What is t^{-2}(t^4sin(2t)-t^2+4t^3) ?

The solution to t^{-2}(t^4sin(2t)-t^2+4t^3) is t^2sin(2t)-1+4t

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simplify t^{-2}(t^4sin(2t)-t^2+4t^3)

simplify

t^{- 2} (t^{4} sin (2 t) - t^{2} + 4 t^{3})

t^{2} sin (2 t) - 1 + 4 t

Solution steps

t^{- 2} (t^{4} sin (2 t) - t^{2} + 4 t^{3})

Apply exponent rule:

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

t^{- 2} = \frac{1}{t ^{2}}

= \frac{1}{t ^{2}} (t^{4} sin (2 t) - t^{2} + 4 t^{3})

Apply the fraction rule:

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

= \frac{1 \cdot ( t ^{4} sin ( 2 t ) - t ^{2} + 4 t ^{3} )}{t ^{2}}

Apply rule:

1 \cdot a = a

1 \cdot (t^{4} sin (2 t) - t^{2} + 4 t^{3}) = (t^{4} sin (2 t) - t^{2} + 4 t^{3})

= \frac{t ^{4} sin ( 2 t ) - t ^{2} + 4 t ^{3}}{t ^{2}}

Factor out common term

t^{2} : t^{2} (t^{2} sin (2 t) - 1 + 4 t)

= \frac{t ^{2} ( t ^{2} sin ( 2 t ) - 1 + 4 t )}{t ^{2}}

Cancel the common factor:

t^{2}

= t^{2} sin (2 t) - 1 + 4 t

42 1 + 2

400 e^{- 0.0244 t}

- e^{- \frac{x ^{2}}{2}} \cdot e^{\frac{x ^{2}}{2}}

2 19^{2}

What is t^{-2}(t^4sin(2t)-t^2+4t^3) ?
The solution to t^{-2}(t^4sin(2t)-t^2+4t^3) is t^2sin(2t)-1+4t