taylor x^{-2},5

Lösung

taylor

x^{- 2}, 5

\frac{1}{25} - \frac{2}{125} (x - 5) + \frac{3}{625} (x - 5)^{2} - \frac{4}{3125} (x - 5)^{3} + \frac{1}{3125} (x - 5)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= \frac{1}{25} + \frac{\frac{d}{d x} ( x ^{- 2} ) ( 5 )}{1 !} (x - 5) + \frac{\frac{d ^{2}}{d x ^{2}} ( x ^{- 2} ) ( 5 )}{2 !} (x - 5)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x ^{- 2} ) ( 5 )}{3 !} (x - 5)^{3} + \dots

Evaluate Derivatives

= \frac{1}{25} + \frac{- \frac{2}{125}}{1 !} (x - 5) + \frac{\frac{6}{625}}{2 !} (x - 5)^{2} + \frac{- \frac{24}{3125}}{3 !} (x - 5)^{3} + \frac{\frac{24}{3125}}{4 !} (x - 5)^{4} + \dots

Fasse zusammen

= \frac{1}{25} - \frac{2}{125} (x - 5) + \frac{3}{625} (x - 5)^{2} - \frac{4}{3125} (x - 5)^{3} + \frac{1}{3125} (x - 5)^{4} + \dots

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