泰勒 e^{40x}

解答

泰勒

e^{40 x}

1 + 40 x + 800 x^{2} + \frac{32000}{3} x^{3} + \frac{320000}{3} x^{4} + \dots

求解步骤

应用泰勒公式

= 1 + \frac{\frac{d}{d x} ( e ^{40 x} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{40 x} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{40 x} ) ( 0 )}{3 !} x^{3} + \dots

求导数

= 1 + \frac{40}{1 !} x + \frac{1600}{2 !} x^{2} + \frac{64000}{3 !} x^{3} + \frac{2560000}{4 !} x^{4} + \dots

整理后得

= 1 + 40 x + 800 x^{2} + \frac{32000}{3} x^{3} + \frac{320000}{3} x^{4} + \dots

y^{^{''}} + 2 y^{^{'}} + 5 y = e^{- t} + e^{- t} cos (2 t)

\int \frac{1}{1 + cos ( 10 x )} d x

\frac{d}{d t} (t - 2)

a re a y = 8 x^{2}, y^{2} = \frac{1}{8} x

d er i v a t i v e y = \frac{2}{x - 2}