Definite integration with unknown function f

Asked Dec 13 '20 at 18:09

Active Dec 13 '20 at 18:09

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I came across this question in a practice test, but I have no idea where to even begin.

If a function $f$ is continuous on $[0, 1]$, show that $$\lim_{n\rightarrow \infty}\int_0^1 \frac{nf(x)}{1+n^2x^2} dx = \frac{\pi}{2}f(0)$$

Any hints would be much appreciated.

asked Dec 13 '20 at 18:09

utkarshk5

2

https://math.stackexchange.com/questions/3899853/if-f-is-continuous-on-0-1-prove-that-lim-n-to-infty-int-01-frac – Evangelopoulos Foivos Dec 13 '20 at 18:13
Thanks! That is the same question. I was unsuccessful in searching it. – utkarshk5 Dec 13 '20 at 18:16
No problem! Hope it helps – Evangelopoulos Foivos Dec 13 '20 at 18:17

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