BC Calculus AP Review Flashcards

6383808471	Double Angle Formula for cos²(θ)		0
6383808472	Double Angle Formula for sin²(θ)		1
6383808473	sin(0)=		2
6383808474	sin(π/4)		3
6383808475	sin⁻¹(-1)		4
6383808476	tan⁻¹(-1)		5
6383808477	1+cot²(θ)		6
6383808478	1+tan²(θ)		7
6383808479	sin(2θ)		8
6383808480	cos(2θ)		9
6383808483	log(AB)		10
6383808484	log(A / B)		11
6383808485	log(A) ^ x		12
6383808486	e^(ln(x))		13
6383808487	ln(x) / ln(a)		14
6383808488	Simplify the expression into one log: 2 ln(x) + ln(x+1) - ln(x-1)		15
6383808489	For what value of x is there a hole, and for what value of x is there a vertical asymptote? f(x) = ((x - a)(x - b))/ ((x - a)(x - c))		16
6383808490	Definition of the Derivative (Using the limit as h→0)		17
6383808492	lim x→₀ sin(x)/x		18
6383808493	lim x→∞ tan⁻¹(x)		19
6383808495	First derivative test for a local max of f at x = a		20
6383808496	First derivative test for a local min of f at x = a		21
6383808497	Second derivative test for a local max of f at x = a		22
6383808498	Second derivative test for a local min of f at x = a		23
6383808499	Test for max and mins of f on [a, b]		24
6383808500	Inflection Points		25
6383808501	ƒ'(x) < 0		26
6383808502	ƒ''(x) < 0 or ƒ'(x) is decreasing		27
6383808503	ƒ'(x) > 0		28
6383808504	ƒ''(x) > 0 or ƒ'(x) is increasing		29
6383808505	Intermediate Value Theorem (IVT)		30
6383808506	Mean Value Theorem (MVT)		31
6383808507	Rolle's Theorem		32
6383808508	Squeeze Theorem		33
6383808510	ƒ(x) is continuous at x = a if...		34
6383808511	Extreme Value Theorem		35
6383808512	Critical Points		36
6383808513	Three types of discontinuities.		37
6383808514	ƒ(x) is differentiable at x = a if...		38
6383808515	Three conditions where ƒ(x) is not differentiable		39
6383808516	Average rate of change of ƒ(x) over [a, b]		40
6383808517	Instantaneous rate of change of ƒ(a)		41
6383808518	d/dx ( tan⁻¹ ( x ) )		42
6383808519	d/dx ( sin⁻¹ ( x ) )		43
6383808521	d/dx ( e ^ x )		44
6383808522	d/dx ( ln x )		45
6383808523	d/dx ( a ^ x )		46
6383808525	d/dx ( sin x )		47
6383808526	d/dx ( cos x )		48
6383808527	d/dx ( tan x )		49
6383808528	d/dx ( sec x )		50
6383808529	d/dx ( csc x )		51
6383808530	d/dx ( cot x )		52
6383808531	Product Rule		53
6383808532	Quotient Rule		54
6383808533	Chain Rule		55
6383808534	d/dx (ƒ(x)³)		56
6383808535	d/dx ( ln ƒ(x) )		57
6383808536	d/dx (e ^ ƒ(x) )		58
6383808537	Derivative of the Inverse of ƒ(x)		59
6383808538	Implicit Differentiation Find dy/dx: x²/9+y²/4=1		60
6383808539	Equation of a line in point-slope form		61
6383808540	Equation of the tangent line to y = ƒ(x) at x = a		62
6383808541	A normal line to a curve is...		63
6383808542	Velocity of a point moving along a line with position at time t given by d(t)		64
6383808543	Speed of a point moving along a line		65
6383808544	Average velocity of s over [a, b]		66
6383808545	Average speed of s over [a, b]		67
6383808546	Average acceleration given v over [a, b]		68
6383808547	An object in motion is at rest when...		69
6383808548	An object in motion reverses direction when...		70
6383808549	Acceleration of a point moving along a line with position at time t given by d(t)		71
6383808550	How to tell if a point moving along the x-axis with velocity v(t) is speeding up or slowing down at some time t?		72
6383808551	Position at time t = b of a particle moving along a line given velocity v(t) and position s(t) at time t = a		73
6383808552	Displacement of a particle moving along a line with velocity v(t) for a ≤ t ≤ b.		74
6383808553	Total distance traveled by a particle moving along a line with velocity v(t) for a ≤ t ≤ b	...	75
6383808554	The total change in ƒ(x) over [a, b] in terms of the rate of change, ƒ'(x)		76
6383808555	Graph of y = 1/x		77
6383808556	Graph of y = e ^ (kx)		78
6383808557	Graph of y = ln x		79
6383808558	Graph of y = sin x		80
6383808559	Graph of y = cos x		81
6383808560	Graph of y = tan x		82
6383808561	Graph of y = tan⁻¹ x		83
6383808562	Graph of y = √(1 - x²)		84
6383808563	Graph of x²/a² + y²/b² = 1		85
6383808564	L'Hopital's Rule		86
6383808565	To find the limits of indeterminate forms: ∞ × 0		87
6383808566	To find the limits of indeterminate forms: 0 ^ 0, 1 ^ ∞, ∞ ^ 0		88
6383808567	If ƒ(x) is increasing, then a left Riemann sum ...		89
6383808568	If ƒ(x) is decreasing, then a left Riemann sum ...		90
6383808569	If ƒ(x) is increasing, then a right Riemann sum ...		91
6383808570	If ƒ(x) is decreasing, then a right Riemann sum ...		92
6383808571	If ƒ(x) is concave up, then the trapezoidal approximation of the integral...		93
6383808572	If ƒ(x) is concave down, then the trapezoidal approximation of the integral...		94
6383808573	If ƒ(x) is concave up, then a midpoint Riemann sum...		95
6383808574	If ƒ(x) is concave down, then a midpoint Riemann sum...		96
6383808575	Area of a trapezoid		97
6383808576	If ƒ(x) is concave down then the linear approximation...		98
6383808577	If ƒ(x) is concave up then the linear approximation...		99
6383808578	The Fundamental Theorem of Calculus (Part I)		100
6383808579	The Fundamental Theorem of Calculus (Part II)		101
6383808581	∫ x ^ n dx =		102
6383808582	∫ e ^ x dx =		103
6383808583	∫ 1/x dx =		104
6383808584	∫ sin x dx =		105
6383808585	∫ cos x dx =		106
6383808586	∫ sec² x dx =		107
6383808587	∫ a ^ x dx =		108
6383808588	∫ tan x dx =		109
6383808589	∫ 1 / (x² + 1) dx =		110
6383808590	∫ 1 / √(1 - x² ) dx =		111
6383808592	The average value of f from x = a to x = b (Mean Value Theorem for Integrals)		112
6383808595	Integral equation for a horizontal shift of 1 unit to the right.		113
6383808596	Adding adjacent integrals		114
6383808597	Swapping the bounds of an integral		115
6383808598	Exponential Growth Solution of dy/dt = kP P(0) = P₀		116
6383808599	lim n→∞ (1 + 1/n) ^ n		117
6383808600	Steps to solve a differential equation		118
6383808601	To find the area between 2 curves using vertical rectangles (dx)		119
6383808602	To find the area between 2 curves using horizontal rectangles (dy)		120
6383808603	Volume of a disc; rotated about a horizontal line		121
6383808604	Volume of a washer; rotated about a horizontal line		122
6383808605	Volume of a disc; rotated about a vertical line		123
6383808606	Volume of a washer; rotated about a vertical line		124
6383808607	Volume of solid if cross sections perpendicular to the x-axis are squares		125
6383808608	Volume of solid if cross sections perpendicular to the x-axis are isosceles right triangles		126
6383808609	Volume of solid if cross sections perpendicular to the x-axis are equilateral triangles		127
6383808610	Volume of solid if cross sections perpendicular to the x-axis are semicircles		128
6383808612	Volume of a prism		129
6383808613	Volume of a cylinder		130
6383808614	Volume of a pyramid		131
6383808615	Volume of a cone		132
6383808616	Volume of a sphere		133
6383808617	Surface Area of a cylinder		134
6383808618	Surface Area of a sphere		135
6383808619	Area of a Sector (in radians)		136
6383808620	Slope of a parametric curve x = x(t) and y = y(t)		137
6383808621	Horizontal Tangent of a parametric curve		138
6383808622	Vertical Tangent of a parametric curve		139
6383808624	Second Derivative of a parametric curve		140
6383808625	Velocity vector of a particle moving in the plane x = x(t) and y = y(t)		141
6383808626	Acceleration vector of a particle moving in the plane x = x(t) and y = y(t)		142
6383808627	Speed of a particle moving in the plane x = x(t) and y = y(t)		143
6383808628	Distance traveled (Arc Length) by a particle moving in the plane with a ≤ t ≤ b x = x(t) and y = y(t)		144
6383808629	Position at time t = b of a particle moving in the plane given x(a), y(a), x′(t), and y′(t).		145
6383808630	Magnitude of a vector in terms of the x and y components		146
6383808634	Graph of θ = c (c is a constant)		147
6383808635	Graph of r = θ		148
6383808636	Graphs of: r = c r = c sin(θ) r = c cos(θ) (c is a constant)		149
6383808637	Graphs of: r = sin(k θ) r = cos(k θ) (k is a constant)		150
6383808638	Graph of: r = 1 + cos(θ)		151
6383808639	Graph of: r = 1 + 2 cos(θ)		152
6383808640	Slope of polar graph r (θ)		153
6383808641	Area enclosed by r = f(θ), α ≤ θ ≤ β		154
6383808642	Double Angle Formula for cos²θ		155
6383808643	Double Angle Formula for sin²θ		156
6383808646	dx/dθ < 0		157
6383808647	dx/dθ > 0		158
6383808648	dy/dθ < 0		159
6383808649	dy/dθ > 0		160
6383808650	Convert from polar (r,θ) to rectangular (x,y)		161
6383808651	Convert from rectangular (x,y) to polar (r,θ)		162
6383808652	Horizontal Tangent of a Polar Graph		163
6383808653	Vertical Tangent of a Polar Graph		164
6383808656	Integration by Parts Formula		165
6383808657	∫ lnx dx = ?		166
6383808658	Improper Integral: ∫ 1/x² dx bounds: [0,1]		167
6383808659	Improper Integral: ∫ f(x) dx bounds: [0,∞]		168
6383808660	Arc length of a function f(x) from x = a to x = b		169
6383808661	Arc length of a polar graph r 0 ≤ θ ≤ π		170
6383808662	Arc Length of a graph defined parametrically with a ≤ t ≤ b x = x(t) and y = y(t)		171
6383808665	Differential equation for exponential growth dP/dt = ?		172
6383808666	Solution of a differential equation for exponential growth		173
6383808667	Differential equation for decay dP/dt = ?		174
6383808668	Solution of a differential equation for decay		175
6383808672	Logistic differential equation dP/dt = ?		176
6383808673	Solution of a logistic differential equation		177
6383808674	Graph of a Logistic Function (include inflection pt.)		178
6383808675	Euler's Method for solving y' = F (x,y) with initial point (x₀ , y₀)		179
6383808676	Power Series for f(x) = 1 / (1 - x) (include IOC)		180
6383808677	Power Series for f(x) = tan⁻¹ x (include IOC)		181
6383808678	Power Series for f(x) = ln (1 + x) (include IOC)		182
6383808679	Taylor Series for f(x) about x = 0 (Maclaurin Series)		183
6383808680	Taylor Series for f(x) about x = c		184
6383808681	Maclaurin Series for f (x) = e∧x (include IOC)		185
6383808682	Maclaurin Series for f (x) = sin x (include IOC)		186
6383808683	Maclaurin Series for f (x) = cos x (include IOC)		187
6383808684	Error for the partial sum, Sn, of an infinite series S		188
6383808685	Error bound of an alternating series		189
6383808686	Lagrange error bound		190
6383808688	Geometric sequence (def. and conv. property)		191
6383808690	Harmonic Series (def. and conv. property)		192
6383808691	p-series (def. and conv. property)		193
6383808692	Divergence Test		194
6383808693	If lim n→∞ a(sub n) = 0, then ∑ a(sub n) for n from 1 to ∞ ...		195
6383808694	Integral Test		196
6383808695	Alternating Series Test		197
6383808696	Direct Comparison Test		198
6383808697	Limit Comparison Test		199
6383808698	Ratio Test		200
6383808699	n-th Root Test		201
6383808700	Interval of Convergence (IOC)		202
6383808701	Radius of Convergence		203