What I'm getting is that the limit of the area is 1/f'''(0). I could have made an algebra error, though. On Wed, Dec 9, 2009 at 12:20 PM, Dan Asimov <dasimov@earthlink.net> wrote:
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
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