Practice Bisection Method (2.2) - Numerical Solutions of Algebraic and Transcendental Equations

Practice: Bisection Method

Lesson 2.2Numerical Solutions of Algebraic and Transcendental Equations

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9 questions

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6 sample questions

Question 1.
What is the Bisection Method used for?
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Think about what roots mean.
Question 2.
Give an example of a function where you can use the Bisection Method.
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Consider quadratic functions.
3Question 3.
What must be true for the Bisection Method to be applicable?
- f(a) * f(b) > 0
- f(a) * f(b) < 0
- f(a) * f(b) = 0
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Recall the sign change condition.
4Question 4.
True or False: The Bisection Method will always provide the exact root of a function.
- True
- False
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Consider how the method narrows down the interval.
Question 5.
Using the Bisection Method, determine the root of the function f(x) = e^(-x) - x by starting with the interval [0, 1]. Describe each step.
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Check how the signs change at your calculated midpoints.
Question 6.
Compare the efficiency of the Bisection Method to the Newton-Raphson Method for a simple quadratic function. Consider starting conditions for both methods.
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Reflect on which method converges faster and under what conditions.

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