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Math Help - limits

  1. #1
    Faz
    Faz is offline
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    limits

    find the following limits


    lim ->infinite ((x^2/x+5)-x)
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  2. #2
    Senior Member
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    Hi Faz

    Quote Originally Posted by Faz View Post
    find the following limits


    lim ->infinite ((x^2/x+5)-x)
    Do you mean  lim_{x \to \infty } \frac{x^2}{x+5}-x?

    Then

     lim_{x \to \infty } \frac{x^2}{x+5}-\frac{x(x+5)}{x+5}

     = lim_{x \to \infty } \frac{x^2- x(x+5)}{x+5}

     = lim_{x \to \infty } \frac{x^2- x^2 - 5x)}{x+5}


     = lim_{x \to \infty }  \frac{-5x}{x+5} = lim_{x \to \infty }  \frac{-5}{1+\frac{5}{x}} = - 5
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