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).

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# Question about a limit

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