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, so watch sign from each side.
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