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Math Help - Limits: Rational Square Root Function

  1. #1
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    Limits: Rational Square Root Function

    PROBLEM:

    \lim_{t\to\0}{\frac{\sqrt{t+1}-\sqrt{t-1}}{t}}

    ATTEMPT:

    I tried transforming the expression by the conjugate to remove the square root expression in hopes of vanishing the t in the denominator, but it appears to result in an indeterminate form. Assuming that a limit exists, what is an appropriate transformation for this function?
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  2. #2
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    Re: Limits: Rational Square Root Function

    Hello, Lambin!

    Is there a typo?


    \lim_{t\to 0}{\frac{\sqrt{t+1}-\sqrt{t-1}}{t}}

    If t = 0, the numerator becomes a complex number, 1 - i.


    Perhaps you mean: . \lim_{t\to0}\frac{\sqrt{1+t} - \sqrt{1-t}}{t}
    Thanks from Lambin
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  3. #3
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    Re: Limits: Rational Square Root Function

    Oh, you are right. I got it now, thanks!
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