What is the Limit Calculator?
Evaluate limits of functions as x approaches a finite value or ±∞. Enter an expression like sin(x)/x with point 0, or (x^2 - 1)/(x - 1) as x approaches 1. The calculator tries direct substitution first, then estimates one-sided and two-sided limits numerically. Detects when left and right limits disagree (DNE). Free, private, and instant in your browser.
How to use the Limit Calculator
- Enter the expression (e.g. sin(x)/x).
- Set the variable and the approach point (0, 1, inf, -inf, pi).
- Choose two-sided, left, or right limit.
- Read the limit value and numerical approach steps.
- Copy the result for homework or notes.
Common use cases
- Checking lim(x→0) sin(x)/x = 1
- Finding removable discontinuities like (x^2 - 1)/(x - 1) at x = 1
- Evaluating limits at infinity for rational functions
Frequently asked questions
- How do I enter infinity?
- Use inf, +inf, infinity, or ∞ for +∞ and -inf or -∞ for negative infinity.
- What does DNE mean?
- Does not exist — the left-hand and right-hand limits are different or do not converge.
- Is this symbolic or numeric?
- Primarily numeric. Direct substitution is used when the expression is defined at the point; otherwise values are estimated from nearby points.
- What expressions are supported?
- Polynomials, +, −, ×, ÷, powers, sin, cos, tan, ln, log, sqrt, exp, abs, pi, and e — same syntax as the Derivative Calculator.
