AP Calculus AB, calculus terms and theorems
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| 5789993239 | 1.) F(c) exists 2.) limit F(x) as x approaches c exists 3.) limit F(x) as x approaches c = F(c) | f is continuous at x=c if... |  | 0 |
| 5789993240 | Yes lim+=lim-=f(c) No, f'(c) doesn't exist because of cusp | Given f(x): Is f continuous @ C Is f' continuous @ C |  | 1 |
| 5789993241 | This is a graph of f'(x). Since f'(C) exists, differentiability implies continuouity, so Yes.
Yes f' decreases on X | Given f'(x): Is f continuous @ c? Is there an inflection point on f @ C? |  | 2 |
| 5789993242 | 1 |  | 3 | |
| 5789993243 | 0 |  | 4 | |
| 5789993244 | Squeeze Theorem | Define: |  | 5 |
| 5790217617 | Define the Squeeze Theorem. | Suppose that g(x)≤f(x) and also suppose that {the limit of g(x) (as x goes to a)} = {the limit of h(x) (as x goes to a)} = L then {the limit of f(x) (as x goes to a) = L} | 6 | |
| 5789993245 | Intermediate Value Theorem | What is the name of the theorem that states: "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)?" | 7 | |
| 5790230306 | 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) | Define the Intermediate Value Theorem. | 8 | |
| 5789993246 | Global Definition of a Derivative | Define: |  | 9 |
| 5790301214 | the limit of {[f(x ⍖ Δx) - f(x)]/Δx} (as Δx approaches 0) | What is the Global Definition of a Derivative? | 10 | |
| 5789993247 | Alternative Definition of a Derivative | Define: f '(x) is the limit of the following difference quotient as x approaches c |  | 11 |
| 5790295970 | f '(x) is the limit of "[f(x)-f(c)]/[x-c]" (as x approaches c) | What is the Alternative Definition of a Derivative? | 12 | |
| 5789993248 | nx^(n-1) |  | 13 | |
| 5789993249 | 1 |  | 14 | |
| 5789993250 | cf'(x) |  | 15 | |
| 5789993251 | f'(x)+g'(x) |  | 16 | |
| 5789993252 | The position function OR s(t) | Define: |  | 17 |
| 5790316854 | -16t² ⍖ v₀t ⍖ s₀ | What is the position function OR s(t) | 18 | |
| 5789993253 | f'(x)-g'(x) |  | 19 | |
| 5789993254 | uvw'+uv'w+u'vw |  | 20 | |
| 5789993255 | cos(x) |  | 21 | |
| 5789993256 | -sin(x) |  | 22 | |
| 5789993257 | sec²(x) |  | 23 | |
| 5789993258 | -csc²(x) |  | 24 | |
| 5789993259 | sec(x)tan(x) |  | 25 | |
| 5789993260 | dy/dx |  | 26 | |
| 5789993261 | The Chain Rule: f'(g(x))g'(x) |  | 27 | |
| 5789993262 | Extreme Value Theorem | What theorem states that 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? | 28 | |
| 5790328865 | 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. | Define the Extreme Value Theorem. | 29 | |
| 5789993263 | Critical Number | If f'(c)=0 or does not exist, and c is in the domain of f, then c is a what? (Derivative is 0 or undefined) | 30 | |
| 5789993264 | Rolle's Theorem | What theorem states that if we 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)? | 31 | |
| 5790331697 | If we 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). | Define Rolle's Theorem. | 32 | |
| 5789993265 | Mean Value Theorem | What theorem states that 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. |  | 33 |
| 5790332219 | 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. f '(c) = [f(b) - f(a)]/[b - a] | Define the Mean Value Theorem. | 34 | |
| 5789993266 | First Derivative Test for local extrema | Define: |  | 35 |
| 5790337688 | Let c be a critical number of a function f that is continuous on the closed interval [a,b] that contains c. If f is differentiable on [a,b], then f(c) can be classified as follows... If f '(x) changes from a negative to a positive at c, then f(c) is a relative minimum of f. If f' (x) changes from a negative to a positive at c, then f(c) is a relative maximum of f | Define the First Derivative Test for local extrema. | 36 | |
| 5789993267 | If k is in the domain of f If f ''(k)=0 or does not exist If f ''(x) changes sign @ x=k | When is x=k a point of inflection? | 37 | |
| 5789993268 | Combo Test (Second Derivative 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. |  | 38 |
| 5789993269 | Horizontal Asymptote | Type of Asymptote? |  | 39 |
| 5789993270 | L'Hopital's Rule | Define: |  | 40 |
| 5789993271 | x+c |  | 41 | |
| 5789993272 | sin(x)+C |  | 42 | |
| 5789993273 | -cos(x)+C |  | 43 | |
| 5789993274 | tan(x)+C |  | 44 | |
| 5789993275 | -cot(x)+C |  | 45 | |
| 5789993276 | sec(x)+C |  | 46 | |
| 5789993277 | -csc(x)+C |  | 47 | |
| 5789993278 | Fundamental Theorem of Calculus #1 | The definite integral of a rate of change is the total change in the original function. |  | 48 |
| 5792115603 | The definite integral of a rate of change is the total change in the original function. ∫ₐᵇ f(x)dx = F(b) - F(a) | What is the 1st fundamental theorem of Calculus? | 49 | |
| 5789993279 | Fundamental Theorem of Calculus #2 |  | 50 | |
| 5792123877 | d/dx (∫ˣ sub-c) f(t)dt = f(x) | What is the second fundamental theorem of Calculus? | 51 | |
| 5789993280 | Mean Value Theorem for integrals or the average value of a functions | Define this statement: |  | 52 |
| 5789993281 | ln(x)+C |  | 53 | |
| 5789993282 | -ln(cosx)+C = ln(secx)+C | hint: tanu = sinu/cosu |  | 54 |
| 5789993283 | ln(sinx)+C = -ln(cscx)+C |  | 55 | |
| 5789993284 | ln(secx+tanx)+C = -ln(secx-tanx)+C |  | 56 | |
| 5789993285 | ln(cscx+cotx)+C = -ln(cscx-cotx)+C |  | 57 | |
| 5789993286 | g'(x) | Assume f and g are inverses of each other. |  | 58 |
| 5789993287 | Exponential growth | Define: N= |  | 59 |
| 5789993288 | Area under a curve | Define: |  | 60 |
| 5789993289 | Formula for Disk Method | Assume the axis of rotation is a boundary of the region, and define: |  | 61 |
| 5789993290 | Formula for Washer Method | Assume the axis of rotation is not a boundary of the region, and define: |  | 62 |
| 5789993291 | Inverse Secant Antiderivative | Define: |  | 63 |
| 5789993292 | Inverse Tangent Antiderivative | Define: |  | 64 |
| 5789993293 | Inverse Sine Antiderivative | Define: |  | 65 |
| 5789993294 | Derivative of eⁿ | Define: |  | 66 |
| 5789993295 | ln(a)*aⁿ+C |  | 67 | |
| 5789993296 | Derivative of ln(u) | Define: |  | 68 |
| 5789993297 | Antiderivative of f(x) from [a,b] | Define: |  | 69 |
| 5789993298 | Opposite Antiderivatives | Define: |  | 70 |
| 5789993299 | Antiderivative of xⁿ | Define: |  | 71 |
| 5789993300 | Adding or subtracting antiderivatives | Define: |  | 72 |
| 5789993301 | Constants in integrals | Define: |  | 73 |
| 5789993302 | Identity function | Define: D: (-∞,+∞) R: (-∞,+∞) |  | 74 |
| 5789993303 | Squaring function | Define: D: (-∞,+∞) R: (o,+∞) |  | 75 |
| 5789993304 | Cubing function | Define: D: (-∞,+∞) R: (-∞,+∞) |  | 76 |
| 5789993305 | Reciprocal function | Define: D: (-∞,+∞) x can't be zero R: (-∞,+∞) y can't be zero |  | 77 |
| 5789993306 | Square root function | Define: D: (0,+∞) R: (0,+∞) |  | 78 |
| 5789993307 | Exponential function | Define: D: (-∞,+∞) R: (0,+∞) |  | 79 |
| 5789993308 | Natural log function | Define: D: (0,+∞) R: (-∞,+∞) |  | 80 |
| 5789993309 | Sine function | Define: D: (-∞,+∞) R: [-1,1] |  | 81 |
| 5789993310 | Cosine function | Define: D: (-∞,+∞) R: [-1,1] |  | 82 |
| 5789993311 | Absolute value function | Define: D: (-∞,+∞) R: [0,+∞) |  | 83 |
| 5789993312 | Greatest integer function | Define: D: (-∞,+∞) R: (-∞,+∞) |  | 84 |
| 5789993313 | Logistic function | Define: D: (-∞,+∞) R: (0, 1) |  | 85 |
| 5789993314 | √3/2 | cos(π/6) | 86 | |
| 5789993315 | √2/2 | cos(π/4) | 87 | |
| 5789993316 | 1/2 | cos(π/3) | 88 | |
| 5789993317 | 0 | cos(π/2) | 89 | |
| 5789993318 | -1/2 | cos(2π/3) | 90 | |
| 5789993319 | −√2/2 | cos(3π/4) | 91 | |
| 5789993320 | −√3/2 | cos(5π/6) | 92 | |
| 5789993321 | -1 | cos(π) | 93 | |
| 5789993325 | 0 | cos(3π/2) | 94 | |
| 5789993326 | 1/2 | cos(5π/3) | 95 | |
| 5789993327 | √2/2 | cos(7π/4) | 96 | |
| 5789993328 | √3/2 | cos(11π/6) | 97 | |
| 5789993329 | 1 | cos(2π) | 98 | |
| 5789993330 | 1/2 | sin(π/6) | 99 | |
| 5789993331 | √2/2 | sin(π/4) | 100 | |
| 5789993332 | √3/2 | sin(π/3) | 101 | |
| 5789993333 | 1 | sin(π/2) | 102 | |
| 5789993334 | √3/2 | sin(2π/3) | 103 | |
| 5789993335 | √2/2 | sin(3π/4) | 104 | |
| 5789993336 | 1/2 | sin(5π/6) | 105 | |
| 5789993337 | 0 | sin(π) | 106 | |
| 5789993338 | −1/2 | sin(7π/6) | 107 | |
| 5789993339 | −√2/2 | sin(5π/4) | 108 | |
| 5789993340 | −√3/2 | sin(4π/3) | 109 | |
| 5789993341 | −1 | sin(3π/2) | 110 | |
| 5789993342 | −√3/2 | sin(5π/3) | 111 | |
| 5789993343 | −√2/2 | sin(7π/4) | 112 | |
| 5789993344 | −1/2 | sin(11π/6) | 113 | |
| 5789993345 | 0 | sin(2π) | 114 | |
| 5789993346 | y = sin(x) | What is this a graph of? |  | 115 |
| 5789993347 | y = cos(x) | What is this a graph of? |  | 116 |
| 5789993348 | y = tan(x) | What is this a graph of? |  | 117 |
| 5789993349 | e^x | d/dx[e^x]= | 118 | |
| 5789993350 | sec²x | d/dx[tanx]= | 119 | |
| 5789993351 | secxtanx | d/dx[secx]= | 120 | |
| 5789993352 | -cscxcotx | d/dx[cscx]= | 121 | |
| 5789993353 | -csc²x | d/dx[cotx]= | 122 | |
| 5789993354 | 1 (This is a Trig identity) | cos²x+sin²x | 123 | |
| 5789993364 | vu'+uv' | d/dx[uv]= | 124 | |
| 5789993365 | (vu'-uv')/v^2 | d/dx[u/v]= | 125 | |
| 5789993366 | v(t) | d/dt[s(t)]= | 126 | |
| 5789993367 | a(t) | d/dt[v(t)]= | 127 | |
| 5789993368 | (Change in Position)/(Change in Time) | Average Velocity | 128 | |
| 5789993369 | (Change in Velocity)/(Change in Time) | Average Acceleration | 129 | |
| 5789993370 | 0 | What is v(t) when an object is stopped? | 130 | |
| 5792171537 | The object is stopped, | What is indicated by a v(t) that equals zero? | 131 | |
| 5789993371 | v(t) < 0 | What is v(t) when an object is moving left? | 132 | |
| 5792172092 | The object is moving left. | What is indicated by a v(t) that is less than zero? | 133 | |
| 5789993372 | v(t) > 0 | What is v(t) when an object is moving right? | 134 | |
| 5792172844 | The object is moving right. | What is indicated by a v(t) that is greater than zero? | 135 | |
| 5789993373 | a(t) and v(t) have the same sign | What is noteworthy about a(t) and v(t) when an object is speeding up? | 136 | |
| 5792173226 | The object is speeding up. | What is indicated by an a(t) and a v(t) that have the same sign? | 137 | |
| 5789993374 | a(t) and v(t) have different signs | What is noteworthy about a(t) and v(t) when an object is slowing down? | 138 | |
| 5792173670 | The object is slowing down. | What is indicated by an a(t) and a v(t) that have different signs? | 139 | |
| 5789993375 | v(t) changes sign | What happens when an object changes direction? | 140 | |
| 5792178018 | The object has changed direction. | What is indicated by v(t) changing sign? | 141 | |
| 5789993376 | vu'+uv' | Express the Product Rule. | 142 | |
| 5789993377 | low d-hi minus high d-lo over low squared | What is the catchy way of remembering the Quotient Rule? | 143 | |
| 5789993378 | s(b) - s(a) | Express Displacement. | 144 | |
| 5789993379 | [s(b)-s(a)] / (b - a) | Express Average Velocity. | 145 | |
| 5789993380 | Vertical because there isn't a Y intercept | Is X equals C horizontal or vertical? Why? | 146 | |
| 5789993381 | Horizontal because there isn't a X intercept | Is Y equals C horizontal or vertical? Why? | 147 | |
| 5789993382 | If you want to find the X intercept, cover up the Y as well as its multiple (i.e. if the y were a 6y, then both the 6 and the y would be covered up), and solve for X, and visa versa. | Describe the cover up method to finding an intercept when the equation of a line is in standard form. | 148 | |
| 5789993383 | m equals y2 minus y1 over x2 minus x1 | What is the point slope formula? | 149 | |
| 5789993384 | Y equals mx plus b | What is the slope intercept formula? | 150 | |
| 5789993385 | They must have the same slope. | What is required for two lines to be parallel to each other? | 151 | |
| 5789993386 | Their slope have to be negative reciprocals of each other. | What is required for two lines to be perpendicular to each other? | 152 | |
| 5789993387 | a point and a slope | What two things are needed to make the equation of a line? | 153 | |
| 5792214054 | It means to approach the limit from the RIGHT side (the positive side of the number line). | When being asked to evaluate a limit, what does a plus symbol after the limit mean? | 154 | |
| 5792215282 | It means to approach the limit from the Left side (the negative side of the number line). | When being asked to evaluate a limit, what does a negative symbol after the limit mean? | 155 | |
| 5832914565 | when adding, subtracting, or multiplying, and even dividing as long as the denominator doesn't equal zero. | Under what conditions is it okay to separate or combine limits that are approaching the same number? | 156 | |
| 5832939155 | Quite simply, take the limit of the variable, and THEN, raise the limit to the exponent. | If you have a limit of a variable raised to an exponent, what can you do? | 157 | |
| 5833232557 | Quite simply plug the number x is approaching into the polynomial and solve. | When taking the limit of a polynomial of x as x approaches some number, what can you do? | 158 | |
| 5846054387 | A vertical asymptote | If a zero cannot be factored out at the denominator, what do you have? | 159 | |
| 5846057008 | a sign analysis test | What do you do to determine whether or not there is a limit when an unfactorable zero in the denominator reveals a vertical asymptote? | 160 | |
| 5846066399 | First, determine the value for x that makes the numerator a zero. Then, pick a number for x between the zero values for the numerator and denominator; plug the number in, and determine the sign of the result. Afterwards, plug in a number that is outside the range previously checked, but on the side of the zero denominator x value. If the two signs match, the limit exists. Otherwise, the limit does NOT exist. | How is the sign analysis test performed when an unfactorable zero in the denominator reveals a vertical asymptote? | 161 | |
| 5846076461 | There is a common factor at that point. | What does it mean when plugging in a x value results in a zero over zero (0/0)? | 162 |
