1. Given f(x,y/) = 0 and a point (Co, yo) such that f(co, yo) = 0, see if the conditions of Theorem 13.6.1 are met. If so, develop the implicit function y(@) in a Taylor series about to, through second-order terms (a) a? +y? - 2y = 0; (1, 1) (d) a(cos my + 1) +ly + 8 =0; (-2, 1) (h) (y - D)ev - x2 + 1 =0; (1, 1 )THEOREM 13.6.1 Implicit Function Theorem Let f(x, y) = 0 be satisfied by a pair of real numbers co, yo so that f (To, yo) = 0, and suppose that f(@, y) is Cl in some neighborhood of (Co, yo ) with of (o,yo) * 0. (5) dy