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(20 points) The function defined by f(x) = cos(x) has zeros at every odd integer. Which zero off does the Bisection method converge when applied on the following each interval. (a) [-1.1, 3.3] (b) [a, b], where -1 < a < 1 and 5 < b < 7. A

(20 points) The function defined by f(x) = cos(x) has zeros at every odd integer. Which zero off does the Bisection method converge when applied on the following each interval. (a) [-1.1, 3.3] (b) [a, b], where -1 < a < 1 and 5 < b < 7. A

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 50E
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2. (20 points) The function defined by \( f(x) = \cos\left(\frac{\pi}{2} x\right) \) has zeros at every odd integer. **Which zero of \( f \) does the Bisection method converge to when applied on the following each interval:** (a) \([-1.1, 3.3]\) (b) \([a, b]\), where \(-1 < a < 1\) and \(5 < b < 7\). **Graph Explanation:** The graph is a plot of the function \( f(x) = \cos\left(\frac{\pi}{2} x\right) \). It illustrates a wave that oscillates between -1 and 1, crossing the x-axis (where the function equals zero) at every odd integer. The graph shows these oscillations and the intersections with the x-axis near x-values of -3, -1, 1, 3, 5, and 7.
Transcribed Image Text:2. (20 points) The function defined by \( f(x) = \cos\left(\frac{\pi}{2} x\right) \) has zeros at every odd integer. **Which zero of \( f \) does the Bisection method converge to when applied on the following each interval:** (a) \([-1.1, 3.3]\) (b) \([a, b]\), where \(-1 < a < 1\) and \(5 < b < 7\). **Graph Explanation:** The graph is a plot of the function \( f(x) = \cos\left(\frac{\pi}{2} x\right) \). It illustrates a wave that oscillates between -1 and 1, crossing the x-axis (where the function equals zero) at every odd integer. The graph shows these oscillations and the intersections with the x-axis near x-values of -3, -1, 1, 3, 5, and 7.
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