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Beliebt Rechnen >

maclaurin ln(e+x)

Lösung

maclaurin

ln (e + x)

Lösung

1 + \frac{1}{e} x - \frac{1}{2 e ^{2}} x^{2} + \frac{1}{3 e ^{3}} x^{3} - \frac{1}{4 e ^{4}} x^{4} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 1 + \frac{\frac{1}{e}}{1 !} x + \frac{- \frac{1}{e ^{2}}}{2 !} x^{2} + \frac{\frac{2}{e ^{3}}}{3 !} x^{3} + \frac{- \frac{6}{e ^{4}}}{4 !} x^{4} + \dots

Fasse zusammen

= 1 + \frac{1}{e} x - \frac{1}{2 e ^{2}} x^{2} + \frac{1}{3 e ^{3}} x^{3} - \frac{1}{4 e ^{4}} x^{4} + \dots

Beliebte Beispiele

integral from 0 to 0.5 of x(4-8x)

integral of xcos(nx)

taylor sqrt(1-2x^2)

limit as x approaches 4 of x-5

derivative of (x^2+5/(e^x))