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How do I prove that the following is true:

$$\lim_{n\to\infty}\int_0^{\pi/2} \frac{\cos(nx)}{n^2+x^2}dx=0$$

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Hint: Note that $-1\leq \cos nx\leq 1$ and hence we can get suitable bounds for the integral and now use Squeeze Theorem. Answer should be $0$.

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  • $\begingroup$ Why the downvote? $\endgroup$ – Paramanand Singh May 9 '17 at 3:36

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