In 15 through 18, we indicate how to prove that the sequence {n(t)}, defined byEqs. (4) through (7), converges.If f /y is continuous in the rectangle D, show that there is a positive constant K such that|f(t, y1) f(t, y2)| K|y1 y2|, (i)where (t, y1) and (t, y2) are any two points in D having the same t coordinate.This inequalityis known as a Lipschitz20 condition.Hint: Hold t fixed and use the mean value theorem on f as a function of y only. Choose Kto be the maximum value of |f /y| in D.

L1 - 3 2 1 2 3 2 − 2 2x(1 − x ) 3+ 3x (1 − x ) 3 ex. a) Simplify: 2 2 (1 − x ) 3 2 1/3 2 3 2 −2/3 2x(1 − x ) + 3x (1 − x ) b) Solve for x: 2 2/3 =0 (1 − x )