taylor 1/((7+x)2)

Lösung

taylor

\frac{1}{( 7 + x ) 2}

\frac{1}{14} - \frac{1}{98} x + \frac{1}{686} x^{2} - \frac{1}{4802} x^{3} + \frac{1}{33614} x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= \frac{1}{14} + \frac{\frac{d}{d x} ( \frac{1}{( 7 + x ) \cdot 2} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{1}{( 7 + x ) \cdot 2} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{1}{( 7 + x ) \cdot 2} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= \frac{1}{14} + \frac{- \frac{1}{98}}{1 !} x + \frac{\frac{1}{343}}{2 !} x^{2} + \frac{- \frac{3}{2401}}{3 !} x^{3} + \frac{\frac{12}{16807}}{4 !} x^{4} + \dots

Fasse zusammen

= \frac{1}{14} - \frac{1}{98} x + \frac{1}{686} x^{2} - \frac{1}{4802} x^{3} + \frac{1}{33614} x^{4} + \dots

x \to 0 lim (x sin (x))

\int_{0}^{l n (21)} x e^{x} d x

\int \frac{3}{x ( x + 3 )} d x

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\frac{d}{d x} (1 - x^{\frac{2}{3}})