lim x/(sqrt(x^2+1000))

x-> + inf

the answer is not as important as its how its actually done. Thanks in advance.

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- Nov 11th 2007, 04:31 PMsimsima_1Evaluating a limit to infinity
lim x/(sqrt(x^2+1000))

x-> + inf

the answer is not as important as its how its actually done. Thanks in advance. - Nov 11th 2007, 04:42 PMJhevon
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

$\displaystyle \lim_{x \to \pm \infty} \frac x{\sqrt{x^2 + 1000}} = \lim_{x \to \pm \infty}\frac x{\sqrt{x^2}} = \lim_{x \to \pm \infty} \frac x{|x|} = \left \{ \begin{array}{lr} 1 & \mbox{ as } x \to \infty \\ -1 & \mbox{ as } x \to - \infty\end{array} \right.$ - Nov 11th 2007, 11:15 PMCaptainBlack