AP Calculus AB Review Flashcards
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| 9482158448 | Limit Definition of Derivative | limit (as h approaches 0)= F(x+h)-F(x)/h |  | 0 |
| 9482158449 | Alternate Definition of Derivative | limit (as x approaches a number c)= f(x)-f(c)/x-c x≠c |  | 1 |
| 9482158450 | limit as x approaches 0: sinx/x | 1 | 2 | |
| 9482158451 | limit as x approaches 0: 1-cosx/x | 0 | 3 | |
| 9482158452 | Continuity Rule | A function is continuous at x = c if: (1) f(c) is defined (2) lim f(x) (x goes to c) exits (3) lim f(x) (x goes to c) = f(c) | 4 | |
| 9482158453 | Basic Derivative | f(x^n)= nx^(n-1) | 5 | |
| 9482158454 | d/dx(sinx) | cosx | 6 | |
| 9482158455 | d/dx(cosx) | -sinx | 7 | |
| 9482158456 | d/dx(tanx) | sec²x | 8 | |
| 9482158457 | d/dx(cotx) | -csc²x | 9 | |
| 9482158458 | d/dx(secx) | secxtanx | 10 | |
| 9482158459 | d/dx(cscx) | -cscxcotx | 11 | |
| 9482158460 | d/dx(lnu) | u'/u | 12 | |
| 9482158461 | d/dx(e^u) | e^u(u') | 13 | |
| 9482158462 | d/dx(a^u) | a^u(lna)(u') | 14 | |
| 9482158463 | Chain rule of f(x)^n | n(f(x)^(n-1))f'(x) | 15 | |
| 9482158464 | Product rule of f(x)g(x) | f'(x)g(x)+g'(x)f(x) | 16 | |
| 9482158465 | Quotient rule of f(x)/g(x) | g(x)f'(x)-f(x)g'(x)/g(x)² | 17 | |
| 9482158466 | Intermediate Value Theorem | if f(x) is continuous on [a,b], then there will be a point x=c that lies in between [a,b] such that f(c) is between f(a) and f(b) | 18 | |
| 9482158467 | Extreme Value Theorem | if f(x) is continuous on [a,b], then f(x) has an absolute max or min on the interval | 19 | |
| 9482158468 | Rolle's Theorem | if f(x) is continuous on [a,b] and differentiable on (a,b), and if f(a)=f(b), then there is at least one point (x=c) on (a,b) [DON'T INCLUDE END POINTS] where f'(c)=0 | 20 | |
| 9482158469 | Mean Value Theorem | if f(x) is continuous on [a,b] and differentiable on (a,b), there is at least one point (x=c) where f'(c)= f(b)-f(a)/b-a | 21 | |
| 9482158470 | If f'(x)=0 | there is a POSSIBLE max or min on f(x) [number line test of f'(x)] | 22 | |
| 9482158471 | If f'(x)>0 | f(x) is increasing | 23 | |
| 9482158472 | If f'(x)<0 | f(x) is decreasing | 24 | |
| 9482158473 | If x=a is a critical value | f'(a)=0 or f'(a)=DNE | 25 | |
| 9482158474 | If f''(x)>0 | f(x) is concave up & f'(x) is increasing | 26 | |
| 9482158475 | If f''(x)<0 | f(x) is concave down & f'(x) is decreasing | 27 | |
| 9482158476 | p(t), x(t), s(t) | means position function | 28 | |
| 9482158477 | p'(t) | v(t)= velocity | 29 | |
| 9482158478 | p''(t) or v'(t) | a(t)= acceleration | 30 | |
| 9482158479 | v(t)=0 | p(t) is at rest or changing direction | 31 | |
| 9482158480 | v(t)>0 | p(t) is moving right | 32 | |
| 9482158481 | v(t)<0 | p(t) is moving left | 33 | |
| 9482158482 | a(t)=0 | v(t) not changing | 34 | |
| 9482158483 | a(t)>0 | v(t) increasing | 35 | |
| 9482158484 | a(t)<0 | v(t) decreasing | 36 | |
| 9482158485 | v(t) and a(t) has same signs | speed of particle increasing | 37 | |
| 9482158486 | v(t) and a(t) has different signs | speed of particle decreasing | 38 | |
| 9482158487 | ∫(x^n)dx | x^(n+1)∕(n+1) +C | 39 | |
| 9482158488 | ∫(1/x)dx | ln|x|+C | 40 | |
| 9482158489 | ∫(e^kx)dx | ekx/k +C | 41 | |
| 9482158490 | ∫sinx dx | -cosx+C | 42 | |
| 9482158491 | ∫cosx dx | sinx+C | 43 | |
| 9482158492 | ∫sec²x dx | tanx+C | 44 | |
| 9482158493 | ∫csc²x dx | -cotx+C | 45 | |
| 9482158494 | ∫secxtanx dx | secx+C | 46 | |
| 9482158495 | ∫cscxcotx | -cscx+C | 47 | |
| 9482158496 | ∫k dx [k IS A CONSTANT] | kx+C | 48 | |
| 9482158497 | 1st fundamental theorem of calculus | (bounded by a to b) ∫f(x)dx= F(b)-F(a) | 49 | |
| 9482158498 | 2nd fundamental theorem | (bounded by 1 to x) d/dx[∫f(t)dt]= f(x)(x') | 50 | |
| 9482158499 | average value | (1/(b-a))[∫f(x)dx] [BOUNDED BY A TO B] | 51 | |
| 9482158500 | Area between curves | A=∫f(x)-g(x) dx | 52 | |
| 9482158501 | Volume (DISK) | V=π∫f(x)²dx | 53 | |
| 9482158502 | Volume (WASHER) | V=π∫f(x)²-g(x)²dx | 54 | |
| 9482158503 | ∫f(x)dx [BOUNDS ARE SAME] | 0 | 55 | |
| 9482158504 | Displacement of particle | ∫v(t)dt | 56 | |
| 9482158505 | total distance of particle | ∫|v(t)|dt | 57 | |
| 9482158506 | position of particle at specific point | p(x)= initial condition + ∫v(t)dt (bounds are initial condition and p(x)) | 58 | |
| 9482158507 | derivative of exponential growth equation: P(t)=Pe^kt | dP/dt=kP | 59 | |
| 9482158508 | Cross section for volume: square [A=s²] | v=∫[f(x)-g(x)]²dx | 60 | |
| 9482158509 | Cross section for volume: isosceles triangle [A=1/2s²] | v= 1/2∫[f(x)-g(x)]²dx | 61 | |
| 9482158510 | Cross section for volume: equilateral triangle [A=√3/4s²] | v= √3/4∫[f(x)-g(x)]²dx | 62 | |
| 9482158511 | Cross section for volume: semicircle [A=1/2πs²] | v= 1/2π∫[f(x)-g(x)]²dx | 63 | |
| 9482158512 | d/dx(sin⁻¹u) | u'/√(1-u²) | 64 | |
| 9482158513 | d/dx(cos⁻¹u) | -u'/√(1-u²) | 65 | |
| 9482158514 | d/dx(tan⁻¹u) | u'/(1+u²) | 66 | |
| 9482158515 | d/dx(cot⁻¹u) | -u'/(1+u²) | 67 | |
| 9482158516 | d/dx(sec⁻¹u) | u'/|u|√(u²-1) | 68 | |
| 9482158517 | d/dx(csc⁻¹u) | u'/|u|√(u²-1) | 69 | |
| 9482158518 | ∫du/√(a²-u²) | (sin⁻¹u/a)+C | 70 | |
| 9482158519 | ∫du/(a²+u²) | (1/a)(tan⁻¹u/a)+C | 71 | |
| 9482158520 | ∫du/|u|√(u²-a²) | (1/a)(sec⁻¹u/a)+C | 72 | |
| 9554294021 | End Behavior Model | g(x) is a right EBM for f(x) if lim (x goes to pos infinity) f(x)/g(x) = 1 g(x) is a left EBM for f(x) if lim (x goes to neg infinity) f(x)/g(x) = 1 | 73 | |
| 9554302018 | Horizontal Asymptotes | If lim f(x) (x goes to pos/neg infinity) = L then y = L is a HA, describes the end behavior of a function (a HA can be crossed) | 74 | |
| 9554314949 | Rules for lim f(x) (x goes to pos/neg infinity) | (1) when lim f(x) (x goes to pos infinity) and degree of x is the same, the ratio of the coefficients is the limit (2) "" when degree in denominator is greater than the degree in numerator, limit = 0 (3) "" when degree in numerator is greater than the degree in denominator, limit DNE but can find end behavior model | 75 | |
| 9554322872 | Vertical Asymptotes | y = f(x) has a VA at x = c if lim f(x) (x goes to c from the right) = pos/neg infinity or lim f(x) (x goes to c from the left) = pos/neg infinity | 76 | |
| 9554344949 | Types of Discontinuity | (1) Removable discontinuity (2) Jump discontinuity (piecewise or absolute value function) (3) Infinite discontinuity (asymptote) | 77 |