What is e^{-at}cos(wt)*u(t) ?

The solution to e^{-at}cos(wt)*u(t) is (tucos(tw))/(e^{at)}

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simplify e^{-at}cos(wt)*u(t)

simplify

e^{- a t} cos (wt) \cdot u (t)

\frac{t u cos ( tw )}{e ^{a t}}

Solution steps

e^{- a t} cos (wt) u (t)

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{e ^{a t}} t u cos (tw)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot cos ( wt ) u t}{e ^{a t}}

Multiply:

1 \cdot cos (wt) = cos (wt)

= \frac{t u cos ( tw )}{e ^{a t}}

100000 (1 + 0.105)^{- 7}

(5 mn) (m^{2} n)

(x y)^{4}

(x - 2)^{2} (x^{2} + x)^{2}

(7 x^{2}) (3 x^{2})

What is e^{-at}cos(wt)*u(t) ?
The solution to e^{-at}cos(wt)*u(t) is (tucos(tw))/(e^{at)}