About this tool
The Limit Calculator is a free, in-browser calculus tool that estimates the limit of a function f(x) as x approaches a chosen point c — including c = +infinity or −infinity — by sampling the function numerically. For a finite c it evaluates f at points marching geometrically closer from each side, c ± 10⁻¹, 10⁻², … down to 10⁻¹³, and watches where the values settle. For c = ±infinity it instead samples at x = ±10¹, 10², … to see the end behaviour.
Everything is computed locally in your browser, so your input never leaves your device. You can choose a two-sided limit or restrict to the left-hand or right-hand limit. The tool compares the left and right sequences: if both converge to the same value L it reports that two-sided limit; if they disagree it shows each one-sided value and flags that the limit does not exist. Runaway magnitudes are reported as +∞ or −∞.
Type f(x) with the usual operators and functions (sin, cos, exp, ln, sqrt, …), the constants pi and e, and implicit multiplication like 2x. The approach point accepts numbers, small expressions, or inf / -inf. A classic example is sin(x)/x as x → 0: although the formula is 0/0 at the point itself, the samples from both sides converge to 1, so the calculator reports a limit of 1.