define function fn:[0,1]->R by fn(x)=(n^p)x*exp(-(n^q)x) where p , q>0 and fn->0 pintwise on[0,1] as n->infinite.
find ||fn||(infinite) and deduce that if p<q then fn converges uniformly on[0.1] whereas if p>=q then fun does not converge uniformly on[0,1] how about [0,1-esillope] and [esillope,1] where 0<esillope<1