# Final Exam Review Chp 3

rename
harryprim's
version from
2015-12-10 01:47

## Section 1

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

d/dx cotx | -csc(x)^2 |

d/dx cscx | -cscx cotx |

d/dx secx | secx tanx |

d/dx tanx | sec(x)^2 |

Cos | 1/sec x-value |

Sin | 1/csc y-value |

cot | cos/sin |

tan | sin/cos |

sin(x)^2+cos(x)^2=? | 1 |

when asked to find the points on a curve where the tangent is horizontal.. | set f'=0 |

## Section 2

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

d/dx(arcsinx) or sin^-1 | 1/√(1-x^2) |

d/dx(arccos) or cos^-1 | -1/√(1-x^2) |

d/dx(arctan) or tan^-1 | 1/(1+x^2) |

## Section 3

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

d/dx(lnx) | 1/x |

d/dx (a^x) | a^x ln(a) |

d/dx(loga(x)) | 1/(x•ln(a)) |

A particle speeds up or slows down when | The velocity and acceleration are both >0 or both <0 |

y=loga(x) is equivalent to | b^y=x |

loga(x/y)= | loga(x)-loga(y) |

loga(xy)= | loga(x)+loga(y) |

What is the linear approximation of f (x) at x = a? | f(x) = f(a) + f ′(a)(x − a) |

Given a function y = f (x), the differential dy is defined as | dy=f'(x)dx |

dx and dy represent what? | the small changes in x and the resulting small changes in y |

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