# Shared Flashcard Set

## Details

series angle/2, and solids
series and half angle
16
Mathematics
12/14/2008

Term
 cos^2(theta)
Definition
 (1+cos(2*0))/2
Term
 sin^2(theta)
Definition
 (1-cos(2*0))/2
Term
 Area in polar
Definition
 int(1/2*r^2d0)
Term
 arc length in polar
Definition
 int(sqroot(r^2+(dr/d0)^2))d0
Term
 geometric series
Definition
 sum:ar^(n-1)=a/(1-r)
Term
 Harmonic Series
Definition
 sum:1/n diverges
Term
 divergence test
Definition
 if lim:n to inf of an doesn't = 0 diverges.
Term
 Alternating Series
Definition
 if series alternates, bn+1 less than bn for all n, and passes divergence test, series converges, conditionally...
Term
 Integral Test
Definition
 if int(1 to inf of f(x)dx) then sum an converges if f(n)=an.
Term
 limit comparison test
Definition
 lim as n to inf of an/bn=c and c greater than 0 then an and bn both diverge or both converge.
Term
 washer method v=
Definition
 int(pi(rout)^2-pi(rin)^2)
Term
 shells method v=
Definition
 int(2*pi*x*f(x)dx)
Term
 by parts integration
Definition
 int(udv)=uv-int(vdu)
Term
 int(tan(x)dx)
Definition
 ln|secx| +C
Term
 int(secxdx)
Definition
 ln|secx+tanx|+C
Term
 midpoint rule
Definition
 intF(x)dx~sum:f(x(bar)i)dx where dx=(b-a)/n and x(bar)i=(x(i-1)+xi)/2
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