Question: Calculate the following limits. Justify your approach: continuity, L'Hopital's ruel, sequences.

1. \(\operatorname{Lim}_{v \rightarrow 2} \frac{v^{2}+2 v-8}{v^{4}-16}\)
2. \(\lim _{x \rightarrow 0} \frac{\operatorname{Ln}\left(x^{2}\right)}{x}\)
3. \(\lim _{x \rightarrow 0} \frac{x-\sin ^{2} x}{2^{x}-x-1}\)
4. \(\operatorname{Lim}_{x \rightarrow-5^{+}} \frac{|x+5|}{x+5}\)
5. \(\operatorname{Lim}_{x \rightarrow \infty} \frac{\sqrt{x^{2}-x-3}}{3 x+5}\)

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