AP Calculus AB, calculus terms and theorems
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| 509430447 | 1 |  | 0 | |
| 509430448 | 0 |  | 1 | |
| 509430449 | Squeeze Theorem |  | 2 | |
| 509430450 | f is continuous at x=c if... |  | 3 | |
| 509430451 | 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 | |
| 509430452 | Global Definition of a Derivative |  | 5 | |
| 509430453 | Alternative Definition of a Derivative | f '(x) is the limit of the following difference quotient as x approaches c |  | 6 |
| 509430454 | nx^(n-1) |  | 7 | |
| 509430455 | 1 |  | 8 | |
| 509430456 | cf'(x) |  | 9 | |
| 509430457 | f'(x)+g'(x) |  | 10 | |
| 509430458 | The position function OR s(t) |  | 11 | |
| 509430459 | f'(x)-g'(x) |  | 12 | |
| 509430460 | uvw'+uv'w+u'vw |  | 13 | |
| 509430461 | cos(x) |  | 14 | |
| 509430462 | -sin(x) |  | 15 | |
| 509430463 | sec²(x) |  | 16 | |
| 509430464 | -csc²(x) |  | 17 | |
| 509430465 | sec(x)tan(x) |  | 18 | |
| 509430466 | dy/dx |  | 19 | |
| 509430467 | f'(g(x))g'(x) |  | 20 | |
| 509430468 | 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 | |
| 509430469 | 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 | |
| 509430470 | 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 | |
| 509430471 | 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 |
| 509430472 | First Derivative Test for local extrema |  | 25 | |
| 509430473 | Point of inflection at x=k |  | 26 | |
| 509430474 | 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 |
| 509430475 | Horizontal Asymptote |  | 28 | |
| 509430476 | L'Hopital's Rule |  | 29 | |
| 509430477 | x+c |  | 30 | |
| 509430478 | sin(x)+C |  | 31 | |
| 509430479 | -cos(x)+C |  | 32 | |
| 509430480 | tan(x)+C |  | 33 | |
| 509430481 | -cot(x)+C |  | 34 | |
| 509430482 | sec(x)+C |  | 35 | |
| 509430483 | -csc(x)+C |  | 36 | |
| 509430484 | Fundamental Theorem of Calculus #1 | The definite integral of a rate of change is the total change in the original function. |  | 37 |
| 509430485 | Fundamental Theorem of Calculus #2 |  | 38 | |
| 509430486 | Mean Value Theorem for integrals or the average value of a functions |  | 39 | |
| 509430487 | ln(x)+C |  | 40 | |
| 509430488 | -ln(cosx)+C = ln(secx)+C | hint: tanu = sinu/cosu |  | 41 |
| 509430489 | ln(sinx)+C = -ln(cscx)+C |  | 42 | |
| 509430490 | ln(secx+tanx)+C = -ln(secx-tanx)+C |  | 43 | |
| 509430491 | ln(cscx+cotx)+C = -ln(cscx-cotx)+C |  | 44 | |
| 509430492 | If f and g are inverses of each other, g'(x) |  | 45 | |
| 509430493 | Exponential growth (use N= ) |  | 46 | |
| 509430494 | Area under a curve |  | 47 | |
| 509430495 | Formula for Disk Method | Axis of rotation is a boundary of the region. |  | 48 |
| 509430496 | Formula for Washer Method | Axis of rotation is not a boundary of the region. |  | 49 |
| 509430497 | Inverse Secant Antiderivative |  | 50 | |
| 509430498 | Inverse Tangent Antiderivative |  | 51 | |
| 509430499 | Inverse Sine Antiderivative |  | 52 | |
| 509430500 | Derivative of eⁿ |  | 53 | |
| 509430501 | ln(a)*aⁿ+C |  | 54 | |
| 509430502 | Derivative of ln(u) |  | 55 | |
| 509430503 | Antiderivative of f(x) from [a,b] |  | 56 | |
| 509430504 | Opposite Antiderivatives |  | 57 | |
| 509430505 | Antiderivative of xⁿ |  | 58 | |
| 509430506 | Adding or subtracting antiderivatives |  | 59 | |
| 509430507 | Constants in integrals |  | 60 | |
| 509430508 | Identity function | D: (-∞,+∞) R: (-∞,+∞) |  | 61 |
| 509430509 | Squaring function | D: (-∞,+∞) R: (o,+∞) |  | 62 |
| 509430510 | Cubing function | D: (-∞,+∞) R: (-∞,+∞) |  | 63 |
| 509430511 | Reciprocal function | D: (-∞,+∞) x can't be zero R: (-∞,+∞) y can't be zero |  | 64 |
| 509430512 | Square root function | D: (0,+∞) R: (0,+∞) |  | 65 |
| 509430513 | Exponential function | D: (-∞,+∞) R: (0,+∞) |  | 66 |
| 509430514 | Natural log function | D: (0,+∞) R: (-∞,+∞) |  | 67 |
| 509430515 | Sine function | D: (-∞,+∞) R: [-1,1] |  | 68 |
| 509430516 | Cosine function | D: (-∞,+∞) R: [-1,1] |  | 69 |
| 509430517 | Absolute value function | D: (-∞,+∞) R: [0,+∞) |  | 70 |
| 509430518 | Greatest integer function | D: (-∞,+∞) R: (-∞,+∞) |  | 71 |
| 509430519 | Logistic function | D: (-∞,+∞) R: (0, 1) |  | 72 |
| 509430520 | 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 |  | 73 |
| 509430521 | 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 | | 74 |
