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AP Calculus Flash Cards Flashcards

AP Calculus AB, calculus terms and theorems

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5921716883f is continuous at x=c if...0
5921716884Intermediate Value TheoremIf f is continuous on [a,b] and k is a number between f(a) and f(b), then there exists at least one number c such that f(c)=k1
5921716885Limit Definition of a Derivative f'(x)=2
5921716887nx^(n-1)3
592171688814
5921716889cf'(x)5
5921716894cos(x)6
5921716895-sin(x)7
5921716896sec²(x)8
5921716897-csc²(x)9
5921716898sec(x)tan(x)10
5921716900f'(g(x))g'(x)11
5921716901Extreme Value TheoremIf f is continuous on [a,b] then f has an absolute maximum and an absolute minimum on [a,b]. The global extrema occur at critical points in the interval or at endpoints of the interval.12
5921716902Critical NumberIf f'(c)=0 or does not exist, and c is in the domain of f, then c is a critical number. (Derivative is 0 or undefined)13
5921716904Mean Value Theorem for DerivativesThe instantaneous rate of change will equal the mean rate of change somewhere in the interval. Or, the tangent line will be parallel to the secant line.14
5921716905First Derivative Test for local extrema15
5921716906Point of inflection at x=k16
59217169072nd derivative testIf f'(c) = 0 and f"(c)<0, there is a local max on f at x=c. If f'(c) = 0 and f"(c)>0, there is a local min on f at x=c.17
6602390150Riemann Sum definition of a definite integral18
5921716908Horizontal Asymptote19
5921716909L'Hopital's Rule20
5921716911sin(x)+C21
5921716912-cos(x)+C22
5921716913tan(x)+C23
5921716914-cot(x)+C24
5921716915sec(x)+C25
5921716916-csc(x)+C26
5921716917Fundamental Theorem of Calculus #1The definite integral of a rate of change is the total change in the original function.27
5921716918Fundamental Theorem of Calculus #228
5921716919Mean Value Theorem for integrals or the average value of a functions29
5921716920ln(x)+C30
5921716921-ln(cosx)+C = ln(secx)+Chint: tanu = sinu/cosu31
5921716922ln(sinx)+C32
5921716923ln(secx+tanx)+C33
5921716924-ln(cscx+cotx)+C34
5921716926dy/dt=kyy=Ce^(kt)35
5921716927Area between two curves36
5921716928Formula for Disk MethodAxis of rotation is a boundary of the region.37
5921716929Formula for Washer MethodAxis of rotation is not a boundary of the region.38
5921716931Inverse Tangent Antiderivative39
5921716932Inverse Sine Antiderivative40
5921716933Derivative of e^(u(x))41
5921716935Derivative of ln(u)u'/u42
5921716936Antiderivative of f(x) from [a,b]43
5921716937Opposite Antiderivatives44
5921716938Antiderivative of xⁿ45
5921716939Adding or subtracting antiderivatives46
5921716940Constants in integrals47
5921716941Identity functionD: (-∞,+∞) R: (-∞,+∞)48
5921716942f(x) = x²D: (-∞,+∞) R: (o,+∞)49
5921716943f(x) = x³D: (-∞,+∞) R: (-∞,+∞)50
5921716944f(x) =1/xD: (-∞,+∞) x can't be zero R: (-∞,+∞) y can't be zero51
5921716945f(x) =√xD: (0,+∞) R: (0,+∞)52
5921716946f(x) = e^xD: (-∞,+∞) R: (0,+∞)53
5921716947f(x) = ln (x)D: (0,+∞) R: (-∞,+∞)54
5921716948Sine functionD: (-∞,+∞) R: [-1,1]55
5921716949Cosine functionD: (-∞,+∞) R: [-1,1]56
5921716950Absolute value functionD: (-∞,+∞) R: [0,+∞)57
6592119959f(x) = √(a²-x²)top half of circle with radius a and center (0,0)58
5921716953Given f(x): Is f continuous @ C Is f' continuous @ CYes lim+=lim-=f(c) No, f'(c) doesn't exist because of cusp59
5921716954Given f'(x): Is f continuous @ c? Is there an inflection point on f @ C?This is a graph of f'(x). Since f'(C) exists, differentiability implies continuouity, so Yes. Yes f' decreases on XC so f''>0 A point of inflection happens on a sign change at f''60
6772869073The derivative of positionvelocity61
6772869108The derivative of velocityacceleration62
6772873195A particle is speeding up ifvelocity and acceleration have the same sign63
6772876486A particle is slowing down ifvelocity and acceleration have opposite signs64
6773304653Slope of tangent line to f(x) at x = cf'(c)65
6773416318Area of a circle66
6773419037Area of a trapezoidA=1/2h(b1+b2)67

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