limit of $\frac{x^{\frac{1}{2}}}{(\frac{1}{2})^x}$ I have to compute the following limit:
$$\lim_{x\to +\infty}\frac{x^{\frac{1}{2}}}{\left(\frac{1}{2}\right)^x},$$
for which we have the indetermination $\frac{+\infty}{0}$.
I know that the final answer is $+\infty$.
However, I am not sure if the way I am solving it is correct
$$\lim_{x\to +\infty}\frac{x^{\frac{1}{2}}}{\left(\frac{1}{2}\right)^x}=\lim_{x\to +\infty} 2^xx^{\frac{1}{2}}=\lim_{x\to +\infty} 2^x . \lim_{x\to +\infty} x^{\frac{1}{2}} = +\infty.+\infty=+\infty,$$
because I know there are some issues when computing $\lim_{x\to \infty} 1^x$, therefore I do not know if doing $\lim_{x\to +\infty}\frac{x^{\frac{1}{2}}}{\left(\frac{1}{2}\right)^x}=\lim_{x\to +\infty} 2^xx^{\frac{1}{2}}$ is correct?
Thank you very much!

$\frac{\infty}{0}$  is not an indeterminate form.
