2.3.1 - How the Newton-Raphson Method Works
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Practice Questions
Test your understanding with targeted questions
What is the initial guess in the Newton-Raphson method?
💡 Hint: It's the starting point for the iterations.
State the formula used in the Newton-Raphson method.
💡 Hint: It's a relationship involving the function and its derivative.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the role of the initial guess in the Newton-Raphson method?
💡 Hint: Think about the relation of the guess to the function's behavior.
True or False: The Newton-Raphson method always guarantees convergence regardless of the initial guess.
💡 Hint: Consider how sensitive the method is to initial conditions.
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Challenge Problems
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Use the Newton-Raphson method to find the square root of 3 starting from an initial guess of 1.5. Show your calculations until convergence.
💡 Hint: Don't forget to check for convergence by calculating the difference!
Explain under what conditions the Newton-Raphson method could fail using an example such as f(x) = x^3.
💡 Hint: What happens at critical points?
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