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Math Help - Help me with a limit problem

  1. #1
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    Help me with a limit problem

    Could anyone help me with this problem:

    I have got a wrong result

    But I find that if I divided the fraction's upper part and lower part by -x instead of x at the same time, I can get the correct result which is 1/4.
    But could anyone explain that, why I can't divided the fraction's upper part and lower part by x at the same time?
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  2. #2
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    1) Never wrote "1/0" again. It doesn't mean anything.
    2) Your problem is the sign. When you square under the radical, it is not the same.

    At least two ways to proceed.
    a) Do you know l'Hospital? That will help.
    b) (-x)^2 = x^2. See if you can figure out why changing the sign on the radical, when moving the x^2 inside, is the right thing to do.
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  3. #3
    MHF Contributor Also sprach Zarathustra's Avatar
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    Quote Originally Posted by piscoau View Post
    Could anyone help me with this problem:

    I have got a wrong result

    But I find that if I divided the fraction's upper part and lower part by -x instead of x at the same time, I can get the correct result which is 1/4.
    But could anyone explain that, why I can't divided the fraction's upper part and lower part by x at the same time?
     \lim_{x\to - \infty} \sqrt{4x^2-x}+2x= \lim_{x\to  \infty} \sqrt{4x^2+x}-2x
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