taylor ln(3x+1),3

Lösung

taylor

ln (3 x + 1), 3

ln (10) + \frac{3}{10} (x - 3) - \frac{9}{200} (x - 3)^{2} + \frac{9}{1000} (x - 3)^{3} - \frac{81}{40000} (x - 3)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= ln (10) + \frac{\frac{d}{d x} ( ln ( 3 x + 1 ) ) ( 3 )}{1 !} (x - 3) + \frac{\frac{d ^{2}}{d x ^{2}} ( ln ( 3 x + 1 ) ) ( 3 )}{2 !} (x - 3)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ln ( 3 x + 1 ) ) ( 3 )}{3 !} (x - 3)^{3} + \dots

Evaluate Derivatives

= ln (10) + \frac{\frac{3}{10}}{1 !} (x - 3) + \frac{- \frac{9}{100}}{2 !} (x - 3)^{2} + \frac{\frac{27}{500}}{3 !} (x - 3)^{3} + \frac{- \frac{243}{5000}}{4 !} (x - 3)^{4} + \dots

Fasse zusammen

= ln (10) + \frac{3}{10} (x - 3) - \frac{9}{200} (x - 3)^{2} + \frac{9}{1000} (x - 3)^{3} - \frac{81}{40000} (x - 3)^{4} + \dots

d er i v a t i v e \frac{1}{( t ^{2} + 3 t + 1 ) ^{\frac{5}{2}}}

d er i v a t i v e y = x^{4} + 8 x^{2} - x

n = 0 \sum \infty \frac{8}{4 ^{n}}

\frac{\partial}{\partial x} (- sin (x^{2} y) x^{2})

\int t \cdot \frac{1}{e ^{t}} d t