The function f below has zeros at +3 and - 3. 3²x² 3² + x² f(x) = Find (to three decimal places) a positive number a so that if co= a, one step of Newton's Method gives #1 = a. a = What does Newton's Method converge to if xo > a? (Write DNE if Newton's Method does not converge.) Find (to three decimal places) two positive numbers, b< c, so that if co Method gives #₁ = c and another gives 2 = b again. b= C = What does Newton's Method converge to if b < x < c? (Write DNE if Newton's Method does not converge.) = b, one step of Newton's

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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The function f below has zeros at +3 and - 3.
3²x²
3² + x²
f(x) =
Find (to three decimal places) a positive number a so that if x = a, one step of Newton's Method
gives *₁ = - a.
a
What does Newton's Method converge to if co > a?
(Write DNE if Newton's Method does not converge.)
Find (to three decimal places) two positive numbers, b< c, so that if co
Method gives a₁ = c and another gives x₂ = b again.
b =
C =
What does Newton's Method converge to if b < x < c?
(Write DNE if Newton's Method does not converge.)
=
b, one step of Newton's
Transcribed Image Text:The function f below has zeros at +3 and - 3. 3²x² 3² + x² f(x) = Find (to three decimal places) a positive number a so that if x = a, one step of Newton's Method gives *₁ = - a. a What does Newton's Method converge to if co > a? (Write DNE if Newton's Method does not converge.) Find (to three decimal places) two positive numbers, b< c, so that if co Method gives a₁ = c and another gives x₂ = b again. b = C = What does Newton's Method converge to if b < x < c? (Write DNE if Newton's Method does not converge.) = b, one step of Newton's
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