[imath]

\lim _{x->+\infty} \frac{(x-\sqrt{x^2-1})^n+(x+\sqrt{x^2-1})^n}{x^n}=\lim _{x->+\infty} \frac{(1-\sqrt{x-\frac{1}{x}})^n+(1+\sqrt{x-\frac{1}{x}})^n}{1}=\infty-\infty

[/imath]

this is as far as i can go

i got undefined form

??

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- Feb 28th 2009, 04:21 AMtransgalacticroot limit question..
[imath]

\lim _{x->+\infty} \frac{(x-\sqrt{x^2-1})^n+(x+\sqrt{x^2-1})^n}{x^n}=\lim _{x->+\infty} \frac{(1-\sqrt{x-\frac{1}{x}})^n+(1+\sqrt{x-\frac{1}{x}})^n}{1}=\infty-\infty

[/imath]

this is as far as i can go

i got undefined form

?? - Feb 28th 2009, 04:34 AMarpitagarwal82
There is an error.

when x goes inside square root, it becomes x^2.

So correct is

Now proceed.