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Calculus Flashcards

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5811122275f is continuous at x=c if...0
5811122276Intermediate 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
5811122277Global Definition of a Derivative2
5811122278Alternative Definition of a Derivativef '(x) is the limit of the following difference quotient as x approaches c3
5811122279nx^(n-1)4
581112228015
5811122281cf'(x)6
5811122282f'(x)+g'(x)7
5811122283f'(x)-g'(x)8
5811122284cos(x)9
5811122285-sin(x)10
5811122286sec²(x)11
5811122287-csc²(x)12
5811122288sec(x)tan(x)13
5811122289f'(g(x))g'(x)14
5811122290Extreme 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.15
5811122291Mean 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.16
5811122292Horizontal Asymptote17
5811122293Reciprocal functionD: (-∞,+∞) x can't be zero R: (-∞,+∞) y can't be zero18
5811122294Square root functionD: (0,+∞) R: (0,+∞)19
5811122295Exponential functionD: (-∞,+∞) R: (0,+∞)20
5811122296Natural log functionD: (0,+∞) R: (-∞,+∞)21
5811122297Sine functionD: (-∞,+∞) R: [-1,1]22
5811122298Cosine functionD: (-∞,+∞) R: [-1,1]23
5811122299Absolute value functionD: (-∞,+∞) R: [0,+∞)24
5811122301√3/2cos(π/6)25
5811122302√2/2cos(π/4)26
58111223031/2cos(π/3)27
5811122308-1cos(π)28
5811122309−√3/2cos(7π/6)29
5811122310−√2/2cos(5π/4)30
5811122311−1/2cos(4π/3)31
58111223120cos(3π/2)32
5811122333What does the graph y = sin(x) look like?33
5811122334What does the graph y = cos(x) look like?34
5811122335What does the graph y = tan(x) look like?35
5811122337d/dx[tanx]=sec²x36
5811122338d/dx[secx]=secxtanx37
5811122339d/dx[cscx]=-cscxcotx38
5811122340d/dx[cotx]=-csc²x39
5811122341Trig Identity: 1=cos²x+sin²x40
5811122351d/dx[uv]=vu'+uv'41
5811122352d/dx[u/v]=(vu'-uv')/v^242
5811122353d/dt[s(t)]=v(t)43
5811122354d/dt[v(t)]=a(t)44
5811122355Average Velocity(Change in Position)/(Change in Time)45
5811122356Average Acceleration(Change in Velocity)/(Change in Time)46
5811122357When is a object stopped?v(t) = 047
5811122358When is an object moving left?v(t) < 048
5811122359When is an object moving right?v(t) > 049
5811122360When is an object speeding up?a(t) and v(t) have same sign50
5811122361When is an object slowing down?a(t) and v(t) have different signs51
5811122362When does an object change direction?v(t) changes sign52
5811122363vu'+uv'Product Rule53
5811122364lo dhi minus hi dlo over loloQuotient Rule54
5811122365s(b) - s(a)Displacement55
5811122366[s(b)-s(a)] / (b - a)Average Velocity56

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