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AP Calculus Flash Cards Flashcards

AP Calculus AB, calculus terms and theorems

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5037527321
5037527330
503752734Squeeze Theorem
503752735f is continuous at x=c if...
503752736Intermediate 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)=k
503752737Global Definition of a Derivative
503752738Alternative Definition of a Derivativef '(x) is the limit of the following difference quotient as x approaches c
503752739nx^(n-1)
5037527401
503752741cf'(x)
503752742f'(x)+g'(x)
503752743The position function OR s(t)
503752744f'(x)-g'(x)
503752745uvw'+uv'w+u'vw
503752746cos(x)
503752747-sin(x)
503752748sec²(x)
503752749-csc²(x)
503752750sec(x)tan(x)
503752751dy/dx
503752752f'(g(x))g'(x)
503752753Extreme 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.
503752754Critical 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)
503752755Rolle's TheoremLet f be continuous on [a,b] and differentiable on (a,b) and if f(a)=f(b) then there is at least one number c on (a,b) such that f'(c)=0 (If the slope of the secant is 0, the derivative must = 0 somewhere in the interval).
503752756Mean Value TheoremThe 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.
503752757First Derivative Test for local extrema
503752758Point of inflection at x=k
503752759Combo Test for local extremaIf 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.
503752760Horizontal Asymptote
503752761L'Hopital's Rule
503752762x+c
503752763sin(x)+C
503752764-cos(x)+C
503752765tan(x)+C
503752766-cot(x)+C
503752767sec(x)+C
503752768-csc(x)+C
503752769Fundamental Theorem of Calculus #1The definite integral of a rate of change is the total change in the original function.
503752770Fundamental Theorem of Calculus #2
503752771Mean Value Theorem for integrals or the average value of a functions
503752772ln(x)+C
503752773-ln(cosx)+C = ln(secx)+Chint: tanu = sinu/cosu
503752774ln(sinx)+C = -ln(cscx)+C
503752775ln(secx+tanx)+C = -ln(secx-tanx)+C
503752776ln(cscx+cotx)+C = -ln(cscx-cotx)+C
503752777If f and g are inverses of each other, g'(x)
503752778Exponential growth (use N= )
503752779Area under a curve
503752780Formula for Disk MethodAxis of rotation is a boundary of the region.
503752781Formula for Washer MethodAxis of rotation is not a boundary of the region.
503752782Inverse Secant Antiderivative
503752783Inverse Tangent Antiderivative
503752784Inverse Sine Antiderivative
503752785Derivative of eⁿ
503752786ln(a)*aⁿ+C
503752787Derivative of ln(u)
503752788Antiderivative of f(x) from [a,b]
503752789Opposite Antiderivatives
503752790Antiderivative of xⁿ
503752791Adding or subtracting antiderivatives
503752792Constants in integrals
503752793Identity functionD: (-∞,+∞) R: (-∞,+∞)
503752794Squaring functionD: (-∞,+∞) R: (o,+∞)
503752795Cubing functionD: (-∞,+∞) R: (-∞,+∞)
503752796Reciprocal functionD: (-∞,+∞) x can't be zero R: (-∞,+∞) y can't be zero
503752797Square root functionD: (0,+∞) R: (0,+∞)
503752798Exponential functionD: (-∞,+∞) R: (0,+∞)
503752799Natural log functionD: (0,+∞) R: (-∞,+∞)
503752800Sine functionD: (-∞,+∞) R: [-1,1]
503752801Cosine functionD: (-∞,+∞) R: [-1,1]
503752802Absolute value functionD: (-∞,+∞) R: [0,+∞)
503752803Greatest integer functionD: (-∞,+∞) R: (-∞,+∞)
503752804Logistic functionD: (-∞,+∞) R: (0, 1)
503752805Given f(x): Is f continuous @ C Is f' continuous @ CYes lim+=lim-=f(c) No, f'(c) doesn't exist because of cusp
503752806Given 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''

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