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Beliebt Rechnen >

maclaurin ln(3+x)

Lösung

maclaurin

ln (3 + x)

Lösung

ln (3) + \frac{1}{3} x - \frac{1}{18} x^{2} + \frac{1}{81} x^{3} - \frac{1}{324} x^{4} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

= ln (3) + \frac{\frac{1}{3}}{1 !} x + \frac{- \frac{1}{9}}{2 !} x^{2} + \frac{\frac{2}{27}}{3 !} x^{3} + \frac{- \frac{2}{27}}{4 !} x^{4} + \dots

Fasse zusammen

= ln (3) + \frac{1}{3} x - \frac{1}{18} x^{2} + \frac{1}{81} x^{3} - \frac{1}{324} x^{4} + \dots

Beliebte Beispiele

integral of 1/(x^2sqrt(x^2-25))

derivative f(x)=3sin(x)+3cos(x)

steigung (-4,8),(-3,8)

derivative sin(1/(x^2))

f^{''}(x)=9x^3+4x^2+7x