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Limit Calculator

Calculate limits of functions step-by-step. Find limits at points, infinity, left-hand and right-hand limits with detailed solutions and graphs.

Enter Your Function ⓘ

\( \displaystyle \lim_{x \to \ } \)

Basic Rational Function

\( \displaystyle \lim_{x \to 2} \frac{x^2 - 4}{x - 2} \)

Limit of a rational function with removable discontinuity.

Sine Function Limit

\( \displaystyle \lim_{x \to 0} \frac{\sin(x)}{x} \)

Famous limit used in calculus and trigonometric functions.

Exponential Limit

\( \displaystyle \lim_{x \to \infty} \left(1 + \frac{1}{x}\right)^x \)

Limit that defines the mathematical constant e.

Square Root Limit

\( \displaystyle \lim_{x \to \infty} \left(\sqrt{x^2 + 1} - x\right) \)

Limit involving difference of square roots at infinity.

Exponential Growth

\( \displaystyle \lim_{x \to 0} \frac{e^x - 1}{x} \)

Limit involving exponential function near zero.

Cosine Function Limit

\( \displaystyle \lim_{x \to 0} \frac{1 - \cos(x)}{x^2} \)

Limit involving trigonometric function and square.

Why Use Our Limit Calculator?

Step-by-Step Solutions

Get detailed step-by-step explanations showing how each limit is calculated.

Multiple Limit Types

Calculate two-sided limits, left-hand limits, right-hand limits, and limits at infinity.

Visual Graphs

See graphical representations of functions near limit points for better understanding.

Smart Detection

Automatically detects discontinuities, asymptotes, and special limit cases.

Handles Infinity

Properly calculates limits approaching positive and negative infinity.

Educational Tool

Perfect for students learning calculus and professionals needing quick calculations.

How to Use the Limit Calculator

1

Enter Function

Type your function using standard mathematical notation. Use x as the variable or choose another variable.

2

Set Limit Point

Enter the value that x approaches. This can be a number, ∞ (infinity), or -∞ (negative infinity).

3

Choose Limit Type

Select two-sided limit (default) or one-sided limits (left-hand or right-hand).

4

Calculate

Click "Calculate Limit" to get the result, step-by-step solution, and graphical representation.