Question

Investigate whether the following limits exist and calculate them: \lim _{n \rightarrow \infty} n^{2} 2^{-\sqrt{n}}, \quad \lim _{n \rightarrow \infty} \frac{\ln (n)}{n}, \quad \lim _{n \rightarrow \infty}\left(1+\frac{1}{n}\right)^{\ln (n)} .

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