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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the result of multiplying \( f(x) \) by \( \delta(x - a) \)?
💡 Hint: Think about what the delta function does at point a.
Question 2
Easy
Where does the Dirac delta function have non-zero value?
💡 Hint: Recall the definition of the Dirac delta function.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What does the multiplication of a function \( f(x) \) by \( \delta(x-a) \) yield?
- Null function
- f(a) \\delta(x-a)
- f(a)
💡 Hint: Think about the sifting property.
Question 2
The Dirac delta function has non-zero values at:
- True
- False
💡 Hint: Recall how the delta function behaves.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
You are given a function \( f(x) = 2x \) and tasked to evaluate the integral \( I = \int_{-5}^{5} f(x) \delta(x - 3) dx \). Find the value of \( I \).
💡 Hint: Recall how the delta function selects the value from the function.
Question 2
Consider an impulse function \( F(t) = 5 \delta(t - 1) \). If this force is applied to a mass of 10 kg, what is the instantaneous acceleration?
💡 Hint: Apply Newton’s law of motion considering instantaneous force.
Challenge and get performance evaluation