AP Calculus AB Review* Flashcards
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| 13755973600 | Limit Definition of Derivative | limit (as h approaches 0)= F(x+h)-F(x)/h ; means take derivative of f(x) |  | 0 |
| 13755973601 | Alternate Definition of Derivative | limit (as x approaches a number c)= f(x)-f(c)/x-c x≠c ; means take derivative of f(x) and plug in a |  | 1 |
| 13755973602 | limit as x approaches 0: sinx/x | 1 | 2 | |
| 13755973603 | limit as x approaches 0: 1-cosx/x | 0 | 3 | |
| 13755973604 | Continuity Rule | If the limit exists (aka left limit and right limit are equal), and the limit equals the function at that point. | 4 | |
| 13755973605 | Basic Derivative | f(x^n)= nX^(n-1) | 5 | |
| 13755973606 | d/dx(sinx) | cosx | 6 | |
| 13755973607 | d/dx(cosx) | -sinx | 7 | |
| 13755973608 | d/dx(tanx) | sec²x | 8 | |
| 13755973609 | d/dx(cotx) | -csc²x | 9 | |
| 13755973610 | d/dx(secx) | secxtanx | 10 | |
| 13755973611 | d/dx(cscx) | -cscxcotx | 11 | |
| 13755973612 | d/dx(lnu) | u'/u | 12 | |
| 13755973613 | d/dx(e^u) | e^u(u') | 13 | |
| 13755973614 | d/dx(a^u) | a^u(lna)(u') | 14 | |
| 13755973615 | Chain rule of f(x)^n | nf(x)f'(x) | 15 | |
| 13755973616 | Product rule of f(x)g(x) | f'(x)g(x)+g'(x)f(x) OR first(d last)+(last)(d First) | 16 | |
| 13755973617 | Quotient rule of f(x)/g(x) | g(x)f'(x)-f(x)g'(x)/g(x)² OR lo(d hi)-hi(d lo) all divided by (lo)^2 | 17 | |
| 13755973618 | 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 | |
| 13755973619 | Extreme Value Theorem | if f(x) is continuous on [a,b], then f(x) has an absolute max or min on the interval | 19 | |
| 13755973620 | 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 | |
| 13755973621 | 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 | |
| 13755973622 | If f'(x)=0 | there is a max or min on f(x) [number line test] | 22 | |
| 13755973623 | If f'(x)>0 | f(x) is increasing | 23 | |
| 13755973624 | If f'(x)<0 | f(x) is decreasing | 24 | |
| 13755973625 | If f''(x)=0 | f(x) has a point of inflection & f'(x) has a max or min | 25 | |
| 13755973626 | If f''(x)>0 | f(x) is concave up & f'(x) is increasing | 26 | |
| 13755973627 | If f''(x)<0 | f(x) is concave down & f'(x) is decreasing | 27 | |
| 13755973628 | p(t), x(t), s(t) | means position function | 28 | |
| 13755973629 | p'(t) or x'(t) or s'(t) | v(t)= velocity | 29 | |
| 13755973630 | p''(t) or v'(t) | a(t)= acceleration | 30 | |
| 13755973631 | v(t)=0 | p(t) is at rest or changing direction | 31 | |
| 13755973632 | v(t)>0 | p(t) is moving right | 32 | |
| 13755973633 | v(t)<0 | p(t) is moving left | 33 | |
| 13755973634 | a(t)=0 | v(t) not changing | 34 | |
| 13755973635 | a(t)>0 | v(t) increasing | 35 | |
| 13755973636 | a(t)<0 | v(t) decreasing | 36 | |
| 13755973637 | v(t) and a(t) has same signs | speed of particle increasing | 37 | |
| 13755973638 | v(t) and a(t) has different signs | speed of particle decreasing | 38 | |
| 13755973639 | ∫(x^n)dx | x^(n+1)∕(n+1) +C | 39 | |
| 13755973640 | ∫(1/x)dx | ln|x|+C | 40 | |
| 13755973641 | ∫(e^kx)dx | ekx/k +C | 41 | |
| 13755973642 | ∫sinx dx | -cosx+C | 42 | |
| 13755973643 | ∫cosx dx | sinx+C | 43 | |
| 13755973644 | ∫sec²x dx | tanx+C | 44 | |
| 13755973645 | ∫csc²x dx | -cotx+C | 45 | |
| 13755973646 | ∫secxtanx dx | secx+C | 46 | |
| 13755973647 | ∫cscxcotx | -cscx+C | 47 | |
| 13755973648 | ∫k dx [k IS A CONSTANT] | kx+C | 48 | |
| 13755973649 | 1st fundamental theorem of calculus | (bounded by a to b) ∫f(x)dx= F(b)-F(a) | 49 | |
| 13755973650 | 2nd fundamental theorem | (bounded by 1 to x) d/dx[∫f(t)dt]= f(x)(x') | 50 | |
| 13755973651 | average value | (1/(b-a))[∫f(x)dx] [BOUNDED BY A TO B] | 51 | |
| 13755973652 | Area between curves | A=∫f(x)-g(x) dx = integral of top - bottom dx OR integral of right- left dy | 52 | |
| 13755973653 | Volume (DISK, no hole) | V=π∫f(x)²dx | 53 | |
| 13755973654 | Volume (WASHER, hole) | V=π∫f(x)²-g(x)²dx, where f(x)=farther equation from axis rotating & g(x)= closer equation from axis rotating | 54 | |
| 13755973655 | ∫f(x)dx [BOUNDS ARE SAME] | 0 | 55 | |
| 13755973656 | Displacement of particle | ∫v(t)dt | 56 | |
| 13755973657 | total distance of particle | ∫|v(t)|dt | 57 | |
| 13755973658 | position of particle at specific point | p(x)= initial condition + ∫v(t)dt (bounds are initial condition and p(x)) | 58 | |
| 13755973659 | derivative of exponential growth equation: P(t)=Pe^kt | dP/dt=kP | 59 | |
| 13755973660 | Cross section for volume: square [A=s²] | v=∫[f(x)-g(x)]²dx | 60 | |
| 13755973661 | Cross section for volume: isosceles triangle [A=1/2s²] | v= 1/2∫[f(x)-g(x)]²dx | 61 | |
| 13755973662 | Cross section for volume: equilateral triangle [A=√3/4s²] | v= √3/4∫[f(x)-g(x)]²dx | 62 | |
| 13755973663 | Cross section for volume: semicircle [A=1/2πs²] | v= 1/2π∫[f(x)-g(x)]²dx | 63 | |
| 13755973664 | d/dx(sin⁻¹u) | u'/√(1-u²) | 64 | |
| 13755973666 | d/dx(tan⁻¹u) | u'/(1+u²) | 65 | |
| 13755973670 | ∫du/√(a²-u²) | (sin⁻¹u/a)+C | 66 | |
| 13755973671 | ∫du/(a²+u²) | (1/a)(tan⁻¹u/a)+C | 67 |