Prove the following statements:
If for every n , f_n form ascend function
and {f_n } uniform convergences
to f at [a, b], then
lim_(n→∞) ∫_a ^b f_n (x) dx →∫_a ^b f(x) dx
known real numbers sequence
{a_n } and {b_n } both of them
convergences to 0.
If {b_n } monotonous descend
and lim_(n→∞) ((a_(n+1) −a_n )/(b_(n+1) −b_n )) .
then lim_(n→∞) (a_n /(2b_n ))=..