Limit

**alexander9408** · January 6th 2013, 04:23 AM

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.

**skeeter** · January 6th 2013, 05:27 AM

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))^ 〗?

$\lim_{x\to1} \frac{2-\sqrt{x+3}}{x-2} = 0$

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

**alexander9408** · January 6th 2013, 06:03 AM

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

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