3. Consider the equation = 0. (a) What is the solution of this equation? (Don't think too hard!) (b) Suppose, for some reason, that we wanted to use Newton's method to try and approximate a solution. Explain why Newton's method fails when applied to the equation with any initial ap- proximation ₁ 0. You should write down a clear formula for x2 that illustrates your explanation. Now sketch a graph that also illustrates your explanation.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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3. Consider the equation
= 0.
(a) What is the solution of this equation? (Don't think too hard!)
(b) Suppose, for some reason, that we wanted to use Newton's method to try and approximate a
solution. Explain why Newton's method fails when applied to the equation with any initial ap-
proximation ₁0. You should write down a clear formula for ₂ that illustrates your explanation.
Now sketch a graph that also illustrates your explanation.
Transcribed Image Text:3. Consider the equation = 0. (a) What is the solution of this equation? (Don't think too hard!) (b) Suppose, for some reason, that we wanted to use Newton's method to try and approximate a solution. Explain why Newton's method fails when applied to the equation with any initial ap- proximation ₁0. You should write down a clear formula for ₂ that illustrates your explanation. Now sketch a graph that also illustrates your explanation.
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