taylor 1/(3+2x)

Lösung

taylor

\frac{1}{3 + 2 x}

\frac{1}{3} - \frac{2}{9} x + \frac{4}{27} x^{2} - \frac{8}{81} x^{3} + \frac{16}{243} x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= \frac{1}{3} + \frac{- \frac{2}{9}}{1 !} x + \frac{\frac{8}{27}}{2 !} x^{2} + \frac{- \frac{16}{27}}{3 !} x^{3} + \frac{\frac{128}{81}}{4 !} x^{4} + \dots

Fasse zusammen

= \frac{1}{3} - \frac{2}{9} x + \frac{4}{27} x^{2} - \frac{8}{81} x^{3} + \frac{16}{243} x^{4} + \dots

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