Evaluate limits of functions as x approaches a value.
Supported: sin, cos, tan, exp, log, sqrt, abs, ^, pi, e
Use "inf" for ∞, "-inf" for −∞
Direct substitution is tried first. If it gives 0/0, try factoring, rationalizing, or L'Hôpital's rule (differentiate numerator and denominator). For ∞/∞, compare growth rates of numerator and denominator.
If lim f(x)/g(x) gives 0/0 or ∞/∞, then lim f(x)/g(x) = lim f'(x)/g'(x). Repeat until the form resolves. Named after Guillaume de l'Hôpital (1661–1704).
lim(x→0) sin(x)/x = 1, lim(x→0) (1+x)^(1/x) = e, lim(x→∞) (1+1/x)^x = e, lim(x→0) (e^x−1)/x = 1. These are foundational in calculus.
A two-sided limit exists only if the left-hand limit (x→a⁻) equals the right-hand limit (x→a⁺). Functions with jumps, holes, or vertical asymptotes may have different one-sided limits.