What is e^{-3t}t^2sin(2t) ?

The solution to e^{-3t}t^2sin(2t) is (t^2sin(2t))/(e^{3t)}

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simplify e^{-3t}t^2sin(2t)

simplify

e^{- 3 t} t^{2} sin (2 t)

\frac{t ^{2} sin ( 2 t )}{e ^{3 t}}

Solution steps

e^{- 3 t} t^{2} sin (2 t)

Apply exponent rule:

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

= \frac{1}{e ^{3 t}} t^{2} sin (2 t)

Multiply fractions:

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

= \frac{1 \cdot t ^{2} sin ( 2 t )}{e ^{3 t}}

Multiply:

1 \cdot t^{2} = t^{2}

= \frac{t ^{2} sin ( 2 t )}{e ^{3 t}}

2.5 x 1 0^{- 8}

e^{- 0.5 t}

5.9 \cdot 1 0^{- 4}

2.718 2^{- 5} \cdot 105.156

5 z^{4}

What is e^{-3t}t^2sin(2t) ?
The solution to e^{-3t}t^2sin(2t) is (t^2sin(2t))/(e^{3t)}