Since the limit exists (say it's ) there is an integer such that if we get and using the triangle inequality we get . Now consider since it's cont. on a compact set so it attains a maximum and a minimum (say resp ) then on
Let be f : [a,inf)-->R is is continuous function and suppose that { limf(x) x-->inf } exist.Prove that f is boundedon [a,inf) so f is bounded function.