Limit Calculator

Use our free limit calculator to evaluate limits of any function as x approaches a value. Supports two-sided, left-hand, and right-hand limits.

Math

Mode

f(x) =

x →

Formula

Evaluate the limit of any function as x approaches a value. Uses numerical evaluation at very close points to determine the left-hand, right-hand, and two-sided limit.

lim_{x→a} f(x) evaluated numerically from left and right

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Enter f(x).
2Enter the value x approaches.
3Select two-sided, left, or right.
4Click Calculate.

Examples

lim x→0 x²

1.From left: 0² = 0
2.From right: 0² = 0
3.Limit = 0

Result: 0

lim x→0 (sin x)/x

1.Numerically ≈ 1

Result: 1

Frequently Asked Questions

Numerically by evaluating f at x = a ± ε where ε ≈ 10⁻¹⁰.

The two-sided limit does not exist.

Use a very large number for a.

Numerical approximation — accurate to ~10 decimal places.

The calculator evaluates the limit, not the function value at a.

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CalculateMe Team

Last updated: 2026-07-14

Limit Calculator

Formula

How It Works

Examples

lim x→0 x²

lim x→0 (sin x)/x

Frequently Asked Questions

How are limits computed?

What if left ≠ right?

Can I compute limits at infinity?

Is it exact?

What about discontinuities?

Related Calculators

Limit Calculator

Formula

How It Works

Examples

lim x→0 x²

lim x→0 (sin x)/x

Frequently Asked Questions

How are limits computed?

What if left ≠ right?

Can I compute limits at infinity?

Is it exact?

What about discontinuities?

Related Calculators