Limits: Rational Square Root Function

PROBLEM:

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

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?

Re: Limits: Rational Square Root Function

Hello, Lambin!

Is there a typo?

Quote:

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

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

Perhaps you mean: .$\displaystyle \lim_{t\to0}\frac{\sqrt{1+t} - \sqrt{1-t}}{t}$

Re: Limits: Rational Square Root Function

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