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## Main Question or Discussion Point

Hi,

I'm having trouble determining this limit:

It's a 0/0 type of expression, so it seems like L'Hopital's rule should be applicable, but no matter how many times I differentiate I keep getting 0/0-expressions. Any hints?

Also, the next question is to solve this integral:

I haven't tried solving it, but since I haven't yet been able to answer any question in this whole damn exercise, I think it's a safe bet that I can't do this either. Any hints here?

I'm having trouble determining this limit:

[tex]\lim_{x\rightarrow0^+}\frac{\sqrt{x}\sin\sqrt{x}}{1-e^{-x}}[/tex]

It's a 0/0 type of expression, so it seems like L'Hopital's rule should be applicable, but no matter how many times I differentiate I keep getting 0/0-expressions. Any hints?

Also, the next question is to solve this integral:

[tex]\int_0^{\pi^2}\sqrt{x}\sin\sqrt{x}dx[/tex]

I haven't tried solving it, but since I haven't yet been able to answer any question in this whole damn exercise, I think it's a safe bet that I can't do this either. Any hints here?