# Limit to infinity question

## Homework Statement

lim_x->∞ of [√x + 2|x|] / [1 + x]

## Homework Equations

lim_x->∞ of 1/[x^n] = 0

## The Attempt at a Solution

Hi everyone,

Here's what I've done so far:

I divided top and bottom by the highest power of x, i.e. x.
So:
[x^-1/2 +/- 2] / [1/x + 1]

And taking the limit of x to ∞ of this:
[0 +/- 2] / [0 + 1] = +/- 2

Is this correct?

Thanks for any help.

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gabbagabbahey
Homework Helper
Gold Member
Why is there a $\pm$ in your answer?...Surely you recognize that $x$ is positive as it approaches $+\infty$?

Why is there a $\pm$ in your answer?...Surely you recognize that $x$ is positive as it approaches $+\infty$?
Thanks, I didn't think about that. But is it correct apart from that?

gabbagabbahey
Homework Helper
Gold Member
Yes.