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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the reformulation for the function f(x)=x²−4 in terms of g(x)?
💡 Hint: Think about how to solve f(x)=0.
Question 2
Easy
If x₀=1, what is the value of x₁ using g(x)=√(4+x)?
💡 Hint: Substitute x₀=1 into g(x).
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 is the main point of fixed-point iteration?
- Finding roots by derivatives
- Reformulating f(x)=0 to x=g(x)
- Finding simple averages
💡 Hint: Consider the principal objective of this numerical method.
Question 2
True or False: Convergence is guaranteed with any initial guess.
- True
- False
💡 Hint: Think about the role of g(x) in iteration.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the equation f(x)=x³-2x-5, derive a suitable g(x) for fixed-point iteration and analyze its convergence.
💡 Hint: Evaluate the derivative for convergence near the expected root.
Question 2
If f(x)=cos(x)-x, use fixed-point iteration to find the root starting from x=0.5, detail the iterations till convergence.
💡 Hint: Count how many iterations it takes to reach a stable x value.
Challenge and get performance evaluation