BC Calculus AP Review Flashcards

9742879873	Double Angle Formula for cos²(θ)		0
9742879874	Double Angle Formula for sin²(θ)		1
9742879875	sin(0)=		2
9742879876	sin(π/4)		3
9742879877	sin⁻¹(-1)		4
9742879878	tan⁻¹(-1)		5
9742879879	1+cot²(θ)		6
9742879880	1+tan²(θ)		7
9742879881	sin(2θ)		8
9742879882	cos(2θ)		9
9742879883	log(AB)		10
9742879884	log(A / B)		11
9742879885	log(A) ^ x		12
9742879886	e^(ln(x))		13
9742879887	ln(x) / ln(a)		14
9742879888	Simplify the expression into one log: 2 ln(x) + ln(x+1) - ln(x-1)		15
9742879889	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
9742879890	Definition of the Derivative (Using the limit as h→0)		17
9742879891	lim x→₀ sin(x)/x		18
9742879892	lim x→∞ tan⁻¹(x)		19
9742879893	First derivative test for a local max of f at x = a		20
9742879894	First derivative test for a local min of f at x = a		21
9742879895	Second derivative test for a local max of f at x = a		22
9742879896	Second derivative test for a local min of f at x = a		23
9742879897	Test for max and mins of f on [a, b]		24
9742879898	Inflection Points		25
9742879899	ƒ'(x) < 0		26
9742879900	ƒ''(x) < 0 or ƒ'(x) is decreasing		27
9742879901	ƒ'(x) > 0		28
9742879902	ƒ''(x) > 0 or ƒ'(x) is increasing		29
9742879903	Intermediate Value Theorem (IVT)		30
9742879904	Mean Value Theorem (MVT)		31
9742879905	Rolle's Theorem		32
9742879906	Squeeze Theorem		33
9742879907	ƒ(x) is continuous at x = a if...		34
9742879908	Extreme Value Theorem		35
9742879909	Critical Points		36
9742879910	Three types of discontinuities.		37
9742879911	ƒ(x) is differentiable at x = a if...		38
9742879912	Three conditions where ƒ(x) is not differentiable		39
9742879913	Average rate of change of ƒ(x) over [a, b]		40
9742879914	Instantaneous rate of change of ƒ(a)		41
9742879915	d/dx ( tan⁻¹ ( x ) )		42
9742879916	d/dx ( sin⁻¹ ( x ) )		43
9742879917	d/dx ( e ^ x )		44
9742879918	d/dx ( ln x )		45
9742879919	d/dx ( a ^ x )		46
9742879920	d/dx ( sin x )		47
9742879921	d/dx ( cos x )		48
9742879922	d/dx ( tan x )		49
9742879923	d/dx ( sec x )		50
9742879924	d/dx ( csc x )		51
9742879925	d/dx ( cot x )		52
9742879926	Product Rule		53
9742879927	Quotient Rule		54
9742879928	Chain Rule		55
9742879929	d/dx (ƒ(x)³)		56
9742879930	d/dx ( ln ƒ(x) )		57
9742879931	d/dx (e ^ ƒ(x) )		58
9742879932	Derivative of the Inverse of ƒ(x)		59
9742879933	Implicit Differentiation Find dy/dx: x²/9+y²/4=1		60
9742879934	Equation of a line in point-slope form		61
9742879935	Equation of the tangent line to y = ƒ(x) at x = a		62
9742879936	A normal line to a curve is...		63
9742879937	Velocity of a point moving along a line with position at time t given by d(t)		64
9742879938	Speed of a point moving along a line		65
9742879939	Average velocity of s over [a, b]		66
9742879940	Average speed of s over [a, b]		67
9742879941	Average acceleration given v over [a, b]		68
9742879942	An object in motion is at rest when...		69
9742879943	An object in motion reverses direction when...		70
9742879944	Acceleration of a point moving along a line with position at time t given by d(t)		71
9742879945	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
9742879946	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
9742879947	Displacement of a particle moving along a line with velocity v(t) for a ≤ t ≤ b.		74
9742880076	Total distance traveled by a particle moving along a line with velocity v(t) for a ≤ t ≤ b	...	75
9742879948	The total change in ƒ(x) over [a, b] in terms of the rate of change, ƒ'(x)		76
9742879949	Graph of y = 1/x		77
9742879950	Graph of y = e ^ (kx)		78
9742879951	Graph of y = ln x		79
9742879952	Graph of y = sin x		80
9742879953	Graph of y = cos x		81
9742879954	Graph of y = tan x		82
9742879955	Graph of y = tan⁻¹ x		83
9742879956	Graph of y = √(1 - x²)		84
9742879957	Graph of x²/a² + y²/b² = 1		85
9742879958	L'Hopital's Rule		86
9742879959	To find the limits of indeterminate forms: ∞ × 0		87
9742879960	To find the limits of indeterminate forms: 0 ^ 0, 1 ^ ∞, ∞ ^ 0		88
9742879961	If ƒ(x) is increasing, then a left Riemann sum ...		89
9742879962	If ƒ(x) is decreasing, then a left Riemann sum ...		90
9742879963	If ƒ(x) is increasing, then a right Riemann sum ...		91
9742879964	If ƒ(x) is decreasing, then a right Riemann sum ...		92
9742879965	If ƒ(x) is concave up, then the trapezoidal approximation of the integral...		93
9742879966	If ƒ(x) is concave down, then the trapezoidal approximation of the integral...		94
9742879967	If ƒ(x) is concave up, then a midpoint Riemann sum...		95
9742879968	If ƒ(x) is concave down, then a midpoint Riemann sum...		96
9742879969	Area of a trapezoid		97
9742879970	If ƒ(x) is concave down then the linear approximation...		98
9742879971	If ƒ(x) is concave up then the linear approximation...		99
9742879972	The Fundamental Theorem of Calculus (Part I)		100
9742879973	The Fundamental Theorem of Calculus (Part II)		101
9742879974	∫ x ^ n dx =		102
9742879975	∫ e ^ x dx =		103
9742879976	∫ 1/x dx =		104
9742879977	∫ sin x dx =		105
9742879978	∫ cos x dx =		106
9742879979	∫ sec² x dx =		107
9742879980	∫ a ^ x dx =		108
9742879981	∫ tan x dx =		109
9742879982	∫ 1 / (x² + 1) dx =		110
9742879983	∫ 1 / √(1 - x² ) dx =		111
9742879984	The average value of f from x = a to x = b (Mean Value Theorem for Integrals)		112
9742879985	Integral equation for a horizontal shift of 1 unit to the right.		113
9742879986	Adding adjacent integrals		114
9742879987	Swapping the bounds of an integral		115
9742879988	Exponential Growth Solution of dy/dt = kP P(0) = P₀		116
9742879989	lim n→∞ (1 + 1/n) ^ n		117
9742879990	Steps to solve a differential equation		118
9742879991	To find the area between 2 curves using vertical rectangles (dx)		119
9742879992	To find the area between 2 curves using horizontal rectangles (dy)		120
9742879993	Volume of a disc; rotated about a horizontal line		121
9742879994	Volume of a washer; rotated about a horizontal line		122
9742879995	Volume of a disc; rotated about a vertical line		123
9742879996	Volume of a washer; rotated about a vertical line		124
9742879997	Volume of solid if cross sections perpendicular to the x-axis are squares		125
9742879998	Volume of solid if cross sections perpendicular to the x-axis are isosceles right triangles		126
9742879999	Volume of solid if cross sections perpendicular to the x-axis are equilateral triangles		127
9742880000	Volume of solid if cross sections perpendicular to the x-axis are semicircles		128
9742880001	Volume of a prism		129
9742880002	Volume of a cylinder		130
9742880003	Volume of a pyramid		131
9742880004	Volume of a cone		132
9742880005	Volume of a sphere		133
9742880006	Surface Area of a cylinder		134
9742880007	Surface Area of a sphere		135
9742880008	Area of a Sector (in radians)		136
9742880009	Slope of a parametric curve x = x(t) and y = y(t)		137
9742880010	Horizontal Tangent of a parametric curve		138
9742880011	Vertical Tangent of a parametric curve		139
9742880012	Second Derivative of a parametric curve		140
9742880013	Velocity vector of a particle moving in the plane x = x(t) and y = y(t)		141
9742880014	Acceleration vector of a particle moving in the plane x = x(t) and y = y(t)		142
9742880015	Speed of a particle moving in the plane x = x(t) and y = y(t)		143
9742880016	Distance traveled (Arc Length) by a particle moving in the plane with a ≤ t ≤ b x = x(t) and y = y(t)		144
9742880017	Position at time t = b of a particle moving in the plane given x(a), y(a), x′(t), and y′(t).		145
9742880018	Magnitude of a vector in terms of the x and y components		146
9742880019	Graph of θ = c (c is a constant)		147
9742880020	Graph of r = θ		148
9742880021	Graphs of: r = c r = c sin(θ) r = c cos(θ) (c is a constant)		149
9742880022	Graphs of: r = sin(k θ) r = cos(k θ) (k is a constant)		150
9742880023	Graph of: r = 1 + cos(θ)		151
9742880024	Graph of: r = 1 + 2 cos(θ)		152
9742880025	Slope of polar graph r (θ)		153
9742880026	Area enclosed by r = f(θ), α ≤ θ ≤ β		154
9742880027	Double Angle Formula for cos²θ		155
9742880028	Double Angle Formula for sin²θ		156
9742880029	dx/dθ < 0		157
9742880030	dx/dθ > 0		158
9742880031	dy/dθ < 0		159
9742880032	dy/dθ > 0		160
9742880033	Convert from polar (r,θ) to rectangular (x,y)		161
9742880034	Convert from rectangular (x,y) to polar (r,θ)		162
9742880035	Horizontal Tangent of a Polar Graph		163
9742880036	Vertical Tangent of a Polar Graph		164
9742880037	Integration by Parts Formula		165
9742880038	∫ lnx dx = ?		166
9742880039	Improper Integral: ∫ 1/x² dx bounds: [0,1]		167
9742880040	Improper Integral: ∫ f(x) dx bounds: [0,∞]		168
9742880041	Arc length of a function f(x) from x = a to x = b		169
9742880042	Arc length of a polar graph r 0 ≤ θ ≤ π		170
9742880043	Arc Length of a graph defined parametrically with a ≤ t ≤ b x = x(t) and y = y(t)		171
9742880044	Differential equation for exponential growth dP/dt = ?		172
9742880045	Solution of a differential equation for exponential growth		173
9742880046	Differential equation for decay dP/dt = ?		174
9742880047	Solution of a differential equation for decay		175
9742880048	Logistic differential equation dP/dt = ?		176
9742880049	Solution of a logistic differential equation		177
9742880050	Graph of a Logistic Function (include inflection pt.)		178
9742880051	Euler's Method for solving y' = F (x,y) with initial point (x₀ , y₀)		179
9742880052	Power Series for f(x) = 1 / (1 - x) (include IOC)		180
9742880053	Power Series for f(x) = tan⁻¹ x (include IOC)		181
9742880054	Power Series for f(x) = ln (1 + x) (include IOC)		182
9742880055	Taylor Series for f(x) about x = 0 (Maclaurin Series)		183
9742880056	Taylor Series for f(x) about x = c		184
9742880057	Maclaurin Series for f (x) = e∧x (include IOC)		185
9742880058	Maclaurin Series for f (x) = sin x (include IOC)		186
9742880059	Maclaurin Series for f (x) = cos x (include IOC)		187
9742880060	Error for the partial sum, Sn, of an infinite series S		188
9742880061	Error bound of an alternating series		189
9742880062	Lagrange error bound		190
9742880063	Geometric sequence (def. and conv. property)		191
9742880064	Harmonic Series (def. and conv. property)		192
9742880065	p-series (def. and conv. property)		193
9742880066	Divergence Test		194
9742880067	If lim n→∞ a(sub n) = 0, then ∑ a(sub n) for n from 1 to ∞ ...		195
9742880068	Integral Test		196
9742880069	Alternating Series Test		197
9742880070	Direct Comparison Test		198
9742880071	Limit Comparison Test		199
9742880072	Ratio Test		200
9742880073	n-th Root Test		201
9742880074	Interval of Convergence (IOC)		202
9742880075	Radius of Convergence		203