Here is an alternate proof of Lemma 2. Let w(t) be a nonnegative function with w(t) C

QUESTION:

Here is an alternate proof of Lemma 2. Let w(t) be a nonnegative function with w(t) C LJ-~W(S) dr (*) on the interval to < t < to+ a. Since w(t) is continuous, we can find a constant A such that 0 < w(t) 9 A for to < t < to+ a. (a) Show that w(t) < LA (t - toj. (b) Use this estimate of w(t) in (*) to obtain AL*(~ - to)2 w(t)< 2 (c) Proceeding inductively, show that w(t) G A Ln (t - to)"/n!, for every integer n. (d) Conclude that w(t) = 0 for to G t < to+ a.