I am practicing limits right now. I am getting confused all the time. If I got that limit is equal to infinity then limit does not exist? 
$$\lim\_{x\to\infty}\bigg(\sqrt{4x^2+x}-x\bigg)= ?$$
$$\lim\_{x\to-\infty}\bigg(\sqrt{4x^2+x}-x\bigg)=?$$ 
 I got that limit of both is equal to infinity. I think I have a mistake.
Can you help me with limits