The Limit Calculator evaluates the value a function approaches as its input approaches a specified point or, where supported, as the input grows without bound. Limits are a central idea in calculus and are used to define derivatives, continuity, and many integration concepts.
What a Limit Means
A limit does not necessarily ask for the function's value exactly at the point. Instead, it describes the behavior of the function as the input gets arbitrarily close to that point. A function can have a limit even when it is not defined at the point itself.
How to Use the Calculator
- Enter the function in the format expected by the tool.
- Specify the variable and the value it approaches.
- Calculate the limit.
- Check whether the result is finite, infinite, or otherwise indicates that the two-sided limit does not exist.
Example
For f(x) = (xΒ² β 1) Γ· (x β 1), direct substitution at x = 1 gives an undefined expression. Factoring gives f(x) = x + 1 for x β 1, so the limit as x approaches 1 is 2.
Checking a Result
A calculator result is most useful when considered with the function's algebraic behavior. One-sided limits may differ, and an apparent numerical result should not be treated as proof when the function has discontinuities or domain restrictions.