taylor ln(x+2)

Lösung

taylor

ln (x + 2)

ln (2) + \frac{1}{2} x - \frac{1}{8} x^{2} + \frac{1}{24} x^{3} - \frac{1}{64} x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= ln (2) + \frac{\frac{1}{2}}{1 !} x + \frac{- \frac{1}{4}}{2 !} x^{2} + \frac{\frac{1}{4}}{3 !} x^{3} + \frac{- \frac{3}{8}}{4 !} x^{4} + \dots

Fasse zusammen

= ln (2) + \frac{1}{2} x - \frac{1}{8} x^{2} + \frac{1}{24} x^{3} - \frac{1}{64} x^{4} + \dots

\int ln (x) ln (x) d x

\int 1 + x^{4} d x

\frac{\partial}{\partial x} (3 x e^{4 x y})

\int \frac{11 x}{x ^{2} + 1} d x

w \to 0 lim (\frac{e ^{2 w} - ( 1 + w )}{w ^{2}})