What is laplacetransform 4+7x+x^2+δ ?

The answer to laplacetransform 4+7x+x^2+δ is 4/s+7/(s^2)+2/(s^3)+δ/s

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laplacetransform 4+7x+x^2+δ

laplace transform

4 + 7 x + x^{2} + δ

\frac{4}{s} + \frac{7}{s ^{2}} + \frac{2}{s ^{3}} + \frac{δ}{s}

Solution steps

L {4 + 7 x + x^{2} + δ}

Use the linearity property of Laplace Transform:

For functions

f (t), g (t)

and constants

a, b : L {a \cdot f (t) + b \cdot g (t)} = a \cdot L {f (t)} + b \cdot L {g (t)}

= L {4} + 7 L {x} + L {x^{2}} + L {δ}

L {4} : \frac{4}{s}

L {x} : \frac{1}{s ^{2}}

L {x^{2}} : \frac{2}{s ^{3}}

L {δ} : \frac{δ}{s}

= \frac{4}{s} + 7 \cdot \frac{1}{s ^{2}} + \frac{2}{s ^{3}} + \frac{δ}{s}

Refine

\frac{4}{s} + 7 \frac{1}{s ^{2}} + \frac{2}{s ^{3}} + \frac{δ}{s} : \frac{4}{s} + \frac{7}{s ^{2}} + \frac{2}{s ^{3}} + \frac{δ}{s}

= \frac{4}{s} + \frac{7}{s ^{2}} + \frac{2}{s ^{3}} + \frac{δ}{s}

x \to 0 lim (\frac{7 x ^{2}}{x ^{2}})

x \to 5 lim (75)

\frac{d}{d t} (a (t - sin (t)))

\frac{7}{x}

\int_{0}^{70} 0.65 (70 - x) d x

What is laplacetransform 4+7x+x^2+δ ?
The answer to laplacetransform 4+7x+x^2+δ is 4/s+7/(s^2)+2/(s^3)+δ/s