taylor 1/(5x+7)

Lösung

taylor

\frac{1}{5 x + 7}

\frac{1}{7} - \frac{5}{49} x + \frac{25}{343} x^{2} - \frac{125}{2401} x^{3} + \frac{625}{16807} x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= \frac{1}{7} + \frac{\frac{d}{d x} ( \frac{1}{5 x + 7} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{1}{5 x + 7} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{1}{5 x + 7} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= \frac{1}{7} + \frac{- \frac{5}{49}}{1 !} x + \frac{\frac{50}{343}}{2 !} x^{2} + \frac{- \frac{750}{2401}}{3 !} x^{3} + \frac{\frac{15000}{16807}}{4 !} x^{4} + \dots

Fasse zusammen

= \frac{1}{7} - \frac{5}{49} x + \frac{25}{343} x^{2} - \frac{125}{2401} x^{3} + \frac{625}{16807} x^{4} + \dots

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