taylor 1/(x-1),13

Lösung

taylor

\frac{1}{x - 1}, 13

\frac{1}{12} - \frac{1}{144} (x - 13) + \frac{1}{1728} (x - 13)^{2} - \frac{1}{20736} (x - 13)^{3} + \frac{1}{248832} (x - 13)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= \frac{1}{12} + \frac{\frac{d}{d x} ( \frac{1}{x - 1} ) ( 13 )}{1 !} (x - 13) + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{1}{x - 1} ) ( 13 )}{2 !} (x - 13)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{1}{x - 1} ) ( 13 )}{3 !} (x - 13)^{3} + \dots

Evaluate Derivatives

= \frac{1}{12} + \frac{- \frac{1}{144}}{1 !} (x - 13) + \frac{\frac{1}{864}}{2 !} (x - 13)^{2} + \frac{- \frac{1}{3456}}{3 !} (x - 13)^{3} + \frac{\frac{1}{10368}}{4 !} (x - 13)^{4} + \dots

Fasse zusammen

= \frac{1}{12} - \frac{1}{144} (x - 13) + \frac{1}{1728} (x - 13)^{2} - \frac{1}{20736} (x - 13)^{3} + \frac{1}{248832} (x - 13)^{4} + \dots

x \to 0 lim (x^{5})

\frac{\partial}{\partial x} (12 + 5 x y)

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