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By following the Solutions of Equations: Newton's Method, kindly answer only Item No. 1. a.), b.) and c.). Thank you.

By following the Solutions of Equations: Newton's Method, kindly answer only Item No. 1. a.), b.) and c.). Thank you.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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By following the Solutions of Equations: Newton's Method, kindly answer only Item No. 1. a.), b.) and c.). Thank you.

Chapter V. Solution of Equations: Newton's Method Elementary Methods: a) factoring b) completing squares c) quadratic formula x= -b+Vb? -4ac 2a d) synthetic division Newton's Method: it can be made to yield a root to any desired degree of accuracy; it is useful in obtaining approximations to imaginary roots, as well as real roots of equations. Formula: Let f(x) = 0 y = f(x) *x2 = X- f(x) f'(x1) steps: to find the roots using Newton's method 1) assign values of x to solve for y 2) plot the two consecutive points whose ordinates one is positive and the other is negative 3) join the two points, taking the value of x where the line crosses the x=axis as the first approximation for x(x1) 4) to find the other approximation for x use formula * until the difference between the two consecutive approximations are nearly negligible. Note: X = first approximation of x (from the graph) f(x1) = the value of f(x) at x = x1 f'(x) = the value of the first derivative of the function of x at x = x Exercises: 1 1. Find the roots: a) cube root of 98 2. Find to two decimal places the positive root of x'+x -3=0 3. Find to three decimal places the real roots of x'+3x-2=0 4. Find, in inches, the radius of a sphere of volume 1 cu. ft. 5. A hallow sphere of outer radius 10 in. weighs one-fifth as much as a solid sphere of the same size and material. Find the inner radius. 6. A metal sphere of radius 2 in. is recast in the form of a cone of height 2 in. surmounted by a hemisphere of the same radius as the cone. Find the radius of the cone. b) square root of 242 c) v80 7. A torpedo has the longitudinal section shown. When submerged, it displaces a volume of water equal to a sphere of radius 1 ft. Find r in ft.
Transcribed Image Text:Chapter V. Solution of Equations: Newton's Method Elementary Methods: a) factoring b) completing squares c) quadratic formula x= -b+Vb? -4ac 2a d) synthetic division Newton's Method: it can be made to yield a root to any desired degree of accuracy; it is useful in obtaining approximations to imaginary roots, as well as real roots of equations. Formula: Let f(x) = 0 y = f(x) *x2 = X- f(x) f'(x1) steps: to find the roots using Newton's method 1) assign values of x to solve for y 2) plot the two consecutive points whose ordinates one is positive and the other is negative 3) join the two points, taking the value of x where the line crosses the x=axis as the first approximation for x(x1) 4) to find the other approximation for x use formula * until the difference between the two consecutive approximations are nearly negligible. Note: X = first approximation of x (from the graph) f(x1) = the value of f(x) at x = x1 f'(x) = the value of the first derivative of the function of x at x = x Exercises: 1 1. Find the roots: a) cube root of 98 2. Find to two decimal places the positive root of x'+x -3=0 3. Find to three decimal places the real roots of x'+3x-2=0 4. Find, in inches, the radius of a sphere of volume 1 cu. ft. 5. A hallow sphere of outer radius 10 in. weighs one-fifth as much as a solid sphere of the same size and material. Find the inner radius. 6. A metal sphere of radius 2 in. is recast in the form of a cone of height 2 in. surmounted by a hemisphere of the same radius as the cone. Find the radius of the cone. b) square root of 242 c) v80 7. A torpedo has the longitudinal section shown. When submerged, it displaces a volume of water equal to a sphere of radius 1 ft. Find r in ft.
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