What the estimate means
The parser supports one variable x; +, −, ×, ÷, powers, parentheses, sqrt, sin, cos, tan, exp, ln, log (base 10), abs, pi, and e. Trigonometric functions use radians. No arbitrary JavaScript is executed. The calculator checks substitution when appropriate, samples independently from the left and right near a finite point, and samples increasing magnitudes for ±infinity.
lim x→0 sin(x)/x ≈ 1. lim x→1 (x²−1)/(x−1) ≈ 2.
When it will not decide
Numerical sampling is not symbolic proof. Oscillation, slow convergence, cancellation, singularities, and unsupported real domains can yield “unsupported / inconclusive.” A two-sided limit is DNE when reliably different one-sided results are found. For 1/x at zero, the left side diverges to −∞ and the right side to +∞.
Privacy and limits
Expressions run locally, are capped in length and nesting, and are not submitted, stored, or added to URLs. This is a bounded educational estimator, not an unrestricted computer algebra system.