展开 0.5(e^{at}+e^{-at})u(t)

解答

展开

0.5 (e^{a t} + e^{- a t}) u (t)

0.5 e^{a t} t u + 0.5 e^{- a t} t u

求解步骤

0.5 (e^{a t} + e^{- a t}) u (t)

= 0.5 (t) u (e^{a t} + e^{- a t})

使用分配律:

a (b + c) = ab + a c

a = 0.5 u (t), b = e^{a t}, c = e^{- a t}

= 0.5 u (t) e^{a t} + 0.5 u (t) e^{- a t}

= 0.5 e^{a t} (t) u + 0.5 e^{- a t} (t) u

去除括号:

(a) = a

= 0.5 e^{a t} t u + 0.5 e^{- a t} t u

e x p an d (x - 5) (x - i) (x + i)

e x p an d \frac{1}{x ( x ^{3} - 1 )}

e x p an d (x - 1) (2 + x + 3)

s im pl i f y 4 (2 - 1)

e x p an d (\frac{x ^{3}}{4} - \frac{1}{x ^{3}})^{2}