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¡¥ Polynomial Approximations to Functions. Theorem 7.1. Let f be a function with derivatives of order n at the point x=0. Then there exists one and only one polynomial P of degree ¡Â n which satisfies the n+1 conditions p(0) = f(0), P`(0) = f`(0), ....., P(n)(0) = f(n)(0). This polynomial is given by the formula P(x) = Tn f(x). Point. point x = a, P(x) |
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