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**Unformatted text preview: **Numerical Analysis - Taylor Polynomial written by Soyoung Ahn 1 Intermediate Value Theorem continuous on min ∈ max ∈ ⇒ For any ∈ , there exists ∈ such that . Mean Value Theorem continuous and differentiable on ⇒ There exists ∈ such that ′ . Integral Mean Value Theorem continuous on nonnegative and integrable on ⇒ There exists ∈ such that . CHAPTER 1. TAYLOR POLYNOMIAL 1.1 The Taylor Polynomial ex > Find a linear polynomial for which ′ ′ for a given function . ⇒ ′ . and : ex > Find a quadratic polynomial for which ′ ′ ″ ″ for a given function . ⇒ ′ ″ . and : ex > and : Find a polynomial of degree for which for all ≥ . ⇒ ⋯ Numerical Analysis - Taylor Polynomial written by Soyoung Ahn 2 Taylor polynomial of degree : ⇒ polynomial of degree...

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