What is the Limit to Infinity of a Rational Function?

[Pyroadept]

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.

 

[gabbagabbahey]

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

 

[Pyroadept]

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]

Yes.