The figure shows the graph of a function f. Suppose that Newton's method is used to approximate the root s of the equation f(x) = 0 with initial approximation x, = yA (a) Draw the tangent lines that are used to find x, and x2, and estimate the numerical values of x, and x2. (Round your answers to one decimal place.) X2 = 9 X3 = (b) Would x, = 8 be a better first approximation? Explain. We know that x, = 8 ---Select--- v be a better first approximation because the tangent line at x = 8 intersects the x-axis ---Select-- s than does the first approximation x, = 6.
The figure shows the graph of a function f. Suppose that Newton's method is used to approximate the root s of the equation f(x) = 0 with initial approximation x, = yA (a) Draw the tangent lines that are used to find x, and x2, and estimate the numerical values of x, and x2. (Round your answers to one decimal place.) X2 = 9 X3 = (b) Would x, = 8 be a better first approximation? Explain. We know that x, = 8 ---Select--- v be a better first approximation because the tangent line at x = 8 intersects the x-axis ---Select-- s than does the first approximation x, = 6.
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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Transcribed Image Text:The figure shows the graph of a function f. Suppose that Newton's method is used to approximate the root s of the equation f(x)
= 0 with initial approximation x, = 6
YA
1-
1
(i)
(a) Draw the tangent lines that are used to find x, and x,, and estimate the numerical values of x, and x,. (Round your answers to one decimal place.)
X2 =
9.
X3 =
(b) Would x,
= 8 be a better first approximation? Explain.
We know that x,
approximation x,
= 8 ---Select--- v be a better first approximation because the tangent line at x = 8 intersects the x-axis ---Select---
s than does the first
= 6.
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