# Limit tends to infinity

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

-

It blows up: the first term is larger than $x$, and the second is larger than $2x$, so the whole thing is larger than $3x-x=2x$. (The lesson here is not to get so bound up in technique that you forget to think about what’s actually going on!)

-
Yeah, thanks. I guess the either the textbook is wrong or my memory failed. I wonder if this exists at first, but I remembered the answer was -3/2, so. –  Paul Smith Apr 2 '13 at 4:38
@Paul: You’re welcome. My guess is that either there was a typo in the problem, or you misremembered it. –  Brian M. Scott Apr 2 '13 at 4:41
$$\text{- It blows up...}$$ $$\text{- Take cover!}$$ –  Pedro Tamaroff Apr 2 '13 at 4:41
@Peter: $$\huge\text{B}\infty\text{M}$$ –  Brian M. Scott Apr 2 '13 at 4:42