Practice Cosine Transform of First Derivative - 10.9.1 | 10. Fourier Cosine and Sine Transforms | Mathematics (Civil Engineering -1)
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Cosine Transform of First Derivative

10.9.1 - Cosine Transform of First Derivative

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Practice Questions

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Question 1 Easy

What is the basic form of the cosine transform for a function?

💡 Hint: Think about the function representation in the integral.

Question 2 Easy

State the formula for the cosine transform of the first derivative.

💡 Hint: Remember how the first derivative relates to frequency.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

Which statement best represents the cosine transform of the first derivative?

F {f'(x)} = sF {f(x)}
F {f'(x)} = -sF {f(x)}
F {f'(x)} = F {f(x)}

💡 Hint: Pay attention to how the derivative interacts with frequency.

Question 2

True or False: The cosine transform simplifies boundary-value problems.

True
False

💡 Hint: Think about the nature of solutions derived using transforms.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given a function f(x) = x^2, derive its cosine transform and then find the cosine transform of its first derivative.

💡 Hint: Use integration by parts for finding the integral.

Challenge 2 Hard

Explain how the relationship between a function and its first derivative can be exploited in real-world applications such as structural beam analysis.

💡 Hint: Consider the role of boundary conditions in structural analysis.

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