solving the limit of $(e^{2x}+x)^{1/x}$ I tried to solve for the following limit: 
$$\lim_{x\rightarrow \infty} (e^{2x}+x)^{1/x}$$
and I reached to the indeterminate form: 
$${4e^{2x}}\over {4e^{2x}}$$ 
if I plug in, I will get another indeterminate form! 

$x>0\implies e^x>x \implies e^2=(e^{2 x})^{1/x}<(e^{2x}+x)^{1/x}<    (2 e^{2x})^{1/x}    =(e^2) (2^{1/x})$..... And $\lim_{x\to \infty}2^{1/x}=1.$
