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Suppose that f and g are infinitely differentiable functions defined on R. Suppose that Pf is...

  • Suppose that f and g are infinitely differentiable functions defined on R. Suppose that Pf is the second order Taylor polynomial for f centered at 0 and that Pg is the second order Taylor polynomial for g centered at 0. Let Pfg be the second order Taylor polynomial for fg centered at 0. Is Pfg = PfPg? If not, is there a relationship between Pfg and PfPg ?

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