How can I solve these two limits :

1. lim when n approches 1 of n[a^1/n -1]

2. lim when x approches 0 of (e^ax - e^bx) / x

Hi Yannick,

I think in the first problem you want the limit as n approaches infinity. In both cases the way to find these limits is to use l'Hospital's Rule. For the first example write n[a^1/n -1] as [a^1/n -1]/[1/n]. I wouls then make the change of variables, x = 1/n to get

Now apply l'Hospital's Rule by differentiating both the numerator and denominator to get

Cheers
Harley