A11. Let
and be a sequence of real
numbers such that for every
Prove that
A10. For
every real number define by the relation
Prove that is a well defined
integrable function, then compute
A9. Let
there be given and the inequality
Prove that:
(i) If holds whenever then
(ii) If holds whenever then
A8. Find
with the intermediate
value property such that
A7. Solve
in real numbers:
A6. Find
all derivable functions such that
A5. Let
be linear on each
interval such that for every integer with Prove that is antiderivable.
A4. Let
be matrices with real
entries such that Prove that
A3. Let
be matrices with complex
entries such that Prove that or
A2. Let
be elements of a ring
, inversable, such that
whenever Prove that
A1. Let
be continuous such
that for every reals , there exist , with such that
Prove that is nondecreasing.
