AP Calculus AB, calculus terms and theorems
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| 10354961332 | f is continuous at x=c if... |  | 0 | |
| 10354961368 | 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 | 1 | |
| 10354961333 | Limit Definition of a Derivative f'(x)= |  | 2 | |
| 10354961334 | nx^(n-1) |  | 3 | |
| 10354961335 | 1 |  | 4 | |
| 10354961336 | cf'(x) |  | 5 | |
| 10354961337 | cos(x) |  | 6 | |
| 10354961338 | -sin(x) |  | 7 | |
| 10354961339 | sec²(x) |  | 8 | |
| 10354961340 | -csc²(x) |  | 9 | |
| 10354961341 | sec(x)tan(x) |  | 10 | |
| 10354961342 | f'(g(x))g'(x) |  | 11 | |
| 10354961369 | 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. | 12 | |
| 10354961370 | 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) | 13 | |
| 10354961371 | Mean Value Theorem for Derivatives | 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. |  | 14 |
| 10354961343 | First Derivative Test for local extrema |  | 15 | |
| 10354961344 | Point of inflection at x=k |  | 16 | |
| 10354961372 | 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. |  | 17 |
| 10354961391 | Riemann Sum definition of a definite integral |  | 18 | |
| 10354961345 | Horizontal Asymptote |  | 19 | |
| 10354961346 | L'Hopital's Rule |  | 20 | |
| 10354961347 | sin(x)+C |  | 21 | |
| 10354961348 | -cos(x)+C |  | 22 | |
| 10354961349 | tan(x)+C |  | 23 | |
| 10354961350 | -cot(x)+C |  | 24 | |
| 10354961351 | sec(x)+C |  | 25 | |
| 10354961352 | -csc(x)+C |  | 26 | |
| 10354961373 | Fundamental Theorem of Calculus #1 | The definite integral of a rate of change is the total change in the original function. |  | 27 |
| 10354961353 | Fundamental Theorem of Calculus #2 |  | 28 | |
| 10354961354 | Mean Value Theorem for integrals or the average value of a functions |  | 29 | |
| 10354961355 | ln(x)+C |  | 30 | |
| 10354961374 | -ln(cosx)+C = ln(secx)+C | hint: tanu = sinu/cosu |  | 31 |
| 10354961356 | ln(sinx)+C |  | 32 | |
| 10354961357 | ln(secx+tanx)+C |  | 33 | |
| 10354961358 | -ln(cscx+cotx)+C |  | 34 | |
| 10354961375 | dy/dt=ky | y=Ce^(kt) |  | 35 |
| 10354961359 | Area between two curves |  | 36 | |
| 10354961376 | Formula for Disk Method | Axis of rotation is a boundary of the region. |  | 37 |
| 10354961377 | Formula for Washer Method | Axis of rotation is not a boundary of the region. |  | 38 |
| 10354961360 | Inverse Tangent Antiderivative |  | 39 | |
| 10354961361 | Inverse Sine Antiderivative |  | 40 | |
| 10354961362 | Derivative of e^(u(x)) |  | 41 | |
| 10354961378 | Derivative of ln(u) | u'/u | 42 | |
| 10354961363 | Antiderivative of f(x) from [a,b] |  | 43 | |
| 10354961364 | Opposite Antiderivatives |  | 44 | |
| 10354961365 | Antiderivative of xⁿ |  | 45 | |
| 10354961366 | Adding or subtracting antiderivatives |  | 46 | |
| 10354961367 | Constants in integrals |  | 47 | |
| 10354961379 | Identity function | D: (-∞,+∞) R: (-∞,+∞) |  | 48 |
| 10354961380 | f(x) = x² | D: (-∞,+∞) R: (o,+∞) |  | 49 |
| 10354961381 | f(x) = x³ | D: (-∞,+∞) R: (-∞,+∞) |  | 50 |
| 10354961382 | f(x) =1/x | D: (-∞,+∞) x can't be zero R: (-∞,+∞) y can't be zero |  | 51 |
| 10354961383 | f(x) =√x | D: (0,+∞) R: (0,+∞) |  | 52 |
| 10354961384 | f(x) = e^x | D: (-∞,+∞) R: (0,+∞) |  | 53 |
| 10354961385 | f(x) = ln (x) | D: (0,+∞) R: (-∞,+∞) |  | 54 |
| 10354961386 | Sine function | D: (-∞,+∞) R: [-1,1] |  | 55 |
| 10354961387 | Cosine function | D: (-∞,+∞) R: [-1,1] |  | 56 |
| 10354961388 | Absolute value function | D: (-∞,+∞) R: [0,+∞) |  | 57 |
| 10354961393 | f(x) = √(a²-x²) | top half of circle with radius a and center (0,0) | 58 | |
| 10354961389 | 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 |  | 59 |
| 10354961390 | 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 | | 60 |
| 10354961394 | The derivative of position | velocity | 61 | |
| 10354961395 | The derivative of velocity | acceleration | 62 | |
| 10354961396 | A particle is speeding up if | velocity and acceleration have the same sign | 63 | |
| 10354961397 | A particle is slowing down if | velocity and acceleration have opposite signs | 64 | |
| 10354961398 | Slope of tangent line to f(x) at x = c | f'(c) | 65 | |
| 10354961392 | Area of a circle |  | 66 | |
| 10354961399 | Area of a trapezoid | A=1/2h(b1+b2) | 67 |
