Forum Studenti

In this section one can find exam papers of 2017. Users are strongly advised to post comments, hints, full solutions.

Exam paper #5 added.

Exam paper #6 added.

Attached are some hints and partial solutions (exam paper 2017-1 coincides with exam paper 2018-1 ).

Hello! I believe there's a mistake in the 5th exam paper's solution. Probably I am wrong, but at least I want to understand why.
In the 3rd exercise, part (a), case , there is the inequality for any in a suitable neighborhood of .
I believe this is wrong.
Indeed, considering WLOG neighborhood = , we can swap and .
Therefore we have and , thus it must be an equality.
So there exists a constant such that for any with small enough we have , which is clearly false.

Moreover I believe that, for is not a (WLM).

That's because (just outlining the main points) if were a (WLM), then would be another (WLM) for small enough ( because of the parity of ), but doesn't satisfy (ELE) for any (but it should be easier to prove there is a small enough value of ).