# Limit of y=((x-1)/x)^x as x approaches inf

1. Aug 24, 2009

### Chris101

I reasoned that (x-1)/x is always less than 1 for positive x. Therefore it will tend to zero as the exponent tends to infinity. But what is confusing is that when working it out for 1 to 100, the value increases.

Is the the limit 0?, and when does the limit "turn".

Last edited: Aug 24, 2009
2. Aug 24, 2009

### Cyosis

The limit is not 0. Use $\lim_{x \to 0} (1+x)^{\frac{1}{x}}=e$.

3. Aug 25, 2009

### n1person

alternatively you can take the natural log of both sides,

ln y = x ln ((x-1)/x) = ln((x-1)/x)/(1/x)

then apply l'hopital's rule to get a nice simple solution, don't forget to then exponent it to solve for y! :)