How limits are evaluated
- Try direct substitution first.
- If substitution gives an indeterminate form, simplify by factoring, rationalizing, or using a known limit.
- Check whether the left and right behavior agree.
Limit Calculator
Evaluate limits as x approaches a value.
Use this calculator as a study checker
Enter the problem carefully, review the interpreted input, and compare each step with your own work. Calculus results can depend on notation, variables, bounds, domains, and assumptions.
- Check the method before copying the answer.
- Use the examples below to test nearby problems.
- Read the calculus guides for worked explanations.
Solution
50 study checks todayEnter an expression or choose an example to calculate.
Limit Examples
What this calculator is for
A limit describes the value a function approaches as the input gets close to a point. Limits define continuity, derivatives, and many core calculus ideas. Use it to check your setup, compare steps with your own work, and review the meaning of the final expression before copying it into homework.
Manual example
- Problem: \(\lim_{x\to2}\frac{x^2-4}{x-2}\).
- Factor the numerator: \(x^2-4=(x-2)(x+2)\).
- Cancel \(x-2\) for \(x\ne2\), then evaluate \(x+2\) at \(x=2\): result \(4\).
Common mistakes to avoid
- Canceling terms that are not common factors.
- Assuming the function value and the limit must be the same.
- Ignoring one-sided behavior near discontinuities.
When to double-check the result
For piecewise functions, one-sided limits, or domain restrictions, make the direction and expression explicit.