(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex] \lim_{t \to \infty} \frac {1-\frac{t}{(t-1)}}{1-\sqrt{\frac{t}{(t-1)}}} [/tex]

2. Relevant equations

3. The attempt at a solution

I am pretty sure that everything I did here was legal, I just wanted to check. I got the right answer, so yeah, heres what I did:

[tex] \lim_{t \to \infty} \frac {1-\frac{t}{(t-1)}}{1-\sqrt{\frac{t}{(t-1)}}} [/tex]

derivative turns out to be:

[tex] \lim_{t \to \infty} \frac{\frac{1}{(t-1)^{2}}}{\frac{1}{2}(\frac{1}{(t-1)^{2}})(\frac{t}{t-1})^{-1/2}} [/tex]

and after the obvious term cancels we have:

[tex] \lim_{t \to \infty} \frac {1}{\frac{1}{2} (\frac{t}{t-1})^{-1/2}} [/tex]

and since it is a reciprocal of a reciprocal this is the same thing:

[tex] \lim_{t \to \infty} 2(\frac{t}{t-1})^{1/2} [/tex]

then with the limit applied:

[tex] \lim_{t \to \infty} 2(\frac{t}{t-1})^{1/2} = 2[/tex]

the step with the flipping of the reciprocals is really all I need check, I am fairly certain everything else is good.

thanks!

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# Homework Help: A seemingly tricky limit - L'Hopital

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