f(x) = x³ – 5x² + 4x – 3 is given. 1. Show that f(x) has a root r in the interval (4, 5) 2. Use bisection method to find an approximate rootr satisfying |rn+1 – In| < 0.0625 3. Find an approximate root r of f(x) by Newton's Method satisfying |rn+1 In < 0.008 (choose approximate root that you found in 2 as initial value.)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Bisection-Newton Methods question.

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f(x) = r3
5x? + 4x – 3 is given.
1. Show that f(a) has a root r in the interval (4, 5)
2. Use bisection method to find an approximate root r satisfying |xn+1– Xn| < 0.0625
3. Find an approximate root r of f(x) by Newton's Method satisfying |an+1 – n| 0.008 (choose approximate root that you found in 2 as initial value.)
Transcribed Image Text:f(x) = r3 5x? + 4x – 3 is given. 1. Show that f(a) has a root r in the interval (4, 5) 2. Use bisection method to find an approximate root r satisfying |xn+1– Xn| < 0.0625 3. Find an approximate root r of f(x) by Newton's Method satisfying |an+1 – n| 0.008 (choose approximate root that you found in 2 as initial value.)
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