lim x/(sqrt(x^2+1000))
x-> + inf
the answer is not as important as its how its actually done. Thanks in advance.
ou can try L'Hopital's but i think it will be a pain here. (we can use L'Hopital's if when we take the limit our function goes to $\displaystyle \frac 00$ or $\displaystyle \frac {\infty}{\infty}$)
instead you should realize that as $\displaystyle x \to \infty$ the + 1000 does not matter. thus
$\displaystyle \lim_{x \to \pm \infty} \frac x{\sqrt{x^2 + 1000}} = \lim_{x \to \pm \infty}\frac x{\sqrt{x^2}} = \lim_{x \to \pm \infty} \frac x{|x|} = \left \{ \begin{array}{lr} 1 & \mbox{ as } x \to \infty \\ -1 & \mbox{ as } x \to - \infty\end{array} \right.$