BC Calculus AP Review Flashcards

9584854110	Double Angle Formula for cos²(θ)		0
9584854111	Double Angle Formula for sin²(θ)		1
9584854112	sin(0)=		2
9584854113	sin(π/4)		3
9584854114	sin⁻¹(-1)		4
9584854115	tan⁻¹(-1)		5
9584854116	1+cot²(θ)		6
9584854117	1+tan²(θ)		7
9584854118	sin(2θ)		8
9584854119	cos(2θ)		9
9584854120	log(AB)		10
9584854121	log(A / B)		11
9584854122	log(A) ^ x		12
9584854123	e^(ln(x))		13
9584854124	ln(x) / ln(a)		14
9584854125	Simplify the expression into one log: 2 ln(x) + ln(x+1) - ln(x-1)		15
9584854126	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
9584854127	Definition of the Derivative (Using the limit as h→0)		17
9584854128	lim x→₀ sin(x)/x		18
9584854129	lim x→∞ tan⁻¹(x)		19
9584854130	First derivative test for a local max of f at x = a		20
9584854131	First derivative test for a local min of f at x = a		21
9584854132	Second derivative test for a local max of f at x = a		22
9584854133	Second derivative test for a local min of f at x = a		23
9584854134	Test for max and mins of f on [a, b]		24
9584854135	Inflection Points		25
9584854136	ƒ'(x) < 0		26
9584854137	ƒ''(x) < 0 or ƒ'(x) is decreasing		27
9584854138	ƒ'(x) > 0		28
9584854139	ƒ''(x) > 0 or ƒ'(x) is increasing		29
9584854140	Intermediate Value Theorem (IVT)		30
9584854141	Mean Value Theorem (MVT)		31
9584854142	Rolle's Theorem		32
9584854143	Squeeze Theorem		33
9584854144	ƒ(x) is continuous at x = a if...		34
9584854145	Extreme Value Theorem		35
9584854146	Critical Points		36
9584854147	Three types of discontinuities.		37
9584854148	ƒ(x) is differentiable at x = a if...		38
9584854149	Three conditions where ƒ(x) is not differentiable		39
9584854150	Average rate of change of ƒ(x) over [a, b]		40
9584854151	Instantaneous rate of change of ƒ(a)		41
9584854152	d/dx ( tan⁻¹ ( x ) )		42
9584854153	d/dx ( sin⁻¹ ( x ) )		43
9584854154	d/dx ( e ^ x )		44
9584854155	d/dx ( ln x )		45
9584854156	d/dx ( a ^ x )		46
9584854157	d/dx ( sin x )		47
9584854158	d/dx ( cos x )		48
9584854159	d/dx ( tan x )		49
9584854160	d/dx ( sec x )		50
9584854161	d/dx ( csc x )		51
9584854162	d/dx ( cot x )		52
9584854163	Product Rule		53
9584854164	Quotient Rule		54
9584854165	Chain Rule		55
9584854166	d/dx (ƒ(x)³)		56
9584854167	d/dx ( ln ƒ(x) )		57
9584854168	d/dx (e ^ ƒ(x) )		58
9584854169	Derivative of the Inverse of ƒ(x)		59
9584854170	Implicit Differentiation Find dy/dx: x²/9+y²/4=1		60
9584854171	Equation of a line in point-slope form		61
9584854172	Equation of the tangent line to y = ƒ(x) at x = a		62
9584854173	A normal line to a curve is...		63
9584854174	Velocity of a point moving along a line with position at time t given by d(t)		64
9584854175	Speed of a point moving along a line		65
9584854176	Average velocity of s over [a, b]		66
9584854177	Average speed of s over [a, b]		67
9584854178	Average acceleration given v over [a, b]		68
9584854179	An object in motion is at rest when...		69
9584854180	An object in motion reverses direction when...		70
9584854181	Acceleration of a point moving along a line with position at time t given by d(t)		71
9584854182	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
9584854183	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
9584854184	Displacement of a particle moving along a line with velocity v(t) for a ≤ t ≤ b.		74
9584854313	Total distance traveled by a particle moving along a line with velocity v(t) for a ≤ t ≤ b	...	75
9584854185	The total change in ƒ(x) over [a, b] in terms of the rate of change, ƒ'(x)		76
9584854186	Graph of y = 1/x		77
9584854187	Graph of y = e ^ (kx)		78
9584854188	Graph of y = ln x		79
9584854189	Graph of y = sin x		80
9584854190	Graph of y = cos x		81
9584854191	Graph of y = tan x		82
9584854192	Graph of y = tan⁻¹ x		83
9584854193	Graph of y = √(1 - x²)		84
9584854194	Graph of x²/a² + y²/b² = 1		85
9584854195	L'Hopital's Rule		86
9584854196	To find the limits of indeterminate forms: ∞ × 0		87
9584854197	To find the limits of indeterminate forms: 0 ^ 0, 1 ^ ∞, ∞ ^ 0		88
9584854198	If ƒ(x) is increasing, then a left Riemann sum ...		89
9584854199	If ƒ(x) is decreasing, then a left Riemann sum ...		90
9584854200	If ƒ(x) is increasing, then a right Riemann sum ...		91
9584854201	If ƒ(x) is decreasing, then a right Riemann sum ...		92
9584854202	If ƒ(x) is concave up, then the trapezoidal approximation of the integral...		93
9584854203	If ƒ(x) is concave down, then the trapezoidal approximation of the integral...		94
9584854204	If ƒ(x) is concave up, then a midpoint Riemann sum...		95
9584854205	If ƒ(x) is concave down, then a midpoint Riemann sum...		96
9584854206	Area of a trapezoid		97
9584854207	If ƒ(x) is concave down then the linear approximation...		98
9584854208	If ƒ(x) is concave up then the linear approximation...		99
9584854209	The Fundamental Theorem of Calculus (Part I)		100
9584854210	The Fundamental Theorem of Calculus (Part II)		101
9584854211	∫ x ^ n dx =		102
9584854212	∫ e ^ x dx =		103
9584854213	∫ 1/x dx =		104
9584854214	∫ sin x dx =		105
9584854215	∫ cos x dx =		106
9584854216	∫ sec² x dx =		107
9584854217	∫ a ^ x dx =		108
9584854218	∫ tan x dx =		109
9584854219	∫ 1 / (x² + 1) dx =		110
9584854220	∫ 1 / √(1 - x² ) dx =		111
9584854221	The average value of f from x = a to x = b (Mean Value Theorem for Integrals)		112
9584854222	Integral equation for a horizontal shift of 1 unit to the right.		113
9584854223	Adding adjacent integrals		114
9584854224	Swapping the bounds of an integral		115
9584854225	Exponential Growth Solution of dy/dt = kP P(0) = P₀		116
9584854226	lim n→∞ (1 + 1/n) ^ n		117
9584854227	Steps to solve a differential equation		118
9584854228	To find the area between 2 curves using vertical rectangles (dx)		119
9584854229	To find the area between 2 curves using horizontal rectangles (dy)		120
9584854230	Volume of a disc; rotated about a horizontal line		121
9584854231	Volume of a washer; rotated about a horizontal line		122
9584854232	Volume of a disc; rotated about a vertical line		123
9584854233	Volume of a washer; rotated about a vertical line		124
9584854234	Volume of solid if cross sections perpendicular to the x-axis are squares		125
9584854235	Volume of solid if cross sections perpendicular to the x-axis are isosceles right triangles		126
9584854236	Volume of solid if cross sections perpendicular to the x-axis are equilateral triangles		127
9584854237	Volume of solid if cross sections perpendicular to the x-axis are semicircles		128
9584854238	Volume of a prism		129
9584854239	Volume of a cylinder		130
9584854240	Volume of a pyramid		131
9584854241	Volume of a cone		132
9584854242	Volume of a sphere		133
9584854243	Surface Area of a cylinder		134
9584854244	Surface Area of a sphere		135
9584854245	Area of a Sector (in radians)		136
9584854246	Slope of a parametric curve x = x(t) and y = y(t)		137
9584854247	Horizontal Tangent of a parametric curve		138
9584854248	Vertical Tangent of a parametric curve		139
9584854249	Second Derivative of a parametric curve		140
9584854250	Velocity vector of a particle moving in the plane x = x(t) and y = y(t)		141
9584854251	Acceleration vector of a particle moving in the plane x = x(t) and y = y(t)		142
9584854252	Speed of a particle moving in the plane x = x(t) and y = y(t)		143
9584854253	Distance traveled (Arc Length) by a particle moving in the plane with a ≤ t ≤ b x = x(t) and y = y(t)		144
9584854254	Position at time t = b of a particle moving in the plane given x(a), y(a), x′(t), and y′(t).		145
9584854255	Magnitude of a vector in terms of the x and y components		146
9584854256	Graph of θ = c (c is a constant)		147
9584854257	Graph of r = θ		148
9584854258	Graphs of: r = c r = c sin(θ) r = c cos(θ) (c is a constant)		149
9584854259	Graphs of: r = sin(k θ) r = cos(k θ) (k is a constant)		150
9584854260	Graph of: r = 1 + cos(θ)		151
9584854261	Graph of: r = 1 + 2 cos(θ)		152
9584854262	Slope of polar graph r (θ)		153
9584854263	Area enclosed by r = f(θ), α ≤ θ ≤ β		154
9584854264	Double Angle Formula for cos²θ		155
9584854265	Double Angle Formula for sin²θ		156
9584854266	dx/dθ < 0		157
9584854267	dx/dθ > 0		158
9584854268	dy/dθ < 0		159
9584854269	dy/dθ > 0		160
9584854270	Convert from polar (r,θ) to rectangular (x,y)		161
9584854271	Convert from rectangular (x,y) to polar (r,θ)		162
9584854272	Horizontal Tangent of a Polar Graph		163
9584854273	Vertical Tangent of a Polar Graph		164
9584854274	Integration by Parts Formula		165
9584854275	∫ lnx dx = ?		166
9584854276	Improper Integral: ∫ 1/x² dx bounds: [0,1]		167
9584854277	Improper Integral: ∫ f(x) dx bounds: [0,∞]		168
9584854278	Arc length of a function f(x) from x = a to x = b		169
9584854279	Arc length of a polar graph r 0 ≤ θ ≤ π		170
9584854280	Arc Length of a graph defined parametrically with a ≤ t ≤ b x = x(t) and y = y(t)		171
9584854281	Differential equation for exponential growth dP/dt = ?		172
9584854282	Solution of a differential equation for exponential growth		173
9584854283	Differential equation for decay dP/dt = ?		174
9584854284	Solution of a differential equation for decay		175
9584854285	Logistic differential equation dP/dt = ?		176
9584854286	Solution of a logistic differential equation		177
9584854287	Graph of a Logistic Function (include inflection pt.)		178
9584854288	Euler's Method for solving y' = F (x,y) with initial point (x₀ , y₀)		179
9584854289	Power Series for f(x) = 1 / (1 - x) (include IOC)		180
9584854290	Power Series for f(x) = tan⁻¹ x (include IOC)		181
9584854291	Power Series for f(x) = ln (1 + x) (include IOC)		182
9584854292	Taylor Series for f(x) about x = 0 (Maclaurin Series)		183
9584854293	Taylor Series for f(x) about x = c		184
9584854294	Maclaurin Series for f (x) = e∧x (include IOC)		185
9584854295	Maclaurin Series for f (x) = sin x (include IOC)		186
9584854296	Maclaurin Series for f (x) = cos x (include IOC)		187
9584854297	Error for the partial sum, Sn, of an infinite series S		188
9584854298	Error bound of an alternating series		189
9584854299	Lagrange error bound		190
9584854300	Geometric sequence (def. and conv. property)		191
9584854301	Harmonic Series (def. and conv. property)		192
9584854302	p-series (def. and conv. property)		193
9584854303	Divergence Test		194
9584854304	If lim n→∞ a(sub n) = 0, then ∑ a(sub n) for n from 1 to ∞ ...		195
9584854305	Integral Test		196
9584854306	Alternating Series Test		197
9584854307	Direct Comparison Test		198
9584854308	Limit Comparison Test		199
9584854309	Ratio Test		200
9584854310	n-th Root Test		201
9584854311	Interval of Convergence (IOC)		202
9584854312	Radius of Convergence		203