Question: Determine whether the limit exists, and where possible, evaluate it. Use de l'Hôpital's rule if it can be applied. Show your work.

1. \(\lim _{x \rightarrow 0}\left(\frac{2}{x}-\frac{4}{\sin x}\right)\)
2. \(\lim _{x \rightarrow \frac{\pi}{2}} \frac{2 \cos (x)}{x-\frac{\pi}{2}}\)
3. \(\lim _{t \rightarrow \infty} \frac{3^{t}}{t^{3}}\)

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