# (Calc 2) 0 and Infinity in limits

rename
valleystudent84's
version from
2016-10-13 16:28

## Section

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

e^∞ = | ∞ |

e^-∞ = | 0 |

(Lim >o+) #/x - = | ∞ |

(Lim >0-) #/x = | -∞ |

Graph of lnx (End Directions) | Left = -∞ _ Right = +∞ |

Graph of e^e (End Directions) | Left = o _ Right = +∞ |

Ln(∞) = | ∞ |

Ln(-∞) = | Undefined |

(Lim >0+) 1/x = | ∞ |

(Lim >0-) 1/x = | -∞ |

o^∞ = | 0 |

0^-∞ = | ∞ |

∞/# = | ∞ |

#/∞ = | 0 |

(L'Hôpital) Bad forms (6) | 0*∞ _ 1^∞ _ ∞^0 _ 0^0 _ ∞ - ∞ _ # (does not apply when yields # other than 0 |

(L'Hôpital) Good Forms (6) | 0/0 _ ∞/∞ = ∞ _ (-∞)-(-∞) = -∞ _ ∞+∞ = ∞ _ 0^∞ = 0 _ o^-∞ = ∞ |

(Lim X >0-) 1/x = 1/-0 = ?? | -∞ |

1/0 ≠ 1/-0 Why? | left is undefined _ Right is APPROACHING 0, not actually 0 value |

When does L'Hôpital's rule NOT apply? | When substitution yields a real # INCLUDING 1 |

## Pages linking here (main versions and versions by same user)

No other pages link to this page. See Linking Quickstart for more info.