泰勒 sin^2(x)

解答

泰勒

sin^{2} (x)

x^{2} - \frac{1}{3} x^{4} + \frac{2}{45} x^{6} - \frac{1}{315} x^{8} + \frac{2}{14175} x^{10} + \dots

求解步骤

应用泰勒公式

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

求导数

= 0 + \frac{0}{1 !} x + \frac{2}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{- 8}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{32}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{- 128}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{512}{10 !} x^{10} + \dots

整理后得

= x^{2} - \frac{1}{3} x^{4} + \frac{2}{45} x^{6} - \frac{1}{315} x^{8} + \frac{2}{14175} x^{10} + \dots

\int \frac{1}{sec ^{2} ( θ )} d θ

\int \frac{4}{3 x} d x

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

\int sin (x) d (sin (x)) d x

t an g e n t y = 4 x e^{x}, (0, 0)