Question

lim x->oo [ sqrt ( x + 1) - sqrt x] , whats the trick here , i get indeterminate

Answer 1

infinity - infinity

Answer 2

faster

Answer 3

\[\sqrt{x+1}-\sqrt{x}=(\sqrt{x+1}-\sqrt{x})(\sqrt{x+1}+\sqrt{x})/(\sqrt{x+1}+\sqrt{x})\]
\[\sqrt{x+1}-\sqrt{x}=((\sqrt{x+1})^2-(\sqrt{x})^2)/(\sqrt{x+1}+\sqrt{x})\]
\[\sqrt{x+1}-\sqrt{x}=((x+1)-(x))/(\sqrt{x+1}+\sqrt{x})\]
\[\sqrt{x+1}-\sqrt{x}=1/(\sqrt{x+1}+\sqrt{x})\]
\[\lim_{x \rightarrow \infty} \sqrt{x+1}-\sqrt{x}=\lim_{x \rightarrow \infty}1/(\sqrt{x+1}+\sqrt{x})\]
\[\lim_{x \rightarrow \infty}\sqrt{x+1}-\sqrt{x}="1/\infty"\]
So, \[\lim_{x \rightarrow \infty}\sqrt{x+1}-\sqrt{x}=0\]

Answer 4

thankyou. you didnt have to do all this. you could have just said, multiply top and bottom by sqrt (x +1) + sqrt x
thankyou my son. may satan be kind to you

Answer 5

never mind...

Answer 6

hey thanks