Finding the limit of a function with e and ln

1. Feb 22, 2005

trap

lim as x->infinity [e^x + x] ^(1/x)

Can anyone help me on this please, thanks.

2. Feb 22, 2005

dextercioby

The limit is "e"...To convince yourself,use the fact that the limit & the natural logarithm commute.

Daniel.

3. Feb 22, 2005

trap

can you take me one step further than that, to get the answer e?

4. Feb 22, 2005

trap

i got it now, thanks for the help

5. Feb 22, 2005

dextercioby

There would be another way to do it,directly,without use of $ln$.Just factor e^{x} and then use the definition of "e":
$$\lim_{u\rightarrow +\infty}(1+\frac{1}{u})^{u}=e$$

Daniel.