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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is meant by a proper rational function?
π‘ Hint: Check the degrees of both polynomials.
Question 2
Easy
What must be included when decomposing complex conjugate poles?
π‘ Hint: Consider the form of the quadratic expression.
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 condition must a rational function meet to apply Partial Fraction Expansion directly?
- The degree of the numerator is less than that of the denominator
- The numerator must be equal to the denominator
- The denominator must have only positive roots
π‘ Hint: Think about how degrees of polynomials work.
Question 2
True or False: The cover-up method can be used to find coefficients for repeated poles.
- True
- False
π‘ Hint: Recall the methods for distinct versus repeated poles.
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Challenge Problems
Push your limits with challenges.
Question 1
Consider X(s) = (s^3 + 5s) / ((s+1)(s^2 + 2s + 5)). Apply PFE to this function and specify the steps needed.
π‘ Hint: Use polynomial long division if needed.
Question 2
Given X(s) = 1 / (s^3 + 2s^2 + s) apply PFE and describe how you would handle the multiple roots present.
π‘ Hint: Start with polynomial factorization.
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