Everyone "knows" that(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\lim_{x\rightarrow ∞}\frac{2^x}{x^2} = ∞.[/tex]

We "know" this because 2^{x}grows faster than x^{2}. I use quotes because this is just what we're told in basic calculus classes. But what about a theorem for this? I've searched through google, looked through various university homework pages, and in all of them I couldn't find any standardized way to determine if one function grows faster than another; no theorem describing this behavior precisely and why.

Obviously this has been covered somewhere, and I just don't know how to find it. Earlier I was trying to find out information about the series (-1)^{n}, and could find very little until I stumbled upon the phrase "Grandi's series." I'm hoping there is something out there describing this issue as well, so I can get some more precise knowledge. Simply looking at the function on my graphing calculator feels insufficient.

So in summary, I'm hoping someone can direct me to a more rigorous and precise set of definitions regarding limits of f(x)/g(x) with x approaching infinity where the relative growth rates of f(x) and g(x) are important in determining that limit. Specifically, why one type of function grows faster than another, and what the criteria are that determine that.

Any insight into this would be very appreciated!

**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!

# I Lim f(x)/g(x) as x->∞ and relative growth rate of functions

Have something to add?

Draft saved
Draft deleted

Loading...

Similar Threads - >∞ relative growth | Date |
---|---|

I Integration by parts | Dec 12, 2017 |

Deriving functions relating to condition numbers | Mar 23, 2017 |

I Relating integral expressions for Euler's constant | Aug 28, 2016 |

B I need help with a related rates question | Jul 24, 2016 |

B A relation which intercepts with... | May 8, 2016 |

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