Common Mistakes
Calculus BC · AP · Contextual Applications of Differentiation
Focus
Using L'Hospital's Rule for Determining Limits of Indeterminate Forms
This topic is assessed on the AP Exam.
Frequent mistakes
### 1. Limit notation misuse
What it looks/sounds like: ‘=’ is used where ‘approaches’ is required.
Why it happens: Limits and function values are treated as identical.
How to fix: Reserve ‘=’ for when the limit equals the function value at a point.
### 2. Related rates: plug too early
What it looks/sounds like: Numeric values are substituted before differentiating.
Why it happens: The equation is not differentiated with respect to time.
How to fix: Differentiate first, then substitute known rates/values.
### 3. L’Hospital without indeterminate form
What it looks/sounds like: L’Hospital is applied to a limit that is not 0/0 or ∞/∞.
Why it happens: The rule is treated as universal.
How to fix: Check indeterminate form before applying L’Hospital.
### 4. Correct work, wrong question
What it looks/sounds like: The algebra is fine but answers a different quantity than the stem asks for.
Why it happens: Attention locks onto the first operation instead of the final ask.
How to fix: Underline the final question; after solving, verify the boxed answer matches it.
### 5. Notation and justification gaps
What it looks/sounds like: Missing units, limit language, or ‘because’ statements AP graders expect.
Why it happens: Notation is treated as decoration rather than part of the score.
How to fix: Add one justification phrase per major step (definition, theorem, or rule).
How to avoid them
1. Draw and label a related-rates diagram. 2. State L’Hospital hypotheses explicitly. 3. Check linearization point and over/under estimate.
Quick self-check
- [ ] Can set up a related-rates equation
- [ ] Can state when L’Hospital applies
- [ ] Can write a linearization formula