(a) Explanation Given information: The figure shows the graph of a function f . suppose that Newton’s method is used to approximate the root r of the equation f ( x ) = 0 with initial approximation x 1 = 1. Calculation: We draw a tangent at x 1 = 1 and we get an approximate value x 2 = 2.6 as a solution. When we draw a tangent at x 2 = 2 (b) To determine To check : x 1 = 5 is the better first approximation.

15th Edition

ISBN: 9781305420878

Author: Stewart

Publisher: CENGAGE L

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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Question

Chapter 3.8, Problem 19E

(a)

To determine

To draw:tangent lines that are used to find x2 and x3, and estimate the numerical values of x2 and x3 .

(b)

To determine

To check: x1=5 is the better first approximation.

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Chapter 3.8, Problem 18E

Chapter 3.8, Problem 20E

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To draw: tangent lines that are used to find x 2 and x 3 , and estimate the numerical values of x 2 and x 3 .

Solution Summary: The figure shows the graph of a function f. suppose that Newton's method is used to approximate the root r of the equation