Final AP Review Flashcards

6666404291	Finding a basic limit		0
6666414037	Finding a basic limit (piecewise function)		1
6666490130	Showing continuity at a point		2
6666504689	Finding limits at infinity		3
6666592801	Finding horizontal asymptotes		4
6666605170	Finding derivative using limit definitions		5
6666609859	Finding average rate of change		6
6666617320	Finding instantaneous rate of change		7
6666623457	Finding approximate derivative using a table of values		8
6666637174	Finding horizontal tangent lines to a curve		9
6666658232	Finding vertical tangent lines to a curve		10
6666667495	Using linear approximations to find values of a function		11
6666680144	Find the derivative of f(g(x))		12
6666690032	Showing that a piecewise function is differentiable at the break point		13
6666704173	Finding critical values/points		14
6666721147	Finding increasing/decreasing behavior of a function		15
6666726158	Finding relative extrema of a function		16
6666750715	Finding inflection points using the second derivative		17
6666756049	Finding inflection points using the graph of the first derivative	Find where f' changes direction (increasing to decreasing or vice versa)	18
6666764185	Finding the absolute max/min of f(x) on a closed interval [a,b]		19
6666776543	Showing that Rolle's Theorem applies to f(x) on [a,b]		20
6666779733	List the guarantee of Rolle's Theorem if it applies		21
6666782238	Showing that the Mean Value Theorem applies to f(x) on [a,b]		22
6666785925	List the guarantee of the Mean Value Theorem if it applies		23
6666861392	Finding increasing/decreasing behavior of f(x) given the graph of f'(x)		24
6666865448	Deciding whether a linear approximation over/underestimates the true function value		25
6666882574	Finding the minimum (maximum) slope of f(x) on [a,b]		26
6666891932	Approximate area using a LEFT Riemann sum with n rectangles		27
6666904460	Approximate area using a RIGHT Riemann sum with n rectangles		28
6666910930	Approximate area using a MIDPOINT Riemann sum		29
6666917786	Approximate area using trapezoids		30
6666928758	Calculate definite integrals from right to left		31
6666939546	State the basic form of the area accumulation function		32
6666953026	Finding the area under a curve that has been shifted up vertically k units		33
6666966827	Given f'(x) and f(a), find f(b)		34
6666989206	Find the derivative of the basic area accumulation function		35
6666990645	Find the derivative of the area accumulation function (chain rule situation		36
6667004002	Finding the area under a curve f(x) on [a,b]		37
6667008912	Finding the area between f(x) and g(x)		38
6667016034	Find the vertical line x=c that divides the area under f(x) on [a,b] into equal pieces		39
6667028158	Find the volume when the area under f(x) is revolved about the x-axis (area is flush up against x-axis)		40
6667058175	Find the volume when the area between f(x) and g(x) is revolved about the x-axis		41
6667063128	Find the volume when the area under f(x) on [a,b] is revolved about the y-axis		42
6667104935	Find cross-sectional volumes		43
6667087680	Given a base that lies between f(x) and g(x) on [a,b], find the volume of the solid formed by projecting squares upwards that are perpendicular to the base.		44
6667141432	Solving first-order separable differential equations		45
6667147932	Find the average value of f(x) on [a,b]		46
6667164859	Setting up an exponential growth situation		47
6667179250	Drawing a slope field		48
6667183403	Given a slope field, find the differential equation		49
6667242866	Given a position function s(t), find velocity and acceleration		50
6667247663	Given v(t) and s(0), find s(t)		51
6667250571	Given a(t), v(0)=0 and s(0), find s(t)		52
6667256824	Given position function s(t), find average velocity from t_1 to t_2 (precalculus idea)		53
6667260768	Given position function s(t), find instantaneous velocity at t=k (calculus idea)		54
6667396088	Given velocity, decide whether a particle is speeding up or slowing down at time t=k		55
6667266878	Given velocity function v(t) on [t1, t2], find the minimum (maximum) acceleration of the particle		56
6667280145	Find the average velocity of the particle on [t1, t2]		57
6667284967	Given the velocity function v(t), find the change in position of the particle (aka displacement) on [t1, t2]		58
6667287871	Given the velocity function v(t), find the total distance traveled by the particle on [t1, t2]	(You can sometimes use a calculator to do the heavy lifting after setting this up.)	59
6667290865	Given the velocity function v(t), find the total distance traveled by the particle on [t1, t2] (no calculator)		60
6667299813	Given the velocity function, find the time at which the particle is furthest from its starting point (also could be furthest to the left/right)		61
6667305510	State the meaning of the integral of a rate of change		62
6667320013	Setting up a "rate-in, rate-out" word problem (for example, a water tank has g gallons to start, the filling rate is F(t), the emptying rate is E(t), how much in tank at m-minute mark?)		63
6667328768	Setting up a "rate-in, rate-out" word problem (for example, a water tank has g gallons to start, the filling rate is F(t), the emptying rate is E(t), how fast is water level changing at m-minute mark?)		64
6667329858	Setting up a "rate-in, rate-out" word problem (for example, a water tank has g gallons to start, the filling rate is F(t), the emptying rate is E(t), when is tank level at a minimum/maximum?)		65