Question 1. Consider the function f(x) = ³x − 6 – ½ sin(2x). (a) Show that f(x) has a unique real root. (b) Find an interval on which the root is guaranteed to exist.
Question 1. Consider the function f(x) = ³x − 6 – ½ sin(2x). (a) Show that f(x) has a unique real root. (b) Find an interval on which the root is guaranteed to exist.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Question 1. Consider the function f(x) = ³x − 6 – ½ sin(2x).
(a) Show that f(x) has a unique real root.
(b) Find an interval on which the root is guaranteed to exist.
(c) Using the interval you found in (b) and the Bisection Method, approximate the root to
within an absolute error of 10-5.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F61219562-9e39-420f-9e0e-460fa8212bb8%2Fc9182fd6-5f25-44cf-bd83-beef28db17b9%2F02hpabe_processed.png&w=3840&q=75)
Transcribed Image Text:Question 1. Consider the function f(x) = ³x − 6 – ½ sin(2x).
(a) Show that f(x) has a unique real root.
(b) Find an interval on which the root is guaranteed to exist.
(c) Using the interval you found in (b) and the Bisection Method, approximate the root to
within an absolute error of 10-5.
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