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79 Cards in this Set
- Front
- Back
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sin^2(x) + cos^2(x) =
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1
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sec^2(x) =
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1 + tan^2(x)
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csc^2(x) =
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1 + cot^2(x)
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sin(-x) =
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-sin(x)
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cos(-x) =
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cos(x)
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tan(-x) =
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-tan(x)
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sin(A+B) =
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sinAcosB+sinBcosA
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sin(A-B) =
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sinAcosB-sinBcosA
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cos(A+B) =
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cosAcosB-sinAsinB
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cos(A-B) =
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cosAcosB+sinAsinB
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sin(2x) =
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2sinxcosx
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cos(2x) =
(3 answers) |
cos^2(x)-sin^2(x) 1-2sin^2(x) 2cos^2(x)-1 |
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tanx =
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sinx / cosx
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cotx =
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cosx / sinx
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secx =
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1/cosx
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scsx =
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1/sinx
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cos(pi/2 - x) =
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sinx
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sin(pi/2 - x) =
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cosx
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d/dx x^n =
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nx^(n-1)
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d/dx (fg) =
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f'g + g'f
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d/dx (f/g) =
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(f'g-g'f)/g^2
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∫x^n dx =
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(1/n+1)x^(n+1)+C
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∫1/x dx =
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ln(x)+C
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∫e^x dx =
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e^x +C
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∫a^x dx =
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(1/ln(a))a^x +C
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∫lnx dx =
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xln(x)-x+C
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∫sinx dx =
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-cosx+C
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∫cosx dx =
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sinx+C
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∫tanx dx =
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ln(secx) + C or -ln(secx) + C
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∫ cotx dx = |
ln(sinx)+C |
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∫secx dx = |
ln(secx + tanx) +C |
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∫cscx dx = |
-ln(cscx + cotx) + C or ln(cscx - ctx) + C |
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∫sec^2(x) dx = |
tanx + C |
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∫secx tanx dx = |
-cotx + C |
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∫csc^2(x) dx = |
-cotx + C |
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∫cscx cotx dx = |
-cscx + C |
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∫tan^2(x) dx |
tanx-x+C |
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∫dx/(a^2 + x^2) = |
(1/a)tan^-1(x/a) + C |
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∫dx/sqrt(a^2-x^2) = |
sin^-1(x/a)+C |
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f(x) is continuous at x=a if: |
1. f(a) exists 2. lim x->a f(x) exists 3. lim x->a f(x) = f(a) |
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d/dx (f(g(x))) = |
f'(g(x))*g'(x)*x' |
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d/dx sinx = |
cosx*x' |
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d/dx cosx = |
-sinx*x' |
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d/dx tanx = |
sec^2(x)*x' |
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d/dx cotx = |
-csc^2(x)*x' |
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d/dx secx = |
secxtanx*x' |
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d/dx cscx = |
-cscxcotx*x' |
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d/dx e^x = |
e^x*x' |
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d/dx a^x = |
ln(a)*a^x*x' |
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d/dx ln(x) = |
x'/x |
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d/dx sin^-1(x) = |
x'/sqrt(1-x^2) |
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d/dx tan^-1(x) = |
x'/(1+x^2) |
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∫a dx = |
ax + C |
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Intermediate Value Theorem (3 things) |
1. If y = f(x) is continuous on [a, b] 2. a < c < b; f(a) and f(b) differ in signs 3. Then f(c) = 0 |
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Rolle's Theorem: (2 things) |
1. If y=f(x) is continuous and differentiable on [a,b]; a<c<b 2. f(a) = f(b) then then f'(c)=0 |
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A function is even if: (2 things) |
1. f(-x)=f(x) 2. Reflects around y axis |
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A function is odd if: (2 things) |
f(-x)=-f(x) Reflects around origin |
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L'Hopital's Rule: (2 things) |
1. If lim x->a f(x)/g(x) = 0/0 or infinity/infinity 2. Then lim x->a f(x)/g(x) = lim x->a f'(x)/g'(x) |
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Trapezoid Rule (equal subdivisions): |
b (b-a)/n∫ f(x) ~ (b-a)/2n[f(a) +2f(x) +2f(x) + f(b)] a |
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f and g are inverses if: |
f(g(x)) = g(f(x)) = x |
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f has an inverse if: (2 things) |
1. Monotonic (always increasing or decreasing) 2. Horizontal line test |
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Mean Value Theorem: (2 things) |
1. f is continuous and differentiable on [a,b] and a<c<b then 2. f'(c)= [f(b)-f(a)]/(b-a) |
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Extreme Value Theorem: (2 things) |
1. If f is continuous on [a,b] 2. Then f has maximum and minimum on [a,b] |
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To find critical points for y=f(x) (3 things) |
1. y'=0 solve for x 2. y' is undefined 3. Endpoints on interval |
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To find max or min value on y=f(x): (2 things) |
1. Check increasing/decreasing with f' chart 2. Use CP in f'' and f''<0 max f''> 0 min |
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f is increasing on [a,b] if: |
f'>0 |
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f is increasing on [a,b] if: |
f'<0 |
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f is concave up if: |
f''>0 |
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f is concave down if: |
f''<0 |
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To locate points of inflection of f(x): (2 things) |
1. f''=0 2. f'' is undefined |
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Distance between two points: |
sqrt[(x2-x1)^2+(y2-y1)^2] |
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d/dx sec^-1 x = |
x'/[abs(x)*sqrt(x^2-1)] |
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Average value of f(x) on [a,b] |
1/(b-a)∫f(x) dx |
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Washers (around x and y axis): |
b around x axis: V= pi∫ R^2-r^2 dx a
b around y axis: V= pi∫ R^2-r^2dy a |
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Discs (around x and y axis): |
b V=pi∫R^2 dx a b V=pi∫R^2 dy a |
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sin^2(x) = |
.5 - .5cos(2x) |
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cos^2(x) = |
.5 + .5 cos(2x) |
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Find absolute max/min points on [a,b] for y = f(x) (3 things) |
1. Find critical points for y = f(x) 2. Plug x = critical points, a,b into f(x) 3. Biggest answer = max; Smallest answer = min |
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nth term test |
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