For each positive integer define

Prove that the following limit and integral cannot be interchange:

*Proof.* First, we have

On the other hand,

Hence,

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Stumbling Robot

A Fraction of a Dot
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Show that we cannot interchange a limit and integral for *f*_{n}(x) = nxe^{-nx2}

For each positive integer define

Prove that the following limit and integral cannot be interchange:

*Proof.* First, we have

On the other hand,

Hence,