I was looking at the definition for a limit when I was wondering what would happen if you changed this(adsbygoogle = window.adsbygoogle || []).push({});

(f(x+h)-f(x))/h

to this

( f(x+h)/f(x) )^(1/h)

with h going to zero in both cases. I did a few calculations with the second limit on my graphing calculator and got this:

function limit

f(x) = x e^(1/x)

f(x) = x^3 e^(3/x)

f(x) = sin(x) e^(1/tax(x))

Does this limit have any kind of importance beyond just being an interesting limit? I was trying to come up with a limit which would measure the ratio a function increases by over a small distance rather than the difference (as for the derivative).

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

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

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

# Question about a limit

**Physics Forums | Science Articles, Homework Help, Discussion**