taylor ln(-3x+2),-2

Lösung

taylor

ln (- 3 x + 2), - 2

3 ln (2) - \frac{3}{8} (x + 2) - \frac{9}{128} (x + 2)^{2} - \frac{9}{512} (x + 2)^{3} - \frac{81}{16384} (x + 2)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= 3 ln (2) + \frac{- \frac{3}{8}}{1 !} (x + 2) + \frac{- \frac{9}{64}}{2 !} (x + 2)^{2} + \frac{- \frac{27}{256}}{3 !} (x + 2)^{3} + \frac{- \frac{243}{2048}}{4 !} (x + 2)^{4} + \dots

Fasse zusammen

= 3 ln (2) - \frac{3}{8} (x + 2) - \frac{9}{128} (x + 2)^{2} - \frac{9}{512} (x + 2)^{3} - \frac{81}{16384} (x + 2)^{4} + \dots

\frac{d}{d x} (\frac{e ^{x - 3}}{x - 2})

x \to - 4 lim (m (x) (3 x + 2) + 2 k)

\int_{5}^{20} (x^{2} x) d x

x \to 0 lim (\frac{5 x}{sin ( x )})

\frac{d}{d x} (lo g_{10} (cos (x)))