Question

How do you find the limit of this problem?

lim (sqrt(x^2 + ax) - sqrt(x^2 +bx)
x-->infinity

Answer 1

\[\lim_{x \rightarrow \infty}(\sqrt{x^{2}+ax}-\sqrt{x^2+bx})\]?

Answer 2

yes

Answer 3

I believe it would be Infinity if a>b and -Infinity if a<b

Answer 4

can you please explain how you got to that answer?

Answer 5

Ahh, I was wrong. Ignore my first answer.

\[\lim_{x \rightarrow \infty}\sqrt{x}(\sqrt{x+a}-\sqrt{x+b})\]\[\lim_{x \rightarrow \infty}\sqrt{x} \times \frac{ (\sqrt{x+a}-\sqrt{x+b}) \times (\sqrt{x+a}+\sqrt{x+b}) }{ \sqrt{x+a}+\sqrt{x+b} }\]\[(a-b) \times \lim_{x \rightarrow \infty}\frac{ \sqrt{x} }{ \sqrt{x+a}+\sqrt{x+b} }\]\[\frac{ a-b }{ 2 }\]