Question: > 
> $\lim\_{x \to \infty} \frac{x}{(R^2+x^2)^{1/2}} $
> 
> 
> 

Attempted applying L'Hopital's Rule to this limit but after two applications I end up up back at the beginning. Am I missing something?

Note: $R$ is a constant here.

Answer: 
Or: first compute
$$
\lim\_{x \to \infty} \frac{x^2}{(R^2+x^2)}
$$
using l'Hopital's rule, then take the square root of your result.
write your Limit as $$\lim\_{x\to \infty}\frac{x}{(x^2)^{1/2}(\frac{R}{x^2}+1)^{1/2}}=\lim\_{x \to \infty}\frac{x}{|x|}\frac{1}{\left(\frac{R}{x^2}+1\right)^{1/2}}$$