Interactive Lab / Limits
Move closer without touching the point.
Choose a function, approach zero from either side, and reduce the distance one power of ten at a time. The same experiment reveals removable singularities, true divergence, and numerical cancellation.
Live State
f(x) = sin(x) / x
Current x0.01
Direct evaluation0.99998333
Reference / stable form0.99998333
Expected behaviorApproaches 1
Absolute discrepancy0
ClassificationRemovable
The formula is undefined at zero, but values from both sides approach 1.
Recorded Samples
| x | Direct | Reference | |difference| |
|---|
What to try
- Use sin(x)/x and approach from both sides. The values should settle near 1.
- Switch to 1/x. The magnitudes grow while the signs disagree across the two sides, so no finite two-sided limit exists.
- Choose (1-cos(x))/x² and move extremely close to zero. Direct floating-point subtraction eventually loses information, while the equivalent stable identity remains near 1/2.