Use Theorem 2 to prove that the (x) is represented by its Maclaurin series for all x.
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Use Theorem 2 to prove that the ƒ(x) is represented by its Maclaurin series for all x.
Using Maclaurin series, determine to exactly what value the following series converges:
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THEOREM 2 Let I = (cR,c + R), where R > 0, and assume that f is infinitely differentiable on 1. Suppose there exists K> 0 such that all derivatives of f are bounded by K on I: f(k)(x) ≤ K Then f is represented by its Taylor series in 1: f(x) = Σ n=0 for all k20 and x = 1 f(n)(c). n! (x  c)" for all x € I
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