Online Tool Store
Limit Evaluator
Estimate the limit of a function as x approaches a finite value or infinity, using a left/right (or magnitude) approach table. Runs entirely in your browser.
This works right here on your device — nothing gets sent out.
Supports + - * / ^, sin, cos, tan, exp, log, sqrt, abs, and parentheses.
A number, or "infinity" / "-infinity" for a limit at infinity.
| x (from left) | f(x) | x (from right) | f(x) |
|---|
Left-hand limit
Right-hand limit
How the limit evaluator works
- Enter a function f(x) and the x-value it should approach — or enter "infinity" / "-infinity" for a limit at infinity.
- For a finite approach value, the tool evaluates f(x) at points increasingly close to that value from both sides.
- For infinity, the tool evaluates f(x) at increasingly large magnitudes (10, 100, 1,000, 10,000, 100,000) in the approached direction.
- Compare the resulting values to see if they converge to a single number.
FAQ
How does this tool estimate a limit?
It numerically evaluates f(x) at points progressively closer to the target value from both the left and right sides, then checks whether those values converge to the same number.
What functions and operators are supported?
Basic arithmetic (+ - * / ^), parentheses, and the functions sin, cos, tan, exp, log, sqrt, and abs, plus the constants pi and e.
Can this handle limits at infinity?
Yes - enter "infinity" or "-infinity" in the "x approaches" field to evaluate the function at increasingly large magnitudes (10, 100, 1,000, 10,000, 100,000) and see whether it settles on a finite value. It also handles limits at a finite x-value, including cases where the function is undefined exactly at that point (like sin(x)/x at x=0).
Is a numerical approximation the same as a proven limit?
No - this is a numerical estimate, not a symbolic proof. It's useful for building intuition and checking your algebraic work, not a substitute for a formal limit derivation.
How we compare
| Feature | Online Tool Store | Graphing by hand | Symbolic CAS software |
|---|---|---|---|
| Instant approach table | ✓ | ✗ | ✗ |
| No install required | ✓ | ✓ | ✗ |
| Handles limits at infinity | ✓ | ✗ | ✓ |
A great way to build intuition for what a limit means before working through the algebra by hand.