[math-fun] Vanishing triangle puzzle

Let f: R -> R be a real analytic function with f(0) = f'(0) = f''(0) = 0. Let N_x denote the normal line at x to the graph of y = f(x), and let A(x) denote the area of the triangle formed by N_x and the x- and y-axes. What is the limit of A(x) as x -> 0 ? --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele