(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: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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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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u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (ū+v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅w) Support your answer mathematically or a with a written explanation. d) If possible, find u. (vxw) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

Question 3 (6 points) u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (u + v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅ w) Support your answer mathematically or a with a written explanation. d) If possible, find u (v × w) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

Chapter 3 Solutions

Biocalculus

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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