Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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

I tried multiply the conjugate and can't work out. Please advise

share|improve this question

1 Answer 1

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!)

share|improve this answer
    
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
1  
$$\text{- It blows up...}$$ $$\text{- Take cover!}$$ –  Pedro Tamaroff Apr 2 '13 at 4:41
2  
@Peter: $$\huge\text{B}\infty\text{M}$$ –  Brian M. Scott Apr 2 '13 at 4:42

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.