maclaurin 9sin(4x)

Lösung

maclaurin

9 sin (4 x)

36 x - 96 x^{3} + \frac{384}{5} x^{5} - \frac{1024}{35} x^{7} + \frac{2048}{315} x^{9} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

= 0 + \frac{\frac{d}{d x} ( 9 sin ( 4 x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( 9 sin ( 4 x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 9 sin ( 4 x ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{36}{1 !} x + \frac{0}{2 !} x^{2} + \frac{- 576}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{9216}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{- 147456}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{2359296}{9 !} x^{9} + \dots

Fasse zusammen

= 36 x - 96 x^{3} + \frac{384}{5} x^{5} - \frac{1024}{35} x^{7} + \frac{2048}{315} x^{9} + \dots

d er i v a t i v e w e^{w}

\frac{\partial}{\partial x} (\frac{x ^{\frac{5}{7}}}{e ^{x}})

x \to 0 lim (\frac{2}{x ^{2} + x} - \frac{2}{x})

d er i v a t i v e \frac{3 t ^{2} + 4 t - 8}{t ^{\frac{3}{2}}}

x \to 0 lim (x^{3} - 4 x^{2} + 9 x - 2)