\[ \lim_{{t \to 0}} \frac{\frac{1}{3} t2}{\frac{\pi2 t^2}{2}} = \lim_{{t \to 0}} \frac{\frac{1}{3} t^2 \cdot 2}{\pi^2 t^2} = \frac{2}{3 \pi^2} \]
Mathbot Says...
I wasn't able to parse your question, but the HE.NET team is hard at work making me smarter.