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The task is to find
$$
L=\lim _{n \rightarrow \infty} n^{2}-\frac{n}{\sin \left(\frac{1}{n}\right)}
$$
For sufficiently large $n$ we have $\sin \left(\frac{1}{n}\right) \approx \frac{1}{n}$ so that
$$
L \approx n^{2}-\frac{n}{\frac{1}{n}}=n^{2}-n^{2}=0
$$
so the limit $L$ is zero. Am I correct?

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