f(t) = sinh?(3t)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Find the Laplace transform using Laplace tables.
![The image displays a mathematical function, which is expressed as:
\[ f(t) = \sinh^2(3t) \]
This denotes that the function \( f(t) \) is the square of the hyperbolic sine of three times \( t \).
Key points about the hyperbolic sine function:
- The hyperbolic sine function, denoted \( \sinh(x) \), is defined as \( \sinh(x) = \frac{e^x - e^{-x}}{2} \).
- In this function, the expression \( \sinh^2(3t) \) means the square of \( \sinh(3t) \).
There are no graphs or diagrams in the image to explain further.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa9d4f1dd-159d-4044-a522-696d25a3cc6c%2Febf1d559-bc9a-4461-87b0-c6a17792ae7b%2Fzxs315r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image displays a mathematical function, which is expressed as:
\[ f(t) = \sinh^2(3t) \]
This denotes that the function \( f(t) \) is the square of the hyperbolic sine of three times \( t \).
Key points about the hyperbolic sine function:
- The hyperbolic sine function, denoted \( \sinh(x) \), is defined as \( \sinh(x) = \frac{e^x - e^{-x}}{2} \).
- In this function, the expression \( \sinh^2(3t) \) means the square of \( \sinh(3t) \).
There are no graphs or diagrams in the image to explain further.
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