Limit Calculator – Free Online Limits Solver
This limit calculator estimates the limit of a function as x approaches a number, infinity or negative infinity. Type a function like sin(x)/x or (1 + 1/x)^x, enter the value x approaches, and choose a two-sided, left or right limit. The tool evaluates the function very close to the point from each side and reports the value, or tells you when the limit does not exist. It is a numerical method that runs in your browser, so treat it as a strong check rather than a proof.
Limit Calculator
Estimate the limit of a function as x approaches a number or infinity.
How to use the Limit Calculator
- Type the function, for example sin(x)/x.
- Enter the value x approaches, such as 0, 2, inf or -inf.
- Choose a two-sided limit, or only the left or right side.
- Read the limit and the left and right values to see how it behaves.
How limits are estimated
The function is evaluated at x = a ± 10⁻³, 10⁻⁴ … 10⁻⁹ (or at large values for infinity). If the values converge, the result is rounded to a recognizable number. If the sides differ or grow without bound, the limit is reported as not existing or as ±∞.
Features
- Limits at a point or at infinity
- Left, right and two-sided limits
- Detects infinite limits and no-limit cases
- Recognizes exact values such as 1, 1/2 and e
- Shows direct substitution when it works
- Free and private
Frequently asked questions
How do I find the limit of a function?
Type the function and the value x approaches. The calculator evaluates the function extremely close to that value from both sides and reports the number the values settle on.
Is the answer exact?
It is a numerical estimate rounded to a recognizable value. It works well for textbook limits, but it is not a symbolic proof, so confirm important results by hand.
What does it mean when the limit does not exist?
The left and right values differ, or the function does not settle on a single number, as with 1/x at 0. The calculator shows both side values so you can see why.
Can I enter infinity?
Yes. Type inf for positive infinity or -inf for negative infinity as the value x approaches.
Why does direct substitution sometimes fail?
Forms like 0/0 are indeterminate at the point itself, so the limit has to be found by looking at nearby values. The calculator does exactly that.