use Integration by Parts to derive 12.6.1 THEOREM 12.6.1 TAYLOR'S THEOREMIff has n+1 continuous derivatives on an open interval I that contains 0,then for each x Є If" (0)f(n) (0)f(x):=f(0) + f'(0) x +-x² +2!+-x" + Rn(x)n!Xwith Rn(x)=1 * (+1) (10)(x = 0)" dt. We call R,(x) the remainder.n!

Step-by-Step Derivation Step 1: Start with the Integral Expression Step 2: Apply Integration by…

Answered: THEOREM 12.6.1 TAYLOR'S THEOREM Iff has…

Linear Algebra: A Modern Introduction

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THEOREM 12.6.1 TAYLOR'S THEOREM Iff has n+1 continuous derivatives on an open interval I that contains 0, then for each x Є I f" (0) f(n) (0) f(x): = f(0) + f'(0) x + -x² + 2! + -x" + Rn(x) n! X with Rn(x) = 1 * (+1) (10)(x = 0)" dt. We call R,(x) the remainder. n!