麦克劳林 1/((1-x^2))

解答

麦克劳林

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

1 + x^{2} + x^{4} + x^{6} + x^{8} + \dots

求解步骤

应用麦克劳林公式

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

求导数

= 1 + \frac{0}{1 !} x + \frac{2}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{24}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{720}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{40320}{8 !} x^{8} + \dots

整理后得

= 1 + x^{2} + x^{4} + x^{6} + x^{8} + \dots

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

y^{^{'}} = (x + y)^{2}

\frac{\partial}{\partial v} (3 u)

\frac{d y}{d x} = (x + y + 1)^{2} - (x + y - 1)^{2}

\int (e^{x} - 5)^{2} d x