Podcast
Play an AI-generated podcast conversation about this lesson
Download our mobile app to listen on the go
Get App
Questions and Answers
What are the conditions for the existence of the Laplace transform $G(s)$ for the function $g(x)$?
What are the conditions for the existence of the Laplace transform $G(s)$ for the function $g(x)$?
- $g(x)$ 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 $x \to \infty$.
What is the property of the Laplace transform that states $L{a g(x) + b h(x)} = a L{g(x)} + b L{h(x)}$, where $a$ and $b$ are constants?
What is the property of the Laplace transform that states $L{a g(x) + b h(x)} = a L{g(x)} + b L{h(x)}$, where $a$ and $b$ are constants?
- Multiplication by $x$ property
- Linearity property (correct)
- Constant Multiple property
- Differentiation property
What is the property of the Laplace transform that states $L{x g(x)} = -G'(s)$?
What is the property of the Laplace transform that states $L{x g(x)} = -G'(s)$?
- Multiplication by $x$ property (correct)
- Constant Multiple property
- Differentiation property
- Linearity property
Flashcards are hidden until you start studying
