# Math Help - find the limit

1. ## find the limit

lim ->∞ 1/x+1

x^{1/x} as x approaches infinity? I know that limit of (1+1/x)^{x} = e (as x-> infty), and limit of (1+x)^{1/x} = e (as x-> 0), but this is slightly different.

Any help is appreciated

2. ## Re: find the limit

Originally Posted by LAPOSH42
lim ->∞ 1/x+1

x^{1/x} as x approaches infinity? I know that limit of (1+1/x)^{x} = e (as x-> infty), and limit of (1+x)^{1/x} = e (as x-> 0), but this is slightly different.

Any help is appreciated
Note that $x^{1/x} = e^{\frac{\ln(x)}{x}}$ so I suggest you apply l'Hospital's theorem to $\frac{\ln(x)}{x}$.

3. ## Re: find the limit

Originally Posted by mr fantastic
Note that $x^{1/x} = e^{\frac{\ln(x)}{x}}$ so I suggest you apply l'Hospital's theorem to $\frac{\ln(x)}{x}$.
And also note that due to the continuity of the exponential function, that $\displaystyle \lim_{x \to a}e^{f(x)} = e^{\lim_{x \to a}f(x)}$