Calculus8 cardsAP (unofficial)

AP Calculus AB: Limits and Continuity flashcards

Key limit facts, continuity conditions and the theorems you are expected to name.

Unofficial study material. This site is an independent educational resource and is not affiliated with or endorsed by the College Board. AP® is a trademark registered by the College Board, which is not involved in producing this content.

Keyboard: Space flips the card; 1 to 4 grade it (Again, Hard, Good, Easy).

All cards in this deck

What does $\lim_{x\to a} f(x) = L$ mean?: As $x$ gets close to $a$ (from both sides, $x \ne a$ ), $f(x)$ gets as close to $L$ as we like.
When does a two-sided limit exist?: When the left-hand and right-hand limits both exist and are equal.
$\lim_{x\to 0} \frac{\sin x}{x}$: $1$ (with $x$ in radians).
$\lim_{x\to 0} \frac{1 - \cos x}{x}$: $0$
Three conditions for continuity at $x = a$: $f(a)$ is defined, $\lim_{x\to a} f(x)$ exists, and the two are equal.
Removable discontinuity: A hole: the limit exists but $f(a)$ is undefined or different from it.
Intermediate Value Theorem: If $f$ is continuous on $[a,b]$ and $N$ is between $f(a)$ and $f(b)$ , some $c$ in $[a,b]$ has $f(c) = N$ .
Horizontal asymptote of a rational function with equal degrees: $y =$ ratio of the leading coefficients.

Go further

Limits Study Guide: the ideas behind these cards, with worked examples.
Derivative Rules cheat sheet
Limit Calculator
Derivative Rules flashcards
All flashcard decks