Limit Calculator

About this tool

What Is a limit? Limit Calculator. The limit calculator evaluates lim f(x) as x → a by sampling the function infinitely close to a, the same idea behind rigorous limits. It reports the two-sided result plus the left and right values. A limit is the value a function gets arbitrarily close to as x approaches a point. For f(x) = (x² − 1)/(x − 1) the function is undefined at x = 1, yet it approaches 2 from both sides, so the limit exists and equals 2. The tool distinguishes a genuine limit from a jump: when the left and right values differ it warns that the two-sided limit does not exist, and it detects infinite limits as well. lim_{x→a} f(x): probe f(a − h) and f(a + h) with h → 0. How to Use Enter the function using x, e.g. (x^2-1)/(x-1). Supported: + − × ÷ ^, sqrt, abs, exp, sin, cos, tan, ln, log10, pi, e. Enter the point a that x approaches. Choose Two-sided, From the left, or From the right to inspect each side. Worked Example Enter the function (x^2-1)/(x-1) and a = 1. The tool returns 2: it evaluates the expression at points very close to 1 without ever setting the denominator to zero. Common Use Cases calculus homework and self-study checking differentiability of piecewise functions engineering continuity analysis curve sketching near singularities Important Notes Values are numerical, so very sharp peaks are sampled densely for accuracy. Infinity is reported as +∞ or −∞ w