Limit Calculator
One- and two-sided limits, numerically and visually
About this calculator
The Limit Calculator estimates lim f(x) as x approaches a point — from the left, the right, or both sides — and also handles limits at ±∞. It samples the approach over shrinking steps, Richardson-extrapolates converging sequences, and classifies each side as a finite value, divergence to +∞ or −∞, or does-not-exist. It compares the limit with f(a) to flag continuity and removable discontinuities (like sin(x)/x at 0), and shows the approach table so you can watch the values converge.
How to use the Limit Calculator calculator
- Enter the values for your problem into the input fields.
- Read the result — it updates instantly as you type.
- Check the formula and the visual explanation to follow how the answer was found.
- Copy the page URL to share the exact calculation.
Common examples
- sin(x)/x as x → 0 → limit 1, a removable discontinuity (f(0) is undefined)
- 1/x at x = 0 → left limit −∞, right limit +∞, so the two-sided limit does not exist
- (1 + 1/x)^x as x → ∞ → converges to e ≈ 2.71828
- abs(x)/x at 0 → left −1, right 1: a jump, the limit does not exist
- 1/x² at x = 0 → both sides diverge to +∞
Frequently asked questions
How does the Limit Calculator calculator work?
Enter your values and the calculator applies the exact mathematical method for this problem, showing the result together with the formula it used. Everything is computed with high-precision arithmetic, so the answer you see is not limited by ordinary floating-point rounding.
When would I use the Limit Calculator calculator?
It is useful for homework and exam preparation, for checking work done by hand, and whenever a step in a larger problem needs this calculation done quickly and reliably.
How accurate are the results?
Calculations run at 30 significant digits of precision internally. Displayed values are rounded for readability, but the underlying result is far more precise than a typical hand or pocket-calculator computation.
Can I share a specific calculation with someone else?
Yes. Every value you enter updates the URL, so copying the address bar and sharing the link reopens the exact same calculation for whoever clicks it.