Limit Calculator
Enter a function of x and the value x approaches. The calculator samples the function from both the left and the right, builds a table of values, and reports the limit when both sides agree — or that the limit does not exist when they differ.
Formula and method
lim_{x→0} sin(x)/x = 1 · lim_{x→0} (eˣ−1)/x = 1 · lim_{x→0} (1−cos x)/x² = ½
Samples the function at values increasingly close to the target point from both the left and the right. Reports the limit when both sides converge to the same value; reports 'does not exist' when they diverge. Handles removable discontinuities (holes), one-sided mismatches and limits at ±∞. Note: this is a numerical estimator — use symbolic algebra or factoring for indeterminate forms that require exact manipulation.
Worked examples
Key terms
Frequently asked questions
How is the limit estimated?
The function is sampled at points closer and closer to the target from both sides; agreement between the two sides indicates the limit.
Can it detect when a limit does not exist?
Yes. If the left-hand and right-hand values disagree, the tool reports that the two-sided limit does not exist.
Does it handle removable discontinuities?
Yes. For a hole such as (x² − 1)/(x − 1) at x = 1 it still finds the limiting value.