maclaurin sin(2x^2)

Lösung

maclaurin

sin (2 x^{2})

2 x^{2} - \frac{4}{3} x^{6} + \frac{4}{15} x^{10} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{4}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- 960}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{967680}{10 !} x^{10} + \dots

Fasse zusammen

= 2 x^{2} - \frac{4}{3} x^{6} + \frac{4}{15} x^{10} + \dots

p a r i t y x^{t a n (x)}

\frac{d}{d x} (\frac{x ^{5}}{5} - \frac{1}{2} x^{- 2})

d er i v a t i v e \frac{4}{x ^{2} + 4}

\int 9 sin^{3} (x co) s^{2} x d x

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