L'Hôpital's Rule is a fundamental theorem in calculus used to evaluate limits that result in indeterminate forms, specifically zero divided by zero or infinity over infinity. The rule relies on the formal definition of continuity and differentiability, asserting that if two functions $f(x)$ and $g(x)$ both approach zero at a point, their limit ratio equals the ratio of their derivatives provided those derivatives exist and are non-zero in the neighborhood. This concept bridges the gap between intuitive geometric approaches to limits and rigorous epsilon-delta formalism within real analysis by utilizing local linear approximations (tangents) to resolve undefined expressions.
L'Hôpital's Rule is a fundamental theorem in calculus used to evaluate limits that result in indeterminate forms, specifically zero divided by zero or infinity over infinity. The rule relies on the f…