# GATE2019: 39

The Laplace transform of the function $f\left ( t \right )=t^{2}+2t+1$ is

1. $\dfrac{1}{s^{3}}+\dfrac{3}{s^{2}}+\dfrac{1}{s} \\$
2. $\dfrac{4}{s^{3}}+\dfrac{4}{s^{2}}+\dfrac{1}{s} \\$
3. $\dfrac{1}{s^{3}}+\dfrac{2}{s^{2}}+\dfrac{1}{s} \\$
4. $\dfrac{2}{s^{3}}+\dfrac{2}{s^{2}}+\dfrac{1}{s}$
in Others
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## Related questions

1
The Laplace transform of $f(t) = 2t + 6$ is $\frac{1}{s}+\frac{2}{s^2}$ $\frac{3}{s}-\frac{6}{s^2}$ $\frac{6}{s}+\frac{2}{s^2}$ $-\frac{6}{s}+\frac{2}{s^2}$
2
What is the solution of the differential equation $\dfrac{\mathrm{dy} }{\mathrm{d} x}=\dfrac{x}{y}$, with the initial condition, at $x=0, y=1?$ $x^{2}=y^{2}+1$ $y^{2}=x^{2}+1$ $y^{2}=2x^{2}+1$ $x^{2}-y^{2}=0$
3
Which one of the following equations represents a one-dimensional wave equation? $\dfrac{\partial u}{\partial t}=C^{2}\dfrac{\partial ^{2}u}{\partial x^{2}} \\$ $\dfrac{\partial ^{2}u}{\partial t^{2}}=C^{2}\dfrac{\partial ^{2}u}{\partial x^{2}} \\$ ... $\dfrac{\partial ^{2}u}{\partial t^{2}}+\dfrac{\partial ^{2}u}{\partial x^{2}}=0$
4
The Laplace transform $F(s)$ of the function $f(t) = \cos (at)$, where $a$ is constant, _________ $\dfrac{s^2}{s^2+a^2} \\$ $\dfrac{a}{s^2+a^2} \\$ $\dfrac{s}{s^2+a^2} \\$ $\dfrac{s}{s^2-a^2}$
The degree of reduction for acetic acid $\left ( C_{2} H_{4}O_{2}\right )$ is ____________.