What is expand (1-e^{-bt})u(t) ?

The solution to expand (1-e^{-bt})u(t) is tu-e^{-bt}tu

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (1-e^{-bt})u(t)

expand

(1 - e^{- b t}) u (t)

t u - e^{- b t} t u

Solution steps

(1 - e^{- b t}) u (t)

= (t) u (1 - e^{- b t})

Apply the distributive law:

a (b - c) = ab - a c

a = u (t), b = 1, c = e^{- b t}

= u (t) \cdot 1 - u (t) e^{- b t}

= 1 \cdot (t) u - e^{- b t} (t) u

Simplify

1 \cdot (t) u - e^{- b t} (t) u : t u - e^{- b t} t u

= t u - e^{- b t} t u

\frac{s ^{2}}{2 ( s - 2 )}

(1 - t) (1) + (t) (1)

\frac{π}{2 ( b + a ) ( ab )} + \frac{π}{4 a ^{3}}

\frac{( x - 1 ) ( x + 1 )}{3 - 2 x}

\frac{4 x ^{3}}{( x ^{4} + 1 ) ^{2}}

What is expand (1-e^{-bt})u(t) ?
The solution to expand (1-e^{-bt})u(t) is tu-e^{-bt}tu