Classic trig limit
Enter sin(x) / x with x approaching 0 to estimate the classic limit.
Limit calculator
Expression guide
Classic limits
sin(x) / x (x^2 - 1) / (x - 1) One-sided behavior
1 / x abs(x) / x Infinity
1 / x (2*x^2 + 1) / x^2 Syntax
ln(x) sqrt(x) exp(x) Use x as the variable. For the approach value, type a number, infinity, or -infinity. ln(x) and log(x) are natural log in this calculator.
Expression -
Approach -
Limit -
Left side -
Right side -
Method -
Privacy Local only
Explanation
-
Sample points
| Side | x | f(x) |
|---|
This first version estimates limits numerically. Oscillating functions, removable holes with unstable samples, and highly singular functions can require algebraic verification.
See examples
Removable discontinuity
Try (x^2 - 1) / (x - 1) as x approaches 1 and compare left and right samples.
One-sided behavior
Use abs(x) / x as x approaches 0 to see why the two-sided limit does not exist.
About this helper
The limit calculator evaluates one function in x near a chosen approach value. It uses Math.js, loaded only on this helper route, to parse the expression and then samples values from the left and right sides, or along a path toward infinity. The result is a numerical estimate, so algebraic verification can still matter for oscillating or highly singular functions. Your formula stays in your browser and is not uploaded.
Is this a symbolic limit calculator?
The first version is numerical. It samples values close to the approach point and classifies finite, infinite, unknown, or does-not-exist behavior.
Which functions can I use?
Use x, arithmetic operators, powers, parentheses, pi, e, sin, cos, tan, ln, log, log10, sqrt, abs, and exp.
Are my functions uploaded?
No. The expression and sample values are processed locally in your browser.