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calc exam 3 review

exam 3 review

ratio test L= lim (a(n+1))/n L>1 --DIVERGENT L<1 ABSOLUETLY CONVERGENT L=1 CANT TELL
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
limit comparison test lim an/bn = c and they behave the same in c is positive and finite
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
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.
simpsons rule deltax/n (f(x)+2f()+4f() ect. f(n))
simpsons rule error k=(max)(f^4(x) ----> 120/(x-1)^6 max = 120 k(b-a)^5/180n^4> es
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
parametric equations MEMORIZE THE SHIT OUT OF THESE!!
length of a curve integral of sqrt((dx/dt)^2+(dy/dt)^2)
integral of (sqrt())
p series 1/n^p p>1 converges p<=1 diverges
geometric series a= first number r= change in each number of series a/(1-r)= what it converges to
REMAINDER PART OF INTEGRAL TEST Rn<= integral from n to inf of equation given
Created by: 1241115874