5.1.3.3 - Newton-Raphson Method
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Practice Questions
Test your understanding with targeted questions
What is the formula for the Newton-Raphson method?
💡 Hint: Remember it's the current guess minus the function value divided by the derivative.
What do you need to calculate to apply the Newton-Raphson method?
💡 Hint: Think about evaluating the slope of the function.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the primary advantage of the Newton-Raphson method?
💡 Hint: Evaluate the options based on the speed of convergence.
True or False: The Newton-Raphson method can work without the derivative.
💡 Hint: Think about how the method is defined and its necessity for derivatives.
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Challenge Problems
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Apply the Newton-Raphson method to approximate the root of the equation x^3 - x - 2 = 0 starting from an initial guess of x0 = 1. Show detailed calculations for three iterations.
💡 Hint: Make sure to calculate both f(x) and f'(x) correctly at each iteration.
Using the equation sin(x) - x/2 = 0, find the root starting with x0 = 1. Illustrate the iterations clearly until convergence is evident.
💡 Hint: Consider using a calculator for the sin function and be careful with radians.
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