Common Mistakes
Calculus AB · AP · Limits and Continuity
Focus
Connecting Limits at Infinity and Horizontal Asymptotes
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. Limit equals function value
What it looks/sounds like: lim f(x) as x→a is set equal to f(a) when a hole exists.
Why it happens: Limit and value language are conflated.
How to fix: Use ‘approaches’ for limits; check the graph for holes/jumps.
### 3. One-sided limit ignored
What it looks/sounds like: A two-sided limit is assumed when left and right disagree.
Why it happens: Only the calculator table is used.
How to fix: Compare left-hand and right-hand behavior explicitly.
### 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. Write one-sided limit notation when graphs differ. 2. Cite continuity/IVT only after checking hypotheses. 3. Use algebraic limits before trusting a decimal estimate.
Quick self-check
- [ ] Can evaluate a limit from a graph correctly
- [ ] Can justify continuity on an interval
- [ ] Can avoid equals/approaches confusion