maclaurin sin(x^3)

Lösung

maclaurin

sin (x^{3})

x^{3} - \frac{1}{6} x^{9} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{6}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{- 60480}{9 !} x^{9} + \frac{0}{10 !} x^{10} + \dots

Fasse zusammen

= x^{3} - \frac{1}{6} x^{9} + \dots

f (t) = 2 t

x \to 1 lim (\frac{x - 1}{x ^{6} - 1})

y^{^{''}} + 4 y = t^{2}

d er i v a t i v e f (x) = e^{\infty}

d er i v a t i v e (5 x^{2} - 2 x + 4) (4 x^{2} + 3 x - 6)