Calculus
Limits Calculator
Sample a function’s behavior near a target point to study two-sided or directional limits.
limitleft-hand limitright-hand limit
Limits Calculator
Evaluate two-sided or one-sided limits numerically.
Left-hand limit
-0.416146
Right-hand limit
-0.416147
Two-sided limit
-0.416147
Limit investigation
The calculator progressively samples closer points to determine whether the function approaches the same value from both sides.
How to use
- Enter f(x) and the point x₀ you want to approach.
- Select whether to evaluate the two-sided limit or only from the left/right.
- Review the sampled values and the resulting limit determination.
Example
Input: f(x) = (sin(x) - sin(2)) / (x - 2), x₀ = 2
Output: Left limit ≈ -0.4158, Right limit ≈ -0.4158, Limit ≈ -0.4158
FAQ & notes
What if the sides disagree?
The calculator reports that the two-sided limit does not exist when left and right samples diverge.
Can it handle limits at infinity?
Supply large positive or negative numbers to approximate limits at infinity for now.