Limit Calculator — Step-by-Step Solutions

The Limit Calculator evaluates the limit of a function as a variable approaches a specified value. It supports limits from the left, from the right, and two-sided limits, including limits approaching infinity.

Enter your function, the variable, and the point it approaches. The calculator uses numerical evaluation to determine the limit value with high precision.

Expression f(x)

Variable

Approaching (a)

Limit

—

Your calculations will appear here

How to Use the Limit Calculator

Enter the function whose limit you want to find.
Specify the variable and the value it approaches.
Choose whether to evaluate the limit from the left, right, or both sides.

Formula and Theory

A limit describes the value that a function approaches as the input approaches a specified value. Limits are fundamental to calculus and are used to define derivatives, integrals, and continuity.

A limit exists if and only if the left-hand limit and right-hand limit both exist and are equal. If they differ, the function has a "jump" discontinuity at that point.

Worked Examples

Example 1: Simple limit

Problem: Find the limit of (x^2 - 4)/(x - 2) as x approaches 2

Solution: Factor: (x-2)(x+2)/(x-2) = x+2. As x approaches 2: 2+2

Answer: 4

Example 2: Limit at infinity

Problem: Find the limit of 1/x as x approaches infinity

Solution: As x gets larger, 1/x gets smaller and approaches 0

Answer: 0

Frequently Asked Questions

What does it mean when a limit does not exist?

A limit does not exist if the function approaches different values from the left and right, oscillates infinitely, or approaches positive or negative infinity.

What is L'Hopital's rule?

When a limit gives an indeterminate form (0/0 or infinity/infinity), L'Hopital's rule says you can take the derivative of the numerator and denominator separately and re-evaluate the limit.