# another proof of Bernoulli’s inequality

For fixed $x>0,x\ne 1$ the function

$${w}_{x}(r)={\int}_{1}^{x}{t}^{r-1}\mathit{d}t=\{\begin{array}{cc}\frac{{x}^{r}-1}{r}\hfill & r\ne 0\hfill \\ \mathrm{log}x\hfill & r=0\hfill \end{array}$$ |

is strictly increasing.

Bernoulli inequality^{} is equivalent^{} to

$$ |

Title | another proof of Bernoulli’s inequality^{} |
---|---|

Canonical name | AnotherProofOfBernoullisInequality |

Date of creation | 2013-03-22 15:45:43 |

Last modified on | 2013-03-22 15:45:43 |

Owner | a4karo (12322) |

Last modified by | a4karo (12322) |

Numerical id | 7 |

Author | a4karo (12322) |

Entry type | Proof |

Classification | msc 26D99 |