Practice Numerical Solutions Of Algebraic And Transcendental Equations (2)

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9 questions

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2 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is the Bisection Method?
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Think about how you narrow down your guess.
Question 2.
Define the Newton-Raphson Method.
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Consider how it improves a guess.
3Question 3.
What does the Bisection Method guarantee?
- Fast convergence
- Guaranteed convergence under proper conditions
- No convergence
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Remember the conditions for it to work.
4Question 4.
Is the Secant Method derivative-free?
- True
- False
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Think about what it uses instead.
Question 5.
Using the Newton-Raphson Method, determine the root of f(x) = x^3 - 2x - 5 starting from x0 = 2.
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Don't forget to calculate the derivative f'(x) = 3x^2 - 2.
Question 6.
Implement the Fixed-Point Iteration method to find the root of x = cos(x) starting with x0 = 0.5. What challenges might arise?
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Consider if the function g(x) = cos(x) supports fixed-point constrains.

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