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Math Help - Limits

  1. #1
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    Limits



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    Quote Originally Posted by alexandriaruth View Post


    Hint: for each problem, multiply by the conjugate over itself, for instance, for the first you would multiply by \frac {\sqrt{x^2 + 14x - 5} + x}{\sqrt{x^2 + 14x - 5} + x}. see if you can take it from there
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  3. #3
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    i have tried that but i keep just rearranging the function and i never get an answer
    14x-5/{(sqrt(x^2)+14x-5)+x}
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by alexandriaruth View Post
    i have tried that but i keep just rearranging the function and i never get an answer
    14x-5/{(sqrt(x^2)+14x-5)+x}
    factor x^2 out of the square root. you get

    \frac {14x - 5}{\sqrt{x^2} \sqrt{1 + \frac {14}x - \frac 5{x^2}} + x} = \frac {14x - 5}{|x| \sqrt{1 + \frac {14}x - \frac 5{x^2}} + x}

    now in this case, since x \to \infty, we have x is positive, and hence, |x| = x, so we get

    \frac {14x - 5}{x \sqrt{1 + \frac {14}x - \frac 5{x^2}} + x}

    now divide the top and bottom by x and take the limit
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