Result of the limit: $\lim_{x \to \infty} \sqrt{x + \sin(x)} - \sqrt{x}$? From my calculations, the limit of 
$\lim_{x \to \infty} \sqrt{x + \sin(x)} - \sqrt{x}$
Is undefined due to $sin(x)$ being a periodic function, but someone told me it should be zero. 
I was just wondering if someone could please confirm what the limit of this function is? Thanks
Corey :) 

I think the limit is $0$, since $sin(x)$ is bounded: At best, it is $1$ or $-1$, but if $x \rightarrow \infty$, a bounded number will look like a const; it won't influence the limit, so basically you have $\sqrt{x}- \sqrt{x}= 0$
