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?
If the limit is infinite, then the limit does not exist.
Yes, that would work. Or
$\displaystyle \lim_{x\to\infty}\frac x{\sqrt{x^2-2x}}$
$\displaystyle =\lim_{x\to\infty}\frac x{\sqrt{x^2\left(1-2/x\right)}}$
$\displaystyle =\lim_{x\to\infty}\frac x{x\sqrt{1-2/x}}$
$\displaystyle =\lim_{x\to\infty}\frac 1{\sqrt{1-2/x}}$
$\displaystyle =\frac 1{\sqrt{1-0}} = 1$