lim as x-0+ of (1+2/x)^x

Question

lim as x->0+ of (1+2/x)^x

anonymous · Answer

i took the natural log on both sides and then rewrote to get infinity/infinity and then used L'Hopital's Rule, but I am having issues simplifying...

hartnn · Answer

so you got till here ?
$\large \ln L = \lim \limits_{x\to0^+ } x \ln (1+2/x)$
right??

then i guess you wrote that as  
$\large \ln L = \lim \limits_{x\to0^+ } \dfrac{\ln (1+2/x)}{\dfrac{1}{x}}$
and applied LH rule ?
what did you get after derivating the numerator and denominator ?

hartnn · Answer

for the derivative of numerator, you'll need CHAIN rule!

anonymous · Answer

that's where it got really messy. i got: 

|dw:1385321006193:dw| 

and (if that is even right) i have no idea where to go from there...)