Calculus Flashcards
Terms : Hide Images [1]
| 1241411988 | 1 |  | 0 | |
| 1241411989 | 0 |  | 1 | |
| 1241411990 | Squeeze Theorem |  | 2 | |
| 1241411991 | f is continuous at x=c if... |  | 3 | |
| 1241411992 | Intermediate Value Theorem | If 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 | 4 | |
| 1241411993 | Global Definition of a Derivative |  | 5 | |
| 1241411994 | Alternative Definition of a Derivative | f '(x) is the limit of the following difference quotient as x approaches c |  | 6 |
| 1241411995 | nx^(n-1) |  | 7 | |
| 1241411996 | 1 |  | 8 | |
| 1241411997 | cf'(x) |  | 9 | |
| 1241411998 | f'(x)+g'(x) |  | 10 | |
| 1241411999 | The position function OR s(t) |  | 11 | |
| 1241412000 | f'(x)-g'(x) |  | 12 | |
| 1241412001 | uvw'+uv'w+u'vw |  | 13 | |
| 1241412002 | cos(x) |  | 14 | |
| 1241412003 | -sin(x) |  | 15 | |
| 1241412004 | sec²(x) |  | 16 | |
| 1241412005 | -csc²(x) |  | 17 | |
| 1241412006 | sec(x)tan(x) |  | 18 | |
| 1241412007 | dy/dx |  | 19 | |
| 1241412008 | f'(g(x))g'(x) |  | 20 | |
| 1241412009 | Extreme Value Theorem | If 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. | 21 | |
| 1241412010 | 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) | 22 | |
| 1241412011 | Rolle's Theorem | Let 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). | 23 | |
| 1241412012 | Mean Value Theorem | The 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. |  | 24 |
| 1241412013 | First Derivative Test for local extrema |  | 25 | |
| 1241412014 | Point of inflection at x=k |  | 26 | |
| 1241412015 | Combo Test for local extrema | If 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. |  | 27 |
| 1241412016 | Horizontal Asymptote |  | 28 | |
| 1241412017 | L'Hopital's Rule |  | 29 | |
| 1241412018 | x+c |  | 30 | |
| 1241412019 | sin(x)+C |  | 31 | |
| 1241412020 | -cos(x)+C |  | 32 | |
| 1241412021 | tan(x)+C |  | 33 | |
| 1241412022 | -cot(x)+C |  | 34 | |
| 1241412023 | sec(x)+C |  | 35 | |
| 1241412024 | -csc(x)+C |  | 36 | |
| 1241412025 | Fundamental Theorem of Calculus #1 | The definite integral of a rate of change is the total change in the original function. |  | 37 |
| 1241412026 | Fundamental Theorem of Calculus #2 |  | 38 | |
| 1241412027 | Mean Value Theorem for integrals or the average value of a functions |  | 39 | |
| 1241412028 | ln(x)+C |  | 40 | |
| 1241412029 | -ln(cosx)+C = ln(secx)+C | hint: tanu = sinu/cosu |  | 41 |
| 1241412030 | ln(sinx)+C = -ln(cscx)+C |  | 42 | |
| 1241412031 | ln(secx+tanx)+C = -ln(secx-tanx)+C |  | 43 | |
| 1241412032 | ln(cscx+cotx)+C = -ln(cscx-cotx)+C |  | 44 | |
| 1241412033 | If f and g are inverses of each other, g'(x) |  | 45 | |
| 1241412034 | Exponential growth (use N= ) |  | 46 | |
| 1241412035 | Area under a curve |  | 47 | |
| 1241412036 | Formula for Disk Method | Axis of rotation is a boundary of the region. |  | 48 |
| 1241412037 | Formula for Washer Method | Axis of rotation is not a boundary of the region. |  | 49 |
| 1241412038 | Inverse Secant Antiderivative |  | 50 | |
| 1241412039 | Inverse Tangent Antiderivative |  | 51 | |
| 1241412040 | Inverse Sine Antiderivative |  | 52 | |
| 1241412041 | Derivative of eⁿ |  | 53 | |
| 1241412042 | ln(a)*aⁿ+C |  | 54 | |
| 1241412043 | Derivative of ln(u) |  | 55 | |
| 1241412044 | Antiderivative of f(x) from [a,b] |  | 56 | |
| 1241412045 | Opposite Antiderivatives |  | 57 | |
| 1241412046 | Antiderivative of xⁿ |  | 58 | |
| 1241412047 | Adding or subtracting antiderivatives |  | 59 | |
| 1241412048 | Constants in integrals |  | 60 | |
| 1241412049 | Identity function | D: (-∞,+∞) R: (-∞,+∞) |  | 61 |
| 1241412050 | Squaring function | D: (-∞,+∞) R: (o,+∞) |  | 62 |
| 1241412051 | Cubing function | D: (-∞,+∞) R: (-∞,+∞) |  | 63 |
| 1241412052 | Reciprocal function | D: (-∞,+∞) x can't be zero R: (-∞,+∞) y can't be zero |  | 64 |
| 1241412053 | Square root function | D: (0,+∞) R: (0,+∞) |  | 65 |
| 1241412054 | Exponential function | D: (-∞,+∞) R: (0,+∞) |  | 66 |
| 1241412055 | Natural log function | D: (0,+∞) R: (-∞,+∞) |  | 67 |
| 1241412056 | Sine function | D: (-∞,+∞) R: [-1,1] |  | 68 |
| 1241412057 | Cosine function | D: (-∞,+∞) R: [-1,1] |  | 69 |
| 1241412058 | Absolute value function | D: (-∞,+∞) R: [0,+∞) |  | 70 |
| 1241412059 | Logistic function | D: (-∞,+∞) R: (0, 1) |  | 71 |
| 1241412060 | cos(π/6) | √3/2 | 72 | |
| 1241412061 | cos(π/4) | √2/2 | 73 | |
| 1241412062 | cos(π/3) | 1/2 | 74 | |
| 1241412063 | cos(π/2) | 0 | 75 | |
| 1241412064 | cos(2π/3) | −1/2 | 76 | |
| 1241412065 | cos(3π/4) | −√2/2 | 77 | |
| 1241412066 | cos(5π/6) | −√3/2 | 78 | |
| 1241412067 | cos(π) | −1 | 79 | |
| 1241412068 | cos(7π/6) | −√3/2 | 80 | |
| 1241412069 | cos(5π/4) | −√2/2 | 81 | |
| 1241412070 | cos(4π/3) | −1/2 | 82 | |
| 1241412071 | cos(3π/2) | 0 | 83 | |
| 1241412072 | cos(5π/3) | 1/2 | 84 | |
| 1241412073 | cos(7π/4) | √2/2 | 85 | |
| 1241412074 | cos(11π/6) | √3/2 | 86 | |
| 1241412075 | cos(2π) | 1 | 87 | |
| 1241412076 | sin(π/6) | 1/2 | 88 | |
| 1241412077 | sin(π/4) | √2/2 | 89 | |
| 1241412078 | sin(π/3) | √3/2 | 90 | |
| 1241412079 | sin(π/2) | 1 | 91 | |
| 1241412080 | sin(2π/3) | √3/2 | 92 | |
| 1241412081 | sin(3π/4) | √2/2 | 93 | |
| 1241412082 | sin(5π/6) | 1/2 | 94 | |
| 1241412083 | sin(π) | 0 | 95 | |
| 1241412084 | sin(7π/6) | −1/2 | 96 | |
| 1241412085 | sin(5π/4) | −√2/2 | 97 | |
| 1241412086 | sin(4π/3) | −√3/2 | 98 | |
| 1241412087 | sin(3π/2) | −1 | 99 | |
| 1241412088 | sin(5π/3) | −√3/2 | 100 | |
| 1241412089 | sin(7π/4) | −√2/2 | 101 | |
| 1241412090 | sin(11π/6) | −1/2 | 102 | |
| 1241412091 | sin(2π) | 0 | 103 | |
| 1241412092 | f(x) = e^(x-2) | Asymptote: y=0 Domain: (-∞, ∞) |  | 104 |
| 1241412093 | f(x)=ln(x-2) | Asymptote: x=2 Domain: (2, ∞) |  | 105 |
| 1241412094 | f(x)=ln(-x) | Asymptote: x=0 Domain: (-∞, 0) |  | 106 |
| 1241412095 | f(x)=e^(x+2) | Asymptote: y=0 Domain: (-∞, ∞) |  | 107 |
| 1241412096 | f(x)= -2+lnx | Asymptote: x=0 Domain: (0, ∞) |  | 108 |
| 1241412097 | f(x)=-lnx | Asymptote: x=0 Domain: (0, ∞) |  | 109 |
| 1241412098 | f(x) = e^(x) +2 | Asymptote: y=2 Domain: (-∞, ∞) |  | 110 |
| 1241412099 | f(x)=ln(x+2) | Asymptote: x=-2 Domain: (-2, ∞) |  | 111 |
| 1241412100 | What does the graph y = sin(x) look like? |  | 112 | |
| 1241412101 | What does the graph y = cos(x) look like? |  | 113 | |
| 1241412102 | What does the graph y = tan(x) look like? |  | 114 | |
| 1241412103 | What does the graph y = csc(x) look like? |  | 115 | |
| 1241412104 | What does the graph y = sec(x) look like? |  | 116 | |
| 1241412105 | What does the graph y = cot(x) look like? |  | 117 | |
| 1241412106 | d/dx[e^x]= | e^x | 118 | |
| 1241412107 | d/dx[a^x]= | a^x*lna | 119 | |
| 1241412108 | d/dx[e^g(x)]= | g'(x)e^g(x) | 120 | |
| 1241412109 | d/dx[a^g(x)]= | g'(x)a^g(x)lna | 121 | |
| 1241412110 | d/dx[cos⁻¹x]= | -1/√(1-x^2) | 122 | |
| 1241412111 | d/dx[sin⁻¹x]= | 1/√(1-x^2) | 123 | |
| 1241412112 | d/dx[tan⁻¹x]= | 1/(1+x^2) | 124 | |
| 1241412113 | d/dx[tanx]= | sec²x | 125 | |
| 1241412114 | d/dx[secx]= | secxtanx | 126 | |
| 1241412115 | d/dx[cscx]= | -cscxcotx | 127 | |
| 1241412116 | d/dx[cotx]= | -csc²x | 128 | |
| 1241412117 | ∫e^xdx= | e^x+C | 129 | |
| 1241412118 | ∫a^xdx= | (a^x)/lna+C | 130 | |
| 1241412119 | ∫1/xdx= | ln|x|+C | 131 | |
| 1241412120 | ∫1/(1+x^2)dx= | tan⁻¹x+C | 132 | |
| 1241412121 | ∫1/(a^2+x^2)dx= | (1/a)(tan⁻¹(x/a)+C | 133 | |
| 1241412122 | ∫1/√(1-x^2)dx= | sin⁻¹x+C | 134 | |
| 1241412123 | ∫tanxdx= | ln|secx|+C | 135 | |
| 1241412124 | Trig Identity: 1= | cos²x+sin²x | 136 | |
| 1241412125 | Trig Identity: sec²x= | tan²x+1 | 137 | |
| 1241412126 | Trig Identity: cos²x= | ½(1+cos(2x)) | 138 | |
| 1241412127 | Trig Identity: sin²x= | ½(1-cos(2x)) | 139 | |
| 1241412128 | Trig Identity: sin(2x)= | 2sinxcosx | 140 | |
| 1241412129 | Trig Identity: cos(2x)= | 1-2sin²x = 2cos²x-1 | 141 | |
| 1241412130 | Integration by Parts: Choice of u | I = Inverse Trig Function L = Natural log (lnx) A = Algebraic Expression (x, x², x³...) T = Trig function (sinx, cosx) E = e^x | 142 | |
| 1241412131 | ∫secxdx= | ln|secx+tanx|+C | 143 | |
| 1241412132 | What does the graph y = sin(x) look like? | | 144 | |
| 1241412133 | What does the graph y = cos(x) look like? | | 145 | |
| 1241412134 | What does the graph y = tan(x) look like? | | 146 | |
| 1241412135 | What does the graph y = csc(x) look like? | | 147 | |
| 1241412136 | What does the graph y = sec(x) look like? | | 148 | |
| 1241412137 | What does the graph y = cot(x) look like? | | 149 | |
| 1241412138 | d/dx[e^x]= | e^x | 150 | |
| 1241412139 | d/dx[a^x]= | a^x*lna | 151 | |
| 1241412140 | d/dx[e^g(x)]= | g'(x)e^g(x) | 152 | |
| 1241412141 | d/dx[a^g(x)]= | g'(x)a^g(x)lna | 153 | |
| 1241412142 | d/dx[cos⁻¹x]= | -1/√(1-x^2) | 154 | |
| 1241412143 | d/dx[sin⁻¹x]= | 1/√(1-x^2) | 155 | |
| 1241412144 | d/dx[tan⁻¹x]= | 1/(1+x^2) | 156 | |
| 1241412145 | d/dx[tanx]= | sec²x | 157 | |
| 1241412146 | d/dx[secx]= | secxtanx | 158 | |
| 1241412147 | d/dx[cscx]= | -cscxcotx | 159 | |
| 1241412148 | d/dx[cotx]= | -csc²x | 160 | |
| 1241412149 | ∫e^xdx= | e^x+C | 161 | |
| 1241412150 | ∫a^xdx= | (a^x)/lna+C | 162 | |
| 1241412151 | ∫1/xdx= | ln|x|+C | 163 | |
| 1241412152 | ∫1/(1+x^2)dx= | tan⁻¹x+C | 164 | |
| 1241412153 | ∫1/(a^2+x^2)dx= | (1/a)(tan⁻¹(x/a)+C | 165 | |
| 1241412154 | ∫1/√(1-x^2)dx= | sin⁻¹x+C | 166 | |
| 1241412155 | ∫tanxdx= | ln|secx|+C | 167 | |
| 1241412156 | Trig Identity: 1= | cos²x+sin²x | 168 | |
| 1241412157 | Trig Identity: sec²x= | tan²x+1 | 169 | |
| 1241412158 | Trig Identity: cos²x= | ½(1+cos(2x)) | 170 | |
| 1241412159 | Trig Identity: sin²x= | ½(1-cos(2x)) | 171 | |
| 1241412160 | Trig Identity: sin(2x)= | 2sinxcosx | 172 | |
| 1241412161 | Trig Identity: cos(2x)= | 1-2sin²x = 2cos²x-1 | 173 | |
| 1241412162 | Integration by Parts: Choice of u | I = Inverse Trig Function L = Natural log (lnx) A = Algebraic Expression (x, x², x³...) T = Trig function (sinx, cosx) E = e^x | 174 | |
| 1241412163 | ∫secxdx= | ln|secx+tanx|+C | 175 |