- #1
JoAuSc
- 198
- 1
I was looking at the definition for a limit when I was wondering what would happen if you changed this
(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).
(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).