Limit Calculator with Steps
Limit calculator lim f(x)
Enter f(x) and choose whether x tends to x0 or to infinity. The tool substitutes, identifies the indeterminate form, then removes it by factoring, using the conjugate or L'Hôpital's rule.
The calculator above evaluates limits at a point or as x approaches infinity, identifies indeterminate forms, and resolves them by factoring, conjugates, or L'Hôpital's rule.
Formulas used
lim(x→0) sin x / x = 1
L'Hôpital: lim f/g = lim f′/g′ (0/0 or ∞/∞)
- Indeterminate forms: 0/0, ∞/∞, ∞ − ∞, 0·∞.
- For rational functions at infinity, divide by the highest power of x.
Worked example
Evaluate the limit of (x² − 4)/(x − 2) as x → 2:
lim (x + 2) = 4
Enter the same values in the calculator above to see every step of the solution.
How to use the calculator
- Type the function and the value x approaches (a number, +∞, or −∞).
- Press the calculate button. The result appears instantly.
- Read the step-by-step solution, rendered with KaTeX, to check your own work.