When NOT to use L'Hôpital?

When form isn't 0/0 or ∞/∞. Don't apply blindly.

For rational functions: ratio of leading coefficients (if same degree); 0 (if denom higher); ±∞ (if numer higher).

lim x→a⁺ (from above) vs. lim x→a⁻ (from below). Two-sided limit exists only if both equal.

Continuous functions?

For continuous f: lim x→a f(x) = f(a). Direct substitution works.

Limit Evaluator (Polynomial Ratio)

lim x→a of polynomial ratios (basic substitution + L'Hopital for 0/0).

Result

lim x→1

-1.000000 (L'Hôpital, 0/0)

Numerator at a = 0.0000; denom = 0.0000.

a1
Numerator at a0.000000
Denominator at a0.000000
Result-1.000000 (L'Hôpital, 0/0)

Step-by-step

Direct substitution: P(1)/Q(1) = 0.0000/0.0000.
0/0 indeterminate — apply L'Hôpital: lim P'(x)/Q'(x).

How to use this calculator

Enter numerator + denominator coefficients.
Enter a (the value x approaches).

About this calculator

Limit of polynomial ratio: substitute directly if denominator non-zero. If 0/0 indeterminate: L'Hôpital's rule (differentiate numerator + denominator separately). Other indeterminate forms: ∞/∞, 0·∞, ∞−∞, 0⁰, ∞⁰, 1^∞ — also handled by L'Hôpital after rewriting. For polynomials at finite a, this calc covers basic + 1× L'Hôpital. Source: Wolfram MathWorld - Limit.