AP Calculus AB Review Flashcards
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| 9905213369 | Limit Definition of Derivative | limit (as h approaches 0)= F(x+h)-F(x)/h |  | 0 |
| 9905213370 | Alternate Definition of Derivative | limit (as x approaches a number c)= f(x)-f(c)/x-c x≠c |  | 1 |
| 9905213371 | limit as x approaches 0: sinx/x | 1 | 2 | |
| 9905213372 | limit as x approaches 0: 1-cosx/x | 0 | 3 | |
| 9905213373 | Continuity Rule | If the limit exists (aka left limit and right limit are equal), and the limit equals the function at that point. | 4 | |
| 9905213374 | Basic Derivative | f(x^n)= nX^(n-1) | 5 | |
| 9905213375 | d/dx(sinx) | cosx | 6 | |
| 9905213376 | d/dx(cosx) | -sinx | 7 | |
| 9905213377 | d/dx(tanx) | sec²x | 8 | |
| 9905213378 | d/dx(cotx) | -csc²x | 9 | |
| 9905213379 | d/dx(secx) | secxtanx | 10 | |
| 9905213380 | d/dx(cscx) | -cscxcotx | 11 | |
| 9905213381 | d/dx(lnu) | u'/u | 12 | |
| 9905213382 | d/dx(e^u) | e^u(u') | 13 | |
| 9905213383 | d/dx(a^u) | a^u(lna)(u') | 14 | |
| 9905213384 | Chain rule of f(x)^n | nf(x)f'(x) | 15 | |
| 9905213385 | Product rule of f(x)g(x) | f'(x)g(x)+g'(x)f(x) | 16 | |
| 9905213386 | Quotient rule of f(x)/g(x) | g(x)f'(x)-f(x)g'(x)/g(x)² | 17 | |
| 9905213387 | 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] | 18 | |
| 9905213388 | Extreme Value Theorem | if f(x) is continuous on [a,b], then f(x) has an absolute max or min on the interval | 19 | |
| 9905213389 | 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 | |
| 9905213390 | 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 | |
| 9905213391 | If f'(x)=0 | there is a max or min on f(x) [number line test] | 22 | |
| 9905213392 | If f'(x)>0 | f(x) is increasing | 23 | |
| 9905213393 | If f'(x)<0 | f(x) is decreasing | 24 | |
| 9905213394 | If f''(x)=0 | f(x) has a point of inflection & f'(x) has a max or min | 25 | |
| 9905213395 | If f''(x)>0 | f(x) is concave up & f'(x) is increasing | 26 | |
| 9905213396 | If f''(x)<0 | f(x) is concave down & f'(x) is decreasing | 27 | |
| 9905213397 | p(t), x(t), s(t) | means position function | 28 | |
| 9905213398 | s'(t) | v(t)= velocity | 29 | |
| 9905213399 | s''(t) or v'(t) | a(t)= acceleration | 30 | |
| 9905213400 | v(t)=0 | p(t) is at rest or changing direction | 31 | |
| 9905213401 | v(t)>0 | p(t) is moving right | 32 | |
| 9905213402 | v(t)<0 | p(t) is moving left | 33 | |
| 9905213403 | a(t)=0 | v(t) not changing | 34 | |
| 9905213404 | a(t)>0 | v(t) increasing | 35 | |
| 9905213405 | a(t)<0 | v(t) decreasing | 36 | |
| 9905213406 | v(t) and a(t) has same signs | speed of particle increasing | 37 | |
| 9905213407 | v(t) and a(t) has different signs | speed of particle decreasing | 38 | |
| 9905213408 | ∫(x^n)dx | x^(n+1)∕(n+1) +C | 39 | |
| 9905213409 | ∫(1/x)dx | ln|x|+C | 40 | |
| 9905213410 | ∫(e^kx)dx | ekx/k +C | 41 | |
| 9905213411 | ∫sinx dx | -cosx+C | 42 | |
| 9905213412 | ∫cosx dx | sinx+C | 43 | |
| 9905213413 | ∫sec²x dx | tanx+C | 44 | |
| 9905213414 | ∫csc²x dx | -cotx+C | 45 | |
| 9905213415 | ∫secxtanx dx | secx+C | 46 | |
| 9905213416 | ∫cscxcotx | -cscx+C | 47 | |
| 9905213417 | ∫k dx [k IS A CONSTANT] | kx+C | 48 | |
| 9905213418 | ∫f(x)dx [BOUNDS ARE SAME] | 0 | 49 | |
| 9905213419 | total distance of particle | ∫|v(t)|dt | 50 |