Reading Cauchy's lecture on the derivative, I see he goes from this limit(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\large \lim _{h \rightarrow 0} \frac{1}{ \log_A((A^h)^{\frac{1}{A^h-1}})}[/tex]

To this one [itex]A^h= 1+\beta[/itex]

[tex]\large \lim _{\beta \rightarrow 0} \frac{1}{ \log_A((1+ \beta)^{\frac{1}{\beta}})}=\frac{1}{\log_A(e)}[/tex]

I understand the intuition behind the technique, and the result. However, is this variable-change rigorous? How can we be sure that [itex] \beta =A^h-1 [/itex] tends to 0 in the same way as [itex] h[/itex] does, or do we just need to know that when [itex] h=0 \Rightarrow \beta=0[/itex], so the limit will be the same?

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Reading Cauchy's lecture on the derivative

Loading...

Similar Threads - Reading Cauchy's lecture | Date |
---|---|

I Cauchy Principal Value | Mar 23, 2017 |

Please help me in reading a mathematical handwriting | Jan 7, 2016 |

Reel Fill Calculation - Calculating line counter reading | Apr 18, 2014 |

Motion Graph and how it acts. Please read. | May 17, 2013 |

Related Rates problems. Please Read. | May 16, 2013 |

**Physics Forums - The Fusion of Science and Community**