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# calc exam 3 review

### exam 3 review

Question | Answer |
---|---|

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 |

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