AP Calculus AB Review Flashcards
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| 9908185440 | Limit Definition of Derivative | limit (as h approaches 0)= F(x+h)-F(x)/h |  | 0 |
| 9908185442 | limit as x approaches 0: sinx/x | 1 | 1 | |
| 9908185443 | limit as x approaches 0: 1-cosx/x | 0 | 2 | |
| 9908185444 | Continuity Rule | If the limit exists (aka left limit and right limit are equal), and the limit equals the function at that point. | 3 | |
| 9908185445 | Basic Derivative | f(x^n)= nX^(n-1) | 4 | |
| 9908185446 | d/dx(sinx) | cosx | 5 | |
| 9908185447 | d/dx(cosx) | -sinx | 6 | |
| 9908185448 | d/dx(tanx) | sec²x | 7 | |
| 9908185452 | d/dx(lnu) | u'/u | 8 | |
| 9908185453 | d/dx(e^u) | e^u(u') | 9 | |
| 9908185454 | d/dx(a^u) | a^u(lna)(u') | 10 | |
| 9908185455 | Chain rule of f(x)^n | nf(x)f'(x) | 11 | |
| 9908185456 | Product rule of f(x)g(x) | f'(x)g(x)+g'(x)f(x) | 12 | |
| 9908185457 | Quotient rule of f(x)/g(x) | g(x)f'(x)-f(x)g'(x)/g(x)² | 13 | |
| 9908185458 | 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] | 14 | |
| 9908185459 | Extreme Value Theorem | if f(x) is continuous on [a,b], then f(x) has an absolute max or min on the interval | 15 | |
| 9908185460 | 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 | 16 | |
| 9908185461 | 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 | 17 | |
| 9908185462 | If f'(x)=0 | there is a max or min on f(x) [number line test] | 18 | |
| 9908185463 | If f'(x)>0 | f(x) is increasing | 19 | |
| 9908185464 | If f'(x)<0 | f(x) is decreasing | 20 | |
| 9908185465 | If f''(x)=0 | f(x) has a point of inflection & f'(x) has a max or min | 21 | |
| 9908185466 | If f''(x)>0 | f(x) is concave up & f'(x) is increasing | 22 | |
| 9908185467 | If f''(x)<0 | f(x) is concave down & f'(x) is decreasing | 23 | |
| 9908185468 | p(t), x(t), s(t) | means position function | 24 | |
| 9908185469 | s'(t) | v(t)= velocity | 25 | |
| 9908185470 | s''(t) or v'(t) | a(t)= acceleration | 26 | |
| 9908185471 | v(t)=0 | p(t) is at rest or changing direction | 27 | |
| 9908185472 | v(t)>0 | p(t) is moving right | 28 | |
| 9908185473 | v(t)<0 | p(t) is moving left | 29 | |
| 9908185474 | a(t)=0 | v(t) not changing | 30 | |
| 9908185475 | a(t)>0 | v(t) increasing | 31 | |
| 9908185476 | a(t)<0 | v(t) decreasing | 32 | |
| 9908185477 | v(t) and a(t) has same signs | speed of particle increasing | 33 | |
| 9908185478 | v(t) and a(t) has different signs | speed of particle decreasing | 34 | |
| 9908185479 | ∫(x^n)dx | x^(n+1)∕(n+1) +C | 35 | |
| 9908185480 | ∫(1/x)dx | ln|x|+C | 36 | |
| 9908185481 | ∫(e^kx)dx | ekx/k +C | 37 | |
| 9908185482 | ∫sinx dx | -cosx+C | 38 | |
| 9908185483 | ∫cosx dx | sinx+C | 39 | |
| 9908185484 | ∫sec²x dx | tanx+C | 40 | |
| 9908185488 | ∫k dx [k IS A CONSTANT] | kx+C | 41 | |
| 9908185489 | ∫f(x)dx [BOUNDS ARE SAME] | 0 | 42 | |
| 9908185490 | total distance of particle | ∫|v(t)|dt | 43 |