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35 Cards in this Set
- Front
- Back
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Trapazoid Rule
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ch.x [f(x0)+2f(x1)....+2f(xn-1)+f(xn)]
--- 2 |
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Midpoint Rule
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ch.x [f(x1)+f(x2)...+f(xn)]
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Simpsons Rule
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ch.x [f(x0)+4f(x)+2f(x)..+2f(x)+4f(x)+f(x]
--- 3 |
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Improper integral equation 1
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lim S(1-t) f(x) dx
(t>inf) |
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Improper integral equation 2
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lim S(0-a) f(x) dx
(t>a) |
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Arc length
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L = S [1+(f'(x))^2)]^{1/2)
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Region Bounded by two curves
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S(intersections) f(x) - g(x) dx
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Area of a solid: Washers
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S(range) A2 - A1
S(range) (pi)R^2 - (pi)r^2 dx |
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Area of solid:Disks
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S(range) A(x) dx
S(range) (pi)r^2 dx |
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Volumes by cylindrical Shells
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S(range) (circum)(height)(width)
S(range) 2(pi)rf(x) dx |
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Average Value
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1 S(a-b) f(x) dx
---- b-a |
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Integration by Parts
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Liate
:S:udv = uv - :S:vdu |
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Trig Sub
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S(a2 - x2)^.5
x = asin(~) |
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(sinx)'
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cosx
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(cosx)'
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-sinx
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Area of a function
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A=lim(n>inf) [f(x1)`x+f(x2)`x..+f(xn)`x]
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change in x
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(b-a)
---- n |
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Fundmental theorem
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if F(x) is f'(x) then all f'(x) are F(x) + c
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(tanx)'
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sec^2(x)
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(cotx)'
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-csc^2(x)
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(secx)'
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tanxsecx
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(cscx)'
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-cscxcotx
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(arcsinx)'
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1
---- (1-x^2)(^.5) |
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(arccosx)'
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-1
---- (1-x2)(^.5) |
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(arctanx)'
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1
---- 1+x(^2) |
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(lnx)
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1
--- x |
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(log(a)x)'
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1 1
-- -- lna x |
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1
S------- = x(^2) + a(^2) |
.1
- arctan(x/a) +c a |
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Ratio test
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IF lim |a(n+1)| =L
(n>inf) | a(n) | [L<1] converge [L>1] diverge |
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Power Series
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Sum(n to inf) Cn(x-a)^n
centred at a |
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Geometric Series
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Sum(0 to inf) x(^n) = 1/(1-x)
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Radius of conv. diverg.
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If in R then series converges
If out of R then series diverges |
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Finding Radius of Convergence
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F = lim(n>inf) |C(n)/C(n+1)|
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Macluarin Series
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f(x) = sum(0 to inf) f(^n)(0) x(^n)
--------- n! |
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Taylor Series
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f(x) = sum(0 to inf) f(^n)(0) (x-a)(^n)
--------- n! |
