maclaurin (-sin(x)2x)/3

Lösung

maclaurin

\frac{- sin ( x ) 2 x}{3}

- \frac{2}{3} x^{2} + \frac{1}{9} x^{4} - \frac{1}{180} x^{6} + \frac{1}{7560} x^{8} - \frac{1}{544320} x^{10} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

= 0 + \frac{\frac{d}{d x} ( \frac{- s i n ( x ) \cdot 2 x}{3} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{- s i n ( x ) \cdot 2 x}{3} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{- s i n ( x ) \cdot 2 x}{3} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{- \frac{4}{3}}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{\frac{8}{3}}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- 4}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{\frac{16}{3}}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{- \frac{20}{3}}{10 !} x^{10} + \dots

Fasse zusammen

= - \frac{2}{3} x^{2} + \frac{1}{9} x^{4} - \frac{1}{180} x^{6} + \frac{1}{7560} x^{8} - \frac{1}{544320} x^{10} + \dots

\frac{d}{d x} (3 x^{9})

\int \frac{1}{12 x ^{5}} d x

x \to - \infty + lim (- 5 x^{3})

\frac{d}{d x} (\frac{x ^{6}}{4 - x ^{5}})

\frac{d}{d x} (3 x^{8})