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Math Help - limit of (sqrt(3x+6)-3)/(x-1) | x->1

  1. #1
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    limit of (sqrt(3x+6)-3)/(x-1) | x->1

    Hi guy,

    I would need help with a math problem in which one I must find the limit value of (sqrt(3x+6)-3)/(x-1) when x->1 wich is 0/0

    Basically, what we have to do is find a way to remove that (x-1) under the division. The best I have done is (sqrt(3) * sqrt(x+2) - 3) / (x-1)

    After that, I'm blocked
    Thank you for your help
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  2. #2
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    Quote Originally Posted by py592 View Post
    Hi guy,

    I would need help with a math problem in which one I must find the limit value of (sqrt(3x+6)-3)/(x-1) when x->1 wich is 0/0

    Basically, what we have to do is find a way to remove that (x-1) under the division. The best I have done is (sqrt(3) * sqrt(x+2) - 3) / (x-1)

    After that, I'm blocked
    Thank you for your help
    \lim_{x\to1} \frac{\sqrt{3x+6} - 3}{x-1} \cdot \frac{\sqrt{3x+6}+3}{\sqrt{3x+6}+3}

    \lim_{x\to1} \frac{3x+6 - 9}{(x-1)\sqrt{3x+6}+3}

    \lim_{x\to1} \frac{3(x-1)}{(x-1)\sqrt{3x+6}+3}

    \lim_{x\to1} \frac{3}{\sqrt{3x+6}+3} = \frac{1}{2}
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  3. #3
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    Oh ! Thank you. I totally forgot that trick
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  4. #4
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    Another approach.

    Divide the numerator and denominator by |x|.
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