If $f_n(x)=nxe^{-nx^2}~\forall~n=1,2,\cdots$ and $x$ real, show that $$\lim_{n \rightarrow \infty} \int_0^1 f_n(x)dx \ne \int_0^1\lim_{n \rightarrow \infty}f_n(x) dx$$ Attempt: By the $Mn$ Test, it comes out that $f_n$ is not uniformly convergent. We also know that if $\{f_n\}$ is a uniformly...

While there could be some meaningful distinction (in theory) this does not seem to work well in practice. I checked a bit manually, and also observed that 150 questions (this are almost 20 percent) of the questions tagged solution-verfication contain the word "prove" (and rather not in the way "I...

I asked a question, and several people stated that it is not clear enough. So I fixed all what they been asking me to, but I did not got a feedback if my fix is satisfiable. Please tell me if the question is clear enough or should I add additional modifications? My goal is to find solution for:...

I am unsure on how to improve a question that was put on hold. Specifically, this question. The people that voted to close said that it is off-topic, and "not about mathematics", but I don't see how they could think that. The question is about understanding mathematical concepts and theorems, the...