Limit Calculator
Solve limits step-by-step with detailed explanations. Calculate limits at infinity, one-sided limits, and more with our advanced limit solver.
Standard Limit
One-Sided Limit
Limit at Infinity
Limit Result: Not calculated
Step 1: Direct Substitution
\(\displaystyle \lim_{x \to 1} \frac{x^2 - 1}{x - 1} = \frac{1^2 - 1}{1 - 1} = \frac{0}{0}\)
→
Indeterminate form (0/0)
Step 2: Factor the Numerator
\(\frac{x^2 - 1}{x - 1} = \frac{(x - 1)(x + 1)}{x - 1}\)
Step 3: Simplify
\(\frac{(x - 1)(x + 1)}{x - 1} = x + 1\)
→
For \(x \ne 1\)
Step 4: Evaluate the Simplified Limit
\(\displaystyle \lim_{x \to 1} (x + 1) = 1 + 1 = 2\)
Graph will appear here after calculation
One-Sided Limit Result: Not calculated
Graph will appear here after calculation
Limit at Infinity Result: Not calculated
Graph will appear here after calculation
About Limit Calculator
Our Limit Calculator is a powerful mathematical tool that helps you evaluate limits of functions step-by-step. Whether you're dealing with standard limits, one-sided limits, or limits at infinity, our calculator provides detailed solutions with explanations.
How to Use the Limit Calculator
To calculate a limit:
- Enter the function you want to evaluate (use standard mathematical notation)
- Specify the variable that approaches a value
- Enter the value the variable approaches (can be a number or infinity)
- Click "Calculate Limit" to see the step-by-step solution
Types of Limits
Our calculator handles several types of limits:
- Standard Limits: Evaluate the limit of a function as the variable approaches a finite value
- One-Sided Limits: Calculate the limit from either the left (x→a⁻) or right (x→a⁺)
- Limits at Infinity: Determine the behavior of a function as the variable approaches positive or negative infinity
Common Limit Techniques
The calculator employs various mathematical techniques to evaluate limits:
- Direct Substitution: The simplest method when the function is continuous at the point
- Factoring: Useful for resolving indeterminate forms like 0/0
- L'Hôpital's Rule: For indeterminate forms (0/0 or ∞/∞) when derivatives exist
- Rationalization: For limits involving roots that lead to indeterminate forms
- Dominant Term Analysis: For limits at infinity