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Limit	The value a function approaches as the input approaches a point		tp-ap-calculus
Continuity at a point	The limit exists, the function is defined, and they are equal		tp-ap-calculus
Removable discontinuity	A hole in a graph		tp-ap-calculus
Jump discontinuity	One-sided limits exist but differ		tp-ap-calculus
Vertical asymptote	A line the function grows without bound near		tp-ap-calculus
Horizontal asymptote	A value the function approaches at infinity		tp-ap-calculus
Intermediate Value Theorem	A continuous function takes every value between f(a) and f(b)		tp-ap-calculus
Derivative	Instantaneous rate of change; slope of the tangent line		tp-ap-calculus
Limit definition of derivative	lim as h to 0 of [f(x+h) - f(x)] / h		tp-ap-calculus
Differentiability implies continuity	A function differentiable at a point is continuous there		tp-ap-calculus
Power rule	d/dx x^n = n x^(n-1)		tp-ap-calculus
Product rule	(fg)' = f'g + fg'		tp-ap-calculus
Quotient rule	(f/g)' = (f'g - fg') / g^2		tp-ap-calculus
Chain rule	d/dx f(g(x)) = f'(g(x)) times g'(x)		tp-ap-calculus
Derivative of sin x	cos x		tp-ap-calculus
Derivative of cos x	-sin x		tp-ap-calculus
Derivative of tan x	sec^2 x		tp-ap-calculus
Derivative of e^x	e^x		tp-ap-calculus
Derivative of ln x	1/x		tp-ap-calculus
Derivative of a^x	a^x ln a		tp-ap-calculus
Derivative of arctan x	1 / (1 + x^2)		tp-ap-calculus
Derivative of arcsin x	1 / sqrt(1 - x^2)		tp-ap-calculus
Implicit differentiation	Differentiate both sides with respect to x, treating y as a function of x		tp-ap-calculus
Related rates	Finding rates of change of connected quantities over time		tp-ap-calculus
Mean Value Theorem	Some point has a tangent slope equal to the average slope over the interval		tp-ap-calculus
Rolle's Theorem	If f(a) = f(b), the derivative is zero somewhere between		tp-ap-calculus
Extreme Value Theorem	A continuous function on a closed interval has a max and a min		tp-ap-calculus
Critical point	A point where f' is zero or undefined		tp-ap-calculus
First derivative test	Sign change of f' identifies local maxima and minima		tp-ap-calculus
Second derivative test	f'' positive means local min; negative means local max at a critical point		tp-ap-calculus
Concave up	f'' is positive		tp-ap-calculus
Inflection point	Where concavity changes		tp-ap-calculus
Optimization	Using derivatives to find the best value of a quantity		tp-ap-calculus
L'Hopital's Rule	For 0/0 or infinity/infinity, differentiate the top and bottom		tp-ap-calculus
Linear approximation	Using the tangent line to estimate nearby values		tp-ap-calculus
Position, velocity, acceleration	First and second derivatives of position		tp-ap-calculus
Speed	Absolute value of velocity		tp-ap-calculus
Riemann sum	Approximating area by adding areas of rectangles		tp-ap-calculus
Left Riemann sum	Uses left endpoints for rectangle heights		tp-ap-calculus
Trapezoidal rule	Approximates area with trapezoids		tp-ap-calculus
Definite integral	Net signed area between a curve and the x-axis		tp-ap-calculus
Antiderivative	A function whose derivative is the given function		tp-ap-calculus
Indefinite integral	The family of antiderivatives, plus C		tp-ap-calculus
Power rule for integrals	Integral of x^n = x^(n+1)/(n+1) + C, for n not equal to -1		tp-ap-calculus
Integral of 1/x	ln |x| + C		tp-ap-calculus
Integral of e^x	e^x + C		tp-ap-calculus
Integral of cos x	sin x + C		tp-ap-calculus
Integral of sin x	-cos x + C		tp-ap-calculus
Fundamental Theorem of Calculus, part 1	d/dx of integral from a to x of f(t) dt equals f(x)		tp-ap-calculus
Fundamental Theorem of Calculus, part 2	Integral from a to b of f = F(b) - F(a)		tp-ap-calculus
u-substitution	Integration technique that reverses the chain rule		tp-ap-calculus
Integration by parts	Integral of u dv = uv - integral of v du		tp-ap-calculus
Average value of a function	(1/(b - a)) times the integral of f from a to b		tp-ap-calculus
Area between curves	Integral of top function minus bottom function		tp-ap-calculus
Disk method	Volume = pi times integral of radius squared		tp-ap-calculus
Washer method	Volume using outer radius squared minus inner radius squared		tp-ap-calculus
Differential equation	An equation involving a function and its derivatives		tp-ap-calculus
Separation of variables	Rewrite so each variable is on one side, then integrate		tp-ap-calculus
Slope field	Graph showing tangent slopes at many points		tp-ap-calculus
Exponential growth model	dy/dt = ky gives y = Ce^(kt)		tp-ap-calculus
Logistic growth	Growth that levels off at a carrying capacity		tp-ap-calculus
Improper integral	Integral with an infinite limit or an infinite discontinuity		tp-ap-calculus
Sequence	An ordered list of numbers		tp-ap-calculus
Series	A sum of the terms of a sequence		tp-ap-calculus
Geometric series	Converges to a/(1 - r) when |r| is less than 1		tp-ap-calculus
Harmonic series	Sum of 1/n; diverges		tp-ap-calculus
p-series	Sum of 1/n^p converges when p is greater than 1		tp-ap-calculus
Ratio test	Series converges if the limit of |a(n+1)/a(n)| is less than 1		tp-ap-calculus
Alternating series test	Terms alternate, decrease, and approach zero imply convergence		tp-ap-calculus
Absolute convergence	The series of absolute values converges		tp-ap-calculus
Taylor series	Infinite polynomial built from a function's derivatives at a point		tp-ap-calculus
Maclaurin series	Taylor series centered at zero		tp-ap-calculus
Maclaurin series for e^x	1 + x + x^2/2! + x^3/3! + ...		tp-ap-calculus
Radius of convergence	Distance from the center within which a power series converges		tp-ap-calculus
Lagrange error bound	Limit on the error of a Taylor polynomial approximation		tp-ap-calculus
Parametric derivative	dy/dx = (dy/dt) / (dx/dt)		tp-ap-calculus
Polar area	Area = 1/2 times integral of r squared d theta		tp-ap-calculus
Arc length	Integral of sqrt(1 + (dy/dx)^2) dx		tp-ap-calculus
Euler's method	Step-by-step numerical approximation of a differential equation		tp-ap-calculus