AP Calculus AB, calculus terms and theorems
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| 2452359116 | 1 |  | 0 | |
| 2452359117 | 0 |  | 1 | |
| 2452359119 | f is continuous at x=c if... |  | 2 | |
| 2452359120 | 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 | 3 | |
| 2452359121 | Definition of a Derivative |  | 4 | |
| 2452359122 | Alternative Definition of a Derivative | f '(x) is the limit of the following difference quotient as x approaches c |  | 5 |
| 2452359123 | nx^(n-1) |  | 6 | |
| 2452359124 | 1 |  | 7 | |
| 2452359125 | cf'(x) |  | 8 | |
| 2452359126 | f'(x)+g'(x) |  | 9 | |
| 2452359128 | f'(x)-g'(x) |  | 10 | |
| 2452359129 | uvw'+uv'w+u'vw |  | 11 | |
| 2452359130 | cos(x) |  | 12 | |
| 2452359131 | -sin(x) |  | 13 | |
| 2452359132 | sec²(x) |  | 14 | |
| 2452359133 | -csc²(x) |  | 15 | |
| 2452359134 | sec(x)tan(x) |  | 16 | |
| 2452359135 | dy/dx |  | 17 | |
| 2452359136 | f'(g(x))g'(x) |  | 18 | |
| 2452359137 | 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. | 19 | |
| 2452359138 | 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) | 20 | |
| 2452359140 | 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. |  | 21 |
| 2452359141 | First Derivative Test for local extrema |  | 22 | |
| 2452359142 | Point of inflection at x=k |  | 23 | |
| 2452359143 | 2nd derivative test | 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. |  | 24 |
| 2452359144 | Horizontal Asymptote |  | 25 | |
| 2452359145 | L'Hopital's Rule |  | 26 | |
| 2452359146 | x+c |  | 27 | |
| 2452359147 | sin(x)+C |  | 28 | |
| 2452359148 | -cos(x)+C |  | 29 | |
| 2452359149 | tan(x)+C |  | 30 | |
| 2452359150 | -cot(x)+C |  | 31 | |
| 2452359151 | sec(x)+C |  | 32 | |
| 2452359152 | -csc(x)+C |  | 33 | |
| 2452359153 | Fundamental Theorem of Calculus #1 | The definite integral of a rate of change is the total change in the original function. |  | 34 |
| 2452359154 | Fundamental Theorem of Calculus #2 |  | 35 | |
| 2452359155 | Mean Value Theorem for integrals or the average value of a functions |  | 36 | |
| 2452359156 | ln(x)+C |  | 37 | |
| 2452359157 | -ln(cosx)+C = ln(secx)+C | hint: tanu = sinu/cosu |  | 38 |
| 2452359158 | ln(sinx)+C = -ln(cscx)+C |  | 39 | |
| 2452359159 | ln(secx+tanx)+C = -ln(secx-tanx)+C |  | 40 | |
| 2452359160 | ln(cscx+cotx)+C = -ln(cscx-cotx)+C |  | 41 | |
| 2452359161 | If f and g are inverses of each other, g'(x) |  | 42 | |
| 2452359162 | Exponential growth (use N= ) |  | 43 | |
| 2452359163 | Area under a curve |  | 44 | |
| 2452359164 | Formula for Disk Method | Axis of rotation is a boundary of the region. |  | 45 |
| 2452359165 | Formula for Washer Method | Axis of rotation is not a boundary of the region. |  | 46 |
| 2452359166 | Inverse Secant Antiderivative |  | 47 | |
| 2452359167 | Inverse Tangent Antiderivative |  | 48 | |
| 2452359168 | Inverse Sine Antiderivative |  | 49 | |
| 2452359169 | Derivative of eⁿ |  | 50 | |
| 2452359170 | ln(a)*aⁿ+C |  | 51 | |
| 2452359171 | Derivative of ln(u) |  | 52 | |
| 2452359172 | Antiderivative of f(x) from [a,b] |  | 53 | |
| 2452359174 | Antiderivative of xⁿ |  | 54 | |
| 2452359175 | Adding or subtracting antiderivatives |  | 55 | |
| 2452359176 | Constants in integrals |  | 56 | |
| 2452359183 | Natural log function | D: (0,+∞) R: (-∞,+∞) |  | 57 |
| 2452359186 | Absolute value function | D: (-∞,+∞) R: [0,+∞) |  | 58 |
| 2452359187 | Greatest integer function | D: (-∞,+∞) R: (-∞,+∞) |  | 59 |
| 2452359188 | Logistic function | D: (-∞,+∞) R: (0, 1) |  | 60 |
| 2452359189 | Given f(x): Is f continuous @ C Is f' continuous @ C | Yes lim+=lim-=f(c) No, f'(c) doesn't exist because of cusp |  | 61 |
| 2452359190 | Given 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 X | | 62 |
