Exam Strategy

Calculus AB · AP · Contextual Applications of Differentiation

CED focus

Using L'Hospital's Rule for Determining Limits of Indeterminate Forms

This topic is assessed on the AP Exam.

Multiple-choice tips

• Ask whether the limit is one-sided, two-sided, or DNE before computing.
• Identify the independent variable (often time) in related-rates MC.
• Eliminate L’Hospital uses when the limit is not indeterminate.
• Check linearization: is the estimate over or under?
• Match units on related-rates distractors.

Free-response tips

• Use ‘approaches’ language; cite IVT or continuity when justifying.
• Draw and label a related-rates diagram before differentiating.
• Show dV/dt (or similar) setup with correct chain rule.
• State L’Hospital hypotheses before applying.
• For linearization, show f(a) + f′(a)(x − a) with a labeled tangent point.

Common traps

• Equating lim f(x) as x→a with f(a) when a hole exists
• Plugging values before differentiating in related rates
• Using L’Hospital on a non-indeterminate form
• Linearizing at the wrong point a

Quick checklist

• [ ] Can set up a related-rates equation with labels
• [ ] Can state when L’Hospital applies
• [ ] Can write a local linearization formula