taylor ln(x),6

Lösung

taylor

ln (x), 6

ln (6) + \frac{1}{6} (x - 6) - \frac{1}{72} (x - 6)^{2} + \frac{1}{648} (x - 6)^{3} - \frac{1}{5184} (x - 6)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= ln (6) + \frac{\frac{d}{d x} ( ln ( x ) ) ( 6 )}{1 !} (x - 6) + \frac{\frac{d ^{2}}{d x ^{2}} ( ln ( x ) ) ( 6 )}{2 !} (x - 6)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ln ( x ) ) ( 6 )}{3 !} (x - 6)^{3} + \dots

Evaluate Derivatives

= ln (6) + \frac{\frac{1}{6}}{1 !} (x - 6) + \frac{- \frac{1}{36}}{2 !} (x - 6)^{2} + \frac{\frac{1}{108}}{3 !} (x - 6)^{3} + \frac{- \frac{1}{216}}{4 !} (x - 6)^{4} + \dots

Fasse zusammen

= ln (6) + \frac{1}{6} (x - 6) - \frac{1}{72} (x - 6)^{2} + \frac{1}{648} (x - 6)^{3} - \frac{1}{5184} (x - 6)^{4} + \dots

\frac{d}{d x} (8 + 3 sin (x))

\int_{0}^{1} x^{\frac{1}{2}} d x

n = 1 \sum \infty \frac{1}{2 ^{n} n !}

x y^{^{'}} + y = 37 x

\frac{d}{d x} (\frac{1}{3} \cdot 3 x)