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Math Help - Limit

  1. #1
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    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.
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  2. #2
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    Re: Limit

    Quote Originally Posted by alexander9408 View Post
    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
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  3. #3
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    Re: Limit

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