麦克劳林 cos(pix),0

解答

麦克劳林

cos (π x), 0

1 - \frac{π ^{2}}{2} x^{2} + \frac{π ^{4}}{24} x^{4} - \frac{π ^{6}}{720} x^{6} + \frac{π ^{8}}{40320} x^{8} + \dots

求解步骤

应用麦克劳林公式

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

求导数

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

整理后得

= 1 - \frac{π ^{2}}{2} x^{2} + \frac{π ^{4}}{24} x^{4} - \frac{π ^{6}}{720} x^{6} + \frac{π ^{8}}{40320} x^{8} + \dots

d er i v a t i v e \frac{16}{x}

\frac{\partial}{\partial y} (3 x^{2})

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

\int \frac{x ^{2}}{x + 4} d x

(1 + ln (x) + \frac{y}{x}) d x + (1 - ln (x)) d y = 0