#separator:tab
#html:false
#tags column:4
Limit	The value a function approaches as the input approaches a number		math-calculus-concepts
One-sided limit	A limit approached only from the left or only from the right		math-calculus-concepts
Limit at infinity	The value a function approaches as x grows without bound		math-calculus-concepts
Continuous at a point	The limit equals the function value there		math-calculus-concepts
Removable discontinuity	A hole in the graph that could be filled in		math-calculus-concepts
Jump discontinuity	The left and right limits exist but differ		math-calculus-concepts
Infinite discontinuity	The function grows without bound near that point (vertical asymptote)		math-calculus-concepts
Intermediate value theorem	A continuous function takes every value between f(a) and f(b)		math-calculus-concepts
Extreme value theorem	A continuous function on a closed interval has a maximum and a minimum		math-calculus-concepts
Differentiable	Having a derivative at a point; the graph is smooth there		math-calculus-concepts
Differentiable implies	Continuous		math-calculus-concepts
Local maximum	A point higher than nearby points		math-calculus-concepts
Local minimum	A point lower than nearby points		math-calculus-concepts
Absolute (global) extremum	The highest or lowest point over the whole domain		math-calculus-concepts
Optimization	Using derivatives to find the best (largest or smallest) value		math-calculus-concepts
Linear approximation	Using the tangent line to estimate nearby values		math-calculus-concepts
Differential	dy = f'(x) dx; a small change in y		math-calculus-concepts
Antiderivative	A function whose derivative is the given function		math-calculus-concepts
Riemann sum	A sum of rectangle areas that approximates an area		math-calculus-concepts
Definite integral	A number: signed area under a curve between limits		math-calculus-concepts
Net change	The integral of a rate of change		math-calculus-concepts
Slope field	A picture of tangent slopes for a differential equation		math-calculus-concepts
Differential equation	An equation involving a function and its derivatives		math-calculus-concepts
Separable differential equation	One where the variables can be moved to opposite sides		math-calculus-concepts
Exponential growth equation	dy/dt = ky has solution y = Ce^(kt)		math-calculus-concepts
Sequence limit	The value the terms approach as n grows		math-calculus-concepts
Geometric series test	Converges if |r| < 1, with sum a/(1 − r)		math-calculus-concepts
p-series	Σ 1/nᵖ converges if p > 1 and diverges if p ≤ 1		math-calculus-concepts
Ratio test	Compare consecutive terms; convergence if the limit of |aₙ₊₁/aₙ| is less than 1		math-calculus-concepts
Alternating series test	Converges if terms alternate sign, decrease in size and go to 0		math-calculus-concepts
Taylor series	A power series that matches a function's derivatives at a point		math-calculus-concepts
Maclaurin series	A Taylor series centered at 0		math-calculus-concepts
Maclaurin series of eˣ	1 + x + x²/2! + x³/3! + ...		math-calculus-concepts
Maclaurin series of sin x	x − x³/3! + x⁵/5! − ...		math-calculus-concepts
Maclaurin series of cos x	1 − x²/2! + x⁴/4! − ...		math-calculus-concepts
Maclaurin series of 1/(1 − x)	1 + x + x² + x³ + ... for |x| < 1		math-calculus-concepts
Radius of convergence	How far from the center a power series converges		math-calculus-concepts
lim (x→0) sin x / x	1		math-calculus-concepts
lim (x→0) (1 − cos x) / x	0		math-calculus-concepts
lim (x→0) (eˣ − 1) / x	1		math-calculus-concepts
lim (x→∞) (1 + 1/x)ˣ	e		math-calculus-concepts
lim (x→∞) 1/x	0		math-calculus-concepts
lim (x→1) (x² − 1)/(x − 1)	2		math-calculus-concepts
lim (x→∞) (3x² + 1)/(x² + 5)	3		math-calculus-concepts
lim (x→0) ln(1 + x)/x	1		math-calculus-concepts
Squeeze theorem	If a function is trapped between two functions with the same limit, it has that limit		math-calculus-concepts
Vertical asymptote	A vertical line the graph approaches where values blow up		math-calculus-concepts
Horizontal asymptote	A horizontal line the graph approaches as x goes to ±∞		math-calculus-concepts
Indeterminate form	A limit form such as 0/0 or ∞/∞ that needs more work		math-calculus-concepts
Partial derivative	A derivative with respect to one variable, others held constant		math-calculus-concepts
Gradient	A vector of partial derivatives pointing in the direction of steepest increase		math-calculus-concepts
Double integral	Integral over a 2D region, finding volume under a surface		math-calculus-concepts
Multivariable calculus	Calculus of functions with more than one input		math-calculus-concepts
Differential vs. derivative	The derivative is a rate; the differential is a small change		math-calculus-concepts
Leibniz notation	dy/dx		math-calculus-concepts
Lagrange notation	f'(x)		math-calculus-concepts
Newton's notation	ẏ, a dot over the variable		math-calculus-concepts
Who developed calculus independently?	Isaac Newton and Gottfried Leibniz		math-calculus-concepts