AP Calculus AB Review Flashcards
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| 9909056206 | Limit Definition of Derivative | limit (as h approaches 0)= F(x+h)-F(x)/h |  | 0 |
| 9909056208 | limit as x approaches 0: sinx/x | 1 | 1 | |
| 9909056209 | limit as x approaches 0: 1-cosx/x | 0 | 2 | |
| 9909056210 | Continuity Rule | If the limit exists (aka left limit and right limit are equal), and the limit equals the function at that point. | 3 | |
| 9909056211 | Basic Derivative | f(x^n)= nX^(n-1) | 4 | |
| 9909056212 | d/dx(sinx) | cosx | 5 | |
| 9909056213 | d/dx(cosx) | -sinx | 6 | |
| 9909056214 | d/dx(tanx) | sec²x | 7 | |
| 9909056218 | d/dx(lnu) | u'/u | 8 | |
| 9909056219 | d/dx(e^u) | e^u(u') | 9 | |
| 9909056220 | d/dx(a^u) | a^u(lna)(u') | 10 | |
| 9909056221 | Chain rule of f(x)^n | nf(x)f'(x) | 11 | |
| 9909056222 | Product rule of f(x)g(x) | f'(x)g(x)+g'(x)f(x) | 12 | |
| 9909056223 | Quotient rule of f(x)/g(x) | g(x)f'(x)-f(x)g'(x)/g(x)² | 13 | |
| 9909056224 | 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 | |
| 9909056225 | Extreme Value Theorem | if f(x) is continuous on [a,b], then f(x) has an absolute max or min on the interval | 15 | |
| 9909056226 | 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 | |
| 9909056227 | 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 | |
| 9909056228 | If f'(x)=0 | there is a max or min on f(x) [number line test] | 18 | |
| 9909056229 | If f'(x)>0 | f(x) is increasing | 19 | |
| 9909056230 | If f'(x)<0 | f(x) is decreasing | 20 | |
| 9909056231 | If f''(x)=0 | f(x) has a point of inflection & f'(x) has a max or min | 21 | |
| 9909056232 | If f''(x)>0 | f(x) is concave up & f'(x) is increasing | 22 | |
| 9909056233 | If f''(x)<0 | f(x) is concave down & f'(x) is decreasing | 23 | |
| 9909056234 | p(t), x(t), s(t) | means position function | 24 | |
| 9909056235 | p'(t) | v(t)= velocity | 25 | |
| 9909056236 | p''(t) or v'(t) | a(t)= acceleration | 26 | |
| 9909056237 | v(t)=0 | p(t) is at rest or changing direction | 27 | |
| 9909056238 | v(t)>0 | p(t) is moving right | 28 | |
| 9909056239 | v(t)<0 | p(t) is moving left | 29 | |
| 9909056240 | a(t)=0 | v(t) not changing | 30 | |
| 9909056241 | a(t)>0 | v(t) increasing | 31 | |
| 9909056242 | a(t)<0 | v(t) decreasing | 32 | |
| 9909056243 | v(t) and a(t) has same signs | speed of particle increasing | 33 | |
| 9909056244 | v(t) and a(t) has different signs | speed of particle decreasing | 34 | |
| 9909056245 | ∫(x^n)dx | x^(n+1)∕(n+1) +C | 35 | |
| 9909056246 | ∫(1/x)dx | ln|x|+C | 36 | |
| 9909056247 | ∫(e^kx)dx | ekx/k +C | 37 | |
| 9909056248 | ∫sinx dx | -cosx+C | 38 | |
| 9909056249 | ∫cosx dx | sinx+C | 39 | |
| 9909056250 | ∫sec²x dx | tanx+C | 40 | |
| 9909056254 | ∫k dx [k IS A CONSTANT] | kx+C | 41 | |
| 9909056255 | 1st fundamental theorem of calculus | (bounded by a to b) ∫f(x)dx= F(b)-F(a) | 42 | |
| 9909056256 | 2nd fundamental theorem | (bounded by 1 to x) d/dx[∫f(t)dt]= f(x)(x') | 43 | |
| 9909056257 | average value | (1/(b-a))[∫f(x)dx] [BOUNDED BY A TO B] | 44 | |
| 9909056258 | Area between curves | A=∫f(x)-g(x) dx | 45 | |
| 9909056259 | Volume (DISK) | V=π∫f(x)²dx | 46 | |
| 9909056260 | Volume (WASHER) | V=π∫f(x)²-g(x)²dx | 47 | |
| 9909056261 | ∫f(x)dx [BOUNDS ARE SAME] | 0 | 48 | |
| 9909056262 | Displacement of particle | ∫v(t)dt | 49 | |
| 9909056263 | total distance of particle | ∫|v(t)|dt | 50 | |
| 9909056264 | position of particle at specific point | p(x)= initial condition + ∫v(t)dt (bounds are initial condition and p(x)) | 51 | |
| 9909056265 | derivative of exponential growth equation: P(t)=Pe^kt | dP/dt=kP | 52 | |
| 9909056266 | Cross section for volume: square [A=s²] | v=∫[f(x)-g(x)]²dx | 53 | |
| 9909056267 | Cross section for volume: isosceles triangle [A=1/2s²] | v= 1/2∫[f(x)-g(x)]²dx | 54 | |
| 9909056268 | Cross section for volume: equilateral triangle [A=√3/4s²] | v= √3/4∫[f(x)-g(x)]²dx | 55 | |
| 9909056269 | Cross section for volume: semicircle [A=1/2πs²] | v= 1/2π∫[f(x)-g(x)]²dx | 56 | |
| 9909056270 | d/dx(sin⁻¹u) | u'/√(1-u²) | 57 | |
| 9909056272 | d/dx(tan⁻¹u) | u'/(1+u²) | 58 |