Front
Integration by Parts (BC)
Back
$\int u dv = uv - \int v du$
The 'reverse product rule'; use the LIATE rule to choose $u$.
Public Deck
AP Calculus Formulas - 40 Essential Rules
Master AP Calculus with 40 flashcards covering limits, derivatives, integrals, and their applications.
AnyFlashcards40 cards
Preview
Front
Definition of a Limit (Formal)
Back
$\lim_{x \to c} f(x) = L$
Used to describe the value a function approaches as the input approaches a specific point.
Front
Limit at Infinity (Rational Functions)
Back
Compare the degrees of the numerator and denominator
If degrees are equal, the limit is the ratio of leading coefficients.
Front
Squeeze Theorem
Back
If $g(x) \leq f(x) \leq h(x)$ and $\lim g(x) = \lim h(x) = L$, then $\lim f(x) = L$
Used to find limits of oscillating functions like $x^2 \sin(1/x)$.
Front
L'Hôpital's Rule
Back
$\lim \frac{f(x)}{g(x)} = \lim \frac{f'(x)}{g'(x)}$
Apply when the limit results in indeterminate forms $0/0$ or $\infty/\infty$.
Front
Definition of Continuity at $x=c$
Back
$f(c)$ exists, $\lim_{x \to c} f(x)$ exists, and $\lim_{x \to c} f(x) = f(c)$
Ensures there are no holes, jumps, or asymptotes at the point.
Front
Intermediate Value Theorem (IVT)
Back
If $f$ is continuous on $[a,b]$, it takes every value between $f(a)$ and $f(b)$
Used to prove a root exists if $f(a) < 0$ and $f(b) > 0$.
Front
Power Rule for Derivatives
Back
$\frac{d}{dx}[x^n] = nx^{n-1}$
Example: The derivative of $x^3$ is $3x^2$.
Front
Product Rule
Back
$\frac{d}{dx}[uv] = u'v + uv'$
Used when differentiating two functions multiplied together.
Front
Quotient Rule
Back
$\frac{d}{dx}[\frac{u}{v}] = \frac{u'v - uv'}{v^2}$
Mnemonic: Low d-High minus High d-Low over Low-Low.
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