taylor 6sin(-x)

Lösung

taylor

6 sin (- x)

- 6 x + x^{3} - \frac{1}{20} x^{5} + \frac{1}{840} x^{7} - \frac{1}{60480} x^{9} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 0 + \frac{\frac{d}{d x} ( 6 sin ( - x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( 6 sin ( - x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 6 sin ( - x ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{- 6}{1 !} x + \frac{0}{2 !} x^{2} + \frac{6}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{- 6}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{6}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{- 6}{9 !} x^{9} + \dots

Fasse zusammen

= - 6 x + x^{3} - \frac{1}{20} x^{5} + \frac{1}{840} x^{7} - \frac{1}{60480} x^{9} + \dots

n = 1 \sum \infty 4 (0.6)^{n - 1}

d er i v a t i v e e^{x} - x^{4}

\int \frac{1}{( 36 + x ^{2} ) ^{\frac{3}{2}}} d x

x \to 0 lim (\frac{tan ( 7 x )}{x})

\frac{\partial}{\partial x} (x^{x})