
| Output | Meaning |
|---|---|
| Direct substitution | The value of f(a), when the expression is defined at a |
| Left-hand limit | The behavior as x approaches from smaller values |
| Right-hand limit | The behavior as x approaches from larger values |
| Convergence table | A sequence of samples closer and closer to the approach value |
Frequently Asked Questions
Sources and References
Calculations are based on the listed reference sources. Links open in a new tab.
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