Question

Prove the theorem that if limx→d h(x) = P and limx→d k(x) = Q and h(x) ≥ k(x) for all x in an open interval containing d, then P ≥ Q by using the formal definition of the limit, showing all work.

Answer 1

in the interval (m,n) since h(x) is greater than k(x) everywhere, for any value of x, therefore for any limit of x=d it sis valid too, since d is a member of the interval (m,n), and limts of d lie in the interval too.

use proper statements to get a "hence, proved" at the end