taylor 2/x ,4

Lösung

taylor

\frac{2}{x}, 4

\frac{1}{2} - \frac{1}{8} (x - 4) + \frac{1}{32} (x - 4)^{2} - \frac{1}{128} (x - 4)^{3} + \frac{1}{512} (x - 4)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= \frac{1}{2} + \frac{\frac{d}{d x} ( \frac{2}{x} ) ( 4 )}{1 !} (x - 4) + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{2}{x} ) ( 4 )}{2 !} (x - 4)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{2}{x} ) ( 4 )}{3 !} (x - 4)^{3} + \dots

Evaluate Derivatives

= \frac{1}{2} + \frac{- \frac{1}{8}}{1 !} (x - 4) + \frac{\frac{1}{16}}{2 !} (x - 4)^{2} + \frac{- \frac{3}{64}}{3 !} (x - 4)^{3} + \frac{\frac{3}{64}}{4 !} (x - 4)^{4} + \dots

Fasse zusammen

= \frac{1}{2} - \frac{1}{8} (x - 4) + \frac{1}{32} (x - 4)^{2} - \frac{1}{128} (x - 4)^{3} + \frac{1}{512} (x - 4)^{4} + \dots

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