MHB Limit to Infinity: Is $$\lim_{{x}\to{\infty}} \sqrt{x^2 + 2x + 1} - x = 1?$$

[tmt1]

I have in my notes that $$\lim_{{x}\to{\infty}} \sqrt{x^2 + 2x + 1} - x = 1$$

Is this right? When I calculate it, I get 0, because the square root of infinity is infinity and then I subtract infinity which is 0.

 

[MarkFL]

You can't legitimately subtract infinities...but what you can do is rewrite the radicand as a square...then the desired result is forthcoming. :D