(0,1) \to D(0,1)" alt="f(0,1) \to D(0,1)" /> has a zero of order k at the origin. Show that the function is bounded in magnitude by .

I want to use Schwarz Lemma because the function is analytic on the unit disc, its image is a subset of the unit disc, and f(0)=0. Then I can definitely say that , but I need more. How might I bring in powers of |z|? Would the other consequence of Schwarz Lemma ( ) help here?