Finding the limit of a function with e and ln

[trap]

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

Can anyone help me on this please, thanks.

 

[dextercioby]

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

Daniel.

 

[trap]

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

 

[trap]

i got it now, thanks for the help

 

[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.