Having trouble on these two questions. I have no idea and help would be much appreciated. Thanks.

Find

$\displaystyle \lim_{t \to 3} \frac{t^2 - 2t - 3}{t^2 + 4t - 21} $

Find

$\displaystyle \lim_{t \to \infty} \sqrt{t^2 + t} - t $

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- Oct 15th 2008, 01:37 PMWWTL@WHLLimits
Having trouble on these two questions. I have no idea and help would be much appreciated. Thanks.

Find

$\displaystyle \lim_{t \to 3} \frac{t^2 - 2t - 3}{t^2 + 4t - 21} $

Find

$\displaystyle \lim_{t \to \infty} \sqrt{t^2 + t} - t $ - Oct 15th 2008, 01:44 PMMoo
Hello,

Factorise !

$\displaystyle t^2-2t-3=(t-3)(t+1)$

and $\displaystyle t^2+4t-21=(t-7)(t+3)$

Quote:

Find

$\displaystyle \lim_{t \to \infty} \sqrt{t^2 + t} - t $

- Oct 15th 2008, 01:57 PMWWTL@WHL
Thanks for the quick reply, Moo. :)

Sorry, I'm still have trouble with this. So substituting 3 in for t, and you have 0 on the numerator, and -3 on the denominator, which suggests it'll tend to 0, as t approaches 3?

But $\displaystyle t^2+4t-21 = 0 $ when t=3 as well. So then you'd have 0/0 which is undefined?

Quote:

Multiply and divide by its conjugate, that is $\displaystyle \frac{\sqrt{t^2+t}{\color{red}+}t}{\sqrt{t^2+t}+t}$

- Oct 15th 2008, 02:03 PMMoo
- Oct 15th 2008, 02:09 PMWWTL@WHL
Thanks. :)

$\displaystyle

\lim_{t \to 3} \frac{t^2 - 2t - 3}{t^2 + 4t - 21}

$ = $\displaystyle \lim_{t \to 3} \frac{t+1}{t+7} = \frac{2}{5} $

Does that seem ok? - Oct 15th 2008, 02:19 PMMoo