Laplace Transform Method

$g(x)$ is piecewise continuous on the interval of integration $0 \leq x < B$ for any positive $B$, and $g(x)$ is of exponential order $e^{cx}$ as $x \to \infty$. (correct)

$g(x)$ is piecewise continuous on the interval of integration $0 \leq x < B$ for any positive $B$, and $g(x)$ is of logarithmic order $\log(x)$ as $x \to \infty$.

$g(x)$ is piecewise continuous on the interval of integration $0 \leq x < B$ for any positive $B$, and $g(x)$ is of trigonometric order $\sin(\omega x)$ as $x \to \infty$.

$g(x)$ is piecewise continuous on the interval of integration $0 \leq x < B$ for any positive $B$, and $g(x)$ is of polynomial order $x^n$ as $x \to \infty$.

Multiplication by $x$ property

Linearity property (correct)

Constant Multiple property

Differentiation property

Multiplication by $x$ property (correct)

Constant Multiple property

Differentiation property

Linearity property