1. ## limits help

I am trying to solve these limits, but have some questions:

1) lim x -> -infinity (3x / (1 + (2/x)) = -infinity. then it says DNE. why?

2) limit x -> -infinity [x/(sqrt(x^2 -2x))] = ? would I divide by x on the top and bottom here?

2. ## Re: limits help

Originally Posted by droidus
1) lim x -> -infinity (3x / (1 + (2/x)) = -infinity. then it says DNE. why?
If the limit is infinite, then the limit does not exist.

Originally Posted by droidus
2) limit x -> -infinity [x/(sqrt(x^2 -2x))] = ? would I divide by x on the top and bottom here?
Yes, that would work. Or

$\displaystyle \lim_{x\to\infty}\frac x{\sqrt{x^2-2x}}$

$\displaystyle =\lim_{x\to\infty}\frac x{\sqrt{x^2\left(1-2/x\right)}}$

$\displaystyle =\lim_{x\to\infty}\frac x{x\sqrt{1-2/x}}$

$\displaystyle =\lim_{x\to\infty}\frac 1{\sqrt{1-2/x}}$

$\displaystyle =\frac 1{\sqrt{1-0}} = 1$