Let f (x, y) = ax + bxy + cy. (a) Find g(x, y), the

Chapter , Problem 6

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Let f (x, y) = ax + bxy + cy. (a) Find g(x, y), the second-order Taylor approximation to f at (0, 0). (b) What is the relationship between g and f ? (c) Prove that R2(x0, h) = 0 for all x0, h R2. (HINT: Show that f is equal to its second-order Taylor approximation at every point.)

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