Question

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

Answer 1

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...

Answer 2

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 ?

Answer 3

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

Answer 4

that's where it got really messy. i got:



and (if that is even right) i have no idea where to go from there...)