How would one find the limit of the following.
as $x\rightarrow\infty$
$(1+\frac{2}{x})^{3x}$
I did the following
$e^{\ln(1+\frac{2}{x})3x}$
$\frac{\ln(1+\frac{2}{x})}{1/3x}$
Then I did de l'Hôpital's rule.
$\frac{\frac{1}{1+2/x}\frac{-1}{x^2}}{-3/x^2}$
This is the part I having trouble in as when you try simplify the complex fraction dont you have to "flip" it.
I get
$\frac{1}{1+2/x}\frac{-2}{x^2}\frac{x^3}{-3}$
The x^2 cancel out and you are left with.
$\frac{2}{3}\frac{1}{1+2/x}$
The final limit is
$e^{\frac{2}{3}}$