1. Prove that the function f(x) = x² sin x + 4x 3 has exactly one root in [0, 2]. Perform the bisection method to find c₂, the third approximation to the location of the root. Determine the number of of iterations needed to find the root with an error of at most 10-4. -

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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1. Prove that the function \( f(x) = x^2 \sin x + 4x - 3 \) has exactly one root in \([0, 2]\). Perform the bisection method to find \( c_2 \), the third approximation to the location of the root. Determine the number of iterations needed to find the root with an error of at most \( 10^{-4} \).
Transcribed Image Text:1. Prove that the function \( f(x) = x^2 \sin x + 4x - 3 \) has exactly one root in \([0, 2]\). Perform the bisection method to find \( c_2 \), the third approximation to the location of the root. Determine the number of iterations needed to find the root with an error of at most \( 10^{-4} \).
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