L'Hôpital's Rule Visualizer – AP Calculus AB

Learning Objectives

Identify indeterminate forms (0/0 or ∞/∞)

Apply L'Hôpital's Rule to evaluate limits

Visualize how the ratio of functions f(x)/g(x) approaches the ratio of their derivatives

Key Equations

\( \lim_{x\to c} \frac{f(x)}{g(x)} = \lim_{x\to c} \frac{f'(x)}{g'(x)} \)

Why It Matters

When limits evaluate to forms like 0/0, normal substitution fails. L'Hôpital's rule uses the rates of change (derivatives) to determine the behavior of the overall ratio near the critical point.