Question

lim x-> infinite rad(x^2 +5)/x-2
Evaluate the limit

Answer 1

\[\lim_{x \rightarrow \infty}\left(\begin{matrix}\sqrt{x ^{2}+5} \\ x-2\end{matrix}\right)\]

Answer 2

use \frac{\sqrt{x^2+5}}{x-2}

\[\frac{\sqrt{x^2+5}}{x-2}\]

Answer 3

\[\frac{\sqrt{x^2+5}}{x-2}\]
\[=\frac{\sqrt{x^2(1+5/x^2)}}{x(1-2/x)}\]

\[=\frac{x\sqrt{1+5/x^2}}{x(1-2/x)}\]

\[=\frac{\sqrt{1+5/x^2}}{1-2/x}\]

now take limit

Answer 4

How did you get 5/x^2?

Answer 5

oh you factored

Answer 6

yep

Answer 7

Okay! I got it! Thanks :)