exam 3 review
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| ratio test | L= lim (a(n+1))/n
L>1 --DIVERGENT
L<1 ABSOLUETLY CONVERGENT
L=1 CANT TELL
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| integral test | must have a positive but decreasing function!!!
integral from 1 to inf of f(n) if n=1.. if n=2 then from 2 to inf and so on.
converges IFF the integral converges
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| limit comparison test | lim an/bn = c and they behave the same in c is positive and finite
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| comparison test | find bn that is greater than or equal to the An and if bn converges so does An and if An is divergent then so is bn
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| root test | take equation to the root n and then take them lim of said equation
L<1if the series is absolutely convergent (and hence convergent).
L>1if the series is divergent.
L=1 the series may be divergent, conditionally convergent, or absolutely convergent.
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| simpsons rule | deltax/n (f(x)+2f()+4f() ect. f(n))
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| simpsons rule error | k=(max)(f^4(x) ----> 120/(x-1)^6 max = 120
k(b-a)^5/180n^4> es
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| partial fractions | seperate denominator and set top equal to constant(s) with one power less than that on the denominator
cross mutiply and set equal to original numerator
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| parametric equations | MEMORIZE THE SHIT OUT OF THESE!!
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| length of a curve | integral of sqrt((dx/dt)^2+(dy/dt)^2)
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| integral of (sqrt()) |
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| p series | 1/n^p
p>1 converges
p<=1 diverges
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| geometric series | a= first number
r= change in each number of series
a/(1-r)= what it converges to
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| REMAINDER PART OF INTEGRAL TEST | Rn<= integral from n to inf of equation given
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