maclaurin f(x)=arctan(3x)

Lösung

maclaurin

f (x) = arctan (3 x)

3 x - 9 x^{3} + \frac{243}{5} x^{5} - \frac{2187}{7} x^{7} + 2187 x^{9} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 0 + \frac{3}{1 !} x + \frac{0}{2 !} x^{2} + \frac{- 54}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{5832}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{- 1574640}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{793618560}{9 !} x^{9} + \dots

Fasse zusammen

= 3 x - 9 x^{3} + \frac{243}{5} x^{5} - \frac{2187}{7} x^{7} + 2187 x^{9} + \dots

\int \frac{cos ( x )}{sin ^{16} ( x )} d x

d er i v a t i v e \frac{x}{x + 7}

n = 0 \sum \infty \frac{1}{( 2 n + 1 )}

\frac{d}{d x} (1 - e^{c o s (1 - x^{2})})

d er i v a t i v e y = arcsin (x^{2})