AP Calculus AB Review Flashcards
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| 13864607087 | Limit Definition of Derivative | limit (as h approaches 0)= F(x+h)-F(x)/h |  | 0 |
| 13864607088 | Alternate Definition of Derivative | limit (as x approaches a number c)= f(x)-f(c)/x-c x≠c |  | 1 |
| 13864607089 | limit as x approaches 0: sinx/x | 1 | 2 | |
| 13864607090 | limit as x approaches 0: 1-cosx/x | 0 | 3 | |
| 13864607091 | Continuity at a point | If the limit exists (left limit and right limit are equal), and the limit equals the function at that point. | 4 | |
| 13864607092 | d/dx (u^n) | n*u^(n-1)u' | 5 | |
| 13864607093 | d/dx (sinu) | (cosu)u' | 6 | |
| 13864607094 | d/dx (cosu) | (-sinu)u' | 7 | |
| 13864607095 | d/dx (tanu) | (sec²u)u' | 8 | |
| 13864607096 | d/dx (cotu) | (-csc²u)u' | 9 | |
| 13864607097 | d/dx (secu) | (secutanu)u' | 10 | |
| 13864607098 | d/dx (cscu) | (-cscucotu)u' | 11 | |
| 13864607099 | d/dx (lnu) | u'/u | 12 | |
| 13864607100 | d/dx (e^u) | e^u(u') | 13 | |
| 13864607101 | d/dx (a^u) | a^u*u'*lna | 14 | |
| 13864607102 | d/dx[f(g(x))] | f'(g(x))g'(x) Chain Rule | 15 | |
| 13864607103 | Product rule of f(x)g(x) | f(x)g'(x)+g(x)f'(x) | 16 | |
| 13864607104 | Quotient rule of f(x)/g(x) | g(x)f'(x)-f(x)g'(x)/g(x)² | 17 | |
| 13864607105 | Intermediate Value Theorem | if f(x) is continuous on [a,b], then there will be a point x=c that lies in between [a,b] | 18 | |
| 13864607106 | Extreme Value Theorem | if f(x) is continuous on [a,b], then f(x) has an absolute max or min on the interval | 19 | |
| 13864607107 | Rolle's Theorem | if f(x) is continuous on [a,b] and differentiable on (a,b), and if f(a)=f(b), then there is at least one point (x=c) on (a,b) where f'(c)=0 | 20 | |
| 13864607108 | Mean Value Theorem | if f(x) is continuous on [a,b] and differentiable on (a,b), there is at least one point (x=c) where f'(c)= F(b)-F(a)/b-a | 21 | |
| 13864607109 | If f'(x)=0 | there is a horizontal tangent and a possible max or min | 22 | |
| 13864860605 | Critical Number | If 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) | 23 | |
| 13864607110 | If f'(x)>0 | f(x) is increasing | 24 | |
| 13864607111 | If f'(x)<0 | f(x) is decreasing | 25 | |
| 13864909165 | f' changes from negative to positive at x = c | f(x) has a relative min at x = c | 26 | |
| 13864927953 | f' changes from positive to negative at x = c | f(x) has a relative max at x = c | 27 | |
| 13864607112 | If f''(x)=0 at x = c | (c, f(c)) is a possible point of inflection | 28 | |
| 13864867604 | point of inflection | the point where the graph changes concavity | 29 | |
| 13864607113 | If f''(x)>0 | f(x) is concave up & f'(x) is increasing | 30 | |
| 13864607114 | If f''(x)<0 | f(x) is concave down & f'(x) is decreasing | 31 | |
| 13864607115 | p(t), x(t), s(t) | means position function | 32 | |
| 13864607116 | p'(t) | v(t)= velocity | 33 | |
| 13864607117 | p''(t) or v'(t) | a(t)= acceleration | 34 | |
| 13864607118 | v(t)=0 | particle or object is at rest or changing direction | 35 | |
| 13864607119 | v(t)>0 | particle or object is moving right (or up) | 36 | |
| 13864607120 | v(t)<0 | particle or object is moving left (or down) | 37 | |
| 13864607121 | a(t)=0 | v(t) not changing | 38 | |
| 13864607122 | a(t)>0 | v(t) increasing | 39 | |
| 13864607123 | a(t)<0 | v(t) decreasing | 40 | |
| 13864607124 | v(t) and a(t) has same signs | speed of particle increasing | 41 | |
| 13864607125 | v(t) and a(t) has different signs | speed of particle decreasing | 42 | |
| 13864607126 | ∫(u^n)du | u^(n+1)∕(n+1) +C | 43 | |
| 13864607127 | ∫(1/u)du or ∫(du/u) | ln|u|+C | 44 | |
| 13864607128 | ∫(e^u)du | e^u +C | 45 | |
| 13864607129 | ∫sinu du | -cosu+C | 46 | |
| 13864607130 | ∫cosu du | sinu+C | 47 | |
| 13864607131 | ∫sec²u du | tanu+C | 48 | |
| 13864607132 | ∫csc²u du | -cotu+C | 49 | |
| 13864607133 | ∫secutanu du | secu+C | 50 | |
| 13864607134 | ∫cscucotu du | -cscu+C | 51 | |
| 13864607135 | ∫k dx [k IS A CONSTANT] | kx+C | 52 | |
| 13864607136 | 1st fundamental theorem of calculus | (bounded by a to b) ∫f(x)dx= F(b)-F(a) | 53 | |
| 13864607137 | 2nd fundamental theorem | (bounded by 1 to x) d/dx[∫f(t)dt]= f(x)(x') | 54 | |
| 13864607138 | average value | (1/(b-a))[∫f(x)dx] [BOUNDED BY A TO B] | 55 | |
| 13864607139 | Area between curves | A=∫f(x)-g(x) dx | 56 | |
| 13864607140 | Volume (DISK) | V=π∫f(x)²dx | 57 | |
| 13864607141 | Volume (WASHER) | V=π∫f(x)²-g(x)²dx | 58 | |
| 13864607142 | ∫f(x)dx from a to a | 0 | 59 | |
| 13864607143 | Displacement of particle | ∫v(t)dt | 60 | |
| 13864607144 | total distance of particle | ∫|v(t)|dt | 61 | |
| 13864895878 | The definite integral of a rate of change of a function | Gives the total change in the original function. | 62 | |
| 13864607145 | position of particle at specific point | p(x)= initial condition + ∫v(t)dt (bounds are initial condition and p(x)) | 63 | |
| 13864607146 | derivative of exponential growth equation: y=Ce^kt | dy/dt=ky | 64 | |
| 13864607147 | Cross section for volume: square [A=s²] | v=∫[f(x)-g(x)]²dx | 65 | |
| 13864607149 | Cross section for volume: equilateral triangle | v= √3/4∫[f(x)-g(x)]²dx | 66 | |
| 13864607150 | Cross section for volume: semicircle | v= (π/8)∫[f(x)-g(x)]²dx | 67 | |
| 13864607151 | d/dx(arcsin(u)) | u'/√(1-u²) | 68 | |
| 13864607152 | d/dx(arccos(u)) | -u'/√(1-u²) | 69 | |
| 13864607153 | d/dx(arctan(u)) | u'/(1+u²) | 70 | |
| 13864607154 | d/dx(arccot(u)) | -u'/(1+u²) | 71 | |
| 13864607155 | d/dx(arcsec(u)) | u'/(|u|√(u²-1)) | 72 | |
| 13864607156 | d/dx(arccsc(u)) | -u'/(|u|√(u²-1)) | 73 | |
| 13864607157 | ∫1/√(a²-u²)du | arcsin(u/a)+C | 74 | |
| 13864607158 | ∫1/(a²+u²)du | (1/a)(arctan(u/a))+C | 75 | |
| 13864607159 | ∫1/(|u|√(u²-a²))du | (1/a)(arcsec(|u|/a))+C | 76 |