1. ## Limit

Is that lim┬(x→1)⁡〖((2-√(x+3))/(x-2))^ 〗=-1/4 ?
And what about lim┬(x→∞)⁡〖(√(9x^2+1)/(x+2))^ 〗? I can't do any factorization , please show me some way to solve it. Thank you.

2. ## Re: Limit

Originally Posted by alexander9408
Is that lim┬(x→1)⁡〖((2-√(x+3))/(x-2))^ 〗=-1/4 ?
And what about lim┬(x→∞)⁡〖(√(9x^2+1)/(x+2))^ 〗?
$\lim_{x\to1} \frac{2-\sqrt{x+3}}{x-2} = 0$

$\lim_{x\to \infty} \frac{\sqrt{9x^2+1}}{x+2} = \lim_{x\to \infty} \frac{\sqrt{9+\frac{1}{x^2}}}{1+\frac{2}{x}} = 3$

3. ## Re: Limit

Oh thank you very much, i didn't thought about that way in solving the problems~!