☰

Limit Calculator

Calculate the limit of a function at a point, e.g., \( \lim_{x \to 2} x^2 \), using numerical evaluation.

Limit Calculator

Please enter a valid function and point.

Calculation Result

Result will appear here

Result copied to clipboard!

About the Limit Calculator

The Limit Calculator computes the limit \( \lim_{x \to a} f(x) \) of a function \( f(x) \) at a point \( a \) using numerical evaluation. It supports functions like \( x^2 \), \( \sin(x)/x \), or \( e^x \). This tool is ideal for calculus students, teachers, and professionals.

  • Features:
    • Computes the limit \( \lim_{x \to a} f(x) \) by evaluating the function near the point \( a \).
    • Supports polynomials, trigonometric functions (sin, cos), exponentials (e^x), and logarithms (ln).
    • Keypad for easy input with digits, variable (\( x \)), operators (+, -, *, /, ^), and functions (sin, cos, ln, e^).
    • Clear and backspace functionality, with a "Copy" button for results.
  • Practical Applications: Useful in calculus for analyzing function behavior, continuity, and derivatives.
  • How to Use
    • Enter a function and point (e.g., \( x^2; 2 \)).
    • Use the keypad to insert digits, variable (\( x \)), operators, and functions (sin, cos, ln, e^).
    • Click "Calc" to compute the limit and view the result, then use "Copy" to copy the result.
    • Use "Clear" to reset, or "⌫" to delete the last character.
    • Share or embed the calculator using the action buttons.
  • Helpful Tips
    • Ensure the function is defined near the point (e.g., avoid undefined operations like division by zero).
    • Use * for multiplication and / for division in complex expressions (e.g., \( \sin(x)/x \)).
    • Point format: Enter a number after a semicolon (e.g., \( x^2; 2 \)).
    • The calculator may not handle indeterminate forms or oscillatory limits accurately.
  • Examples
    • Example 1: Polynomial: \( \lim_{x \to 2} x^2 \)
      • Input: \( x^2; 2 \)
      • Steps: Evaluate \( x^2 \) near \( x = 2 \).
      • Result: Limit = 4.
    • Example 2: Trigonometric: \( \lim_{x \to 0} \frac{\sin(x)}{x} \)
      • Input: \( \sin(x)/x; 0 \)
      • Steps: Evaluate \( \sin(x)/x \) near \( x = 0 \).
      • Result: Limit = 1.
    • Example 3: Exponential: \( \lim_{x \to 0} e^x \)
      • Input: \( e^x; 0 \)
      • Steps: Evaluate \( e^x \) near \( x = 0 \).
      • Result: Limit = 1.

Calculate limits with ease using this Limit Calculator. Share or embed it on your site!