Limits on the AP Calculus AB exam punish notation slips and wrong hypotheses more than raw algebra speed.
1. One-sided limits you “merged” by habit
If a piecewise graph or formula changes behaviour at a point, compute left and right limits separately. If they disagree, the two-sided limit does not exist — do not average them.
2. Continuity requires three checks
f(c) defined, limit exists, limit equals f(c). Students often show the limit exists and forget the actual value at c for continuity questions.
3. Indeterminate forms vs “looks indeterminate”
Only move to L'Hôpital when you genuinely have a 0/0 or ∞/∞ form after substitution. If you differentiate prematurely, you can destroy the limit’s structure.
4. Asymptotes vs holes
A hole needs a factor that cancels in simplification and a finite limit. A vertical asymptote shows up when a one-sided limit blows up — watch sign from each side.
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