maclaurin x/(1+4x^2),6

Lösung

maclaurin

\frac{x}{1 + 4 x ^{2}}, 6

x - 4 x^{3} + 16 x^{5} - 64 x^{7} + 256 x^{9} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 0 + \frac{1}{1 !} x + \frac{0}{2 !} x^{2} + \frac{- 24}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{1920}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{- 322560}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{92897280}{9 !} x^{9} + \dots

Fasse zusammen

= x - 4 x^{3} + 16 x^{5} - 64 x^{7} + 256 x^{9} + \dots

\frac{\partial}{\partial x} (in x y)

\int \frac{y ^{2}}{16} d y

y^{^{''}} - y = 0

n = 0 \sum \infty \frac{n !}{10 8 ^{n}}

\int \frac{sec ^{2} ( 5 x )}{tan ( 5 x ) - 4} d x