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Which of the following is an accurate conclusion that can be made using the existence and uniqueness theorem for first-order nonlinear equations for this initial value problem? Throughout, f (x, y) = ³√y-9 (x + 2)² x3 dy dx c³ √/y=9 (x + 2)² with y (3) = 9 The initial value problem has a unique solution because f (x, y) is continuous on a rectangle containing the point (3,9) on its boundary. • The initial value problem is not guaranteed to have a unique solution because fx (x, y) is not continuous when x = -2. The initial value problem has a unique solution because both f (x, y) and fy (x, y) continuous on a rectangle containing the point (3,9). The initial value problem is not guaranteed to have a unique local solution because there is no rectangle surrounding the point (3,9) on which both f (x, y) and f, (x, y) are continuous.

Which of the following is an accurate conclusion that can be made using the existence and uniqueness theorem for first-order nonlinear equations for this initial value problem? Throughout, f (x, y) = ³√y-9 (x + 2)² x3 dy dx c³ √/y=9 (x + 2)² with y (3) = 9 The initial value problem has a unique solution because f (x, y) is continuous on a rectangle containing the point (3,9) on its boundary. • The initial value problem is not guaranteed to have a unique solution because fx (x, y) is not continuous when x = -2. The initial value problem has a unique solution because both f (x, y) and fy (x, y) continuous on a rectangle containing the point (3,9). The initial value problem is not guaranteed to have a unique local solution because there is no rectangle surrounding the point (3,9) on which both f (x, y) and f, (x, y) are continuous.

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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X Your answer is incorrect. Which of the following is an accurate conclusion that can be made using the existence and uniqueness theorem for first-order nonlinear equations for this initial value problem? Throughout, f (x, y) = √√y-9 (x + 2)² x3 dy dx - x³√x 9 (x + 2)² with y (3) = 9 The initial value problem has a unique solution because ƒ (x, y) is continuous on a rectangle containing the point (3, 9) on its boundary. • The initial value problem is not guaranteed to have a unique solution because fx (x, y) is not continuous when x = 2. The initial value problem has a unique solution because both f (x, y) and ƒ, (x, y) continuous on a rectangle containing the point (3,9). The initial value problem is not guaranteed to have a unique local solution because there is no rectangle surrounding the point (3,9) on which both f (x, y) and ƒy (x, y) are continuous.
Transcribed Image Text:X Your answer is incorrect. Which of the following is an accurate conclusion that can be made using the existence and uniqueness theorem for first-order nonlinear equations for this initial value problem? Throughout, f (x, y) = √√y-9 (x + 2)² x3 dy dx - x³√x 9 (x + 2)² with y (3) = 9 The initial value problem has a unique solution because ƒ (x, y) is continuous on a rectangle containing the point (3, 9) on its boundary. • The initial value problem is not guaranteed to have a unique solution because fx (x, y) is not continuous when x = 2. The initial value problem has a unique solution because both f (x, y) and ƒ, (x, y) continuous on a rectangle containing the point (3,9). The initial value problem is not guaranteed to have a unique local solution because there is no rectangle surrounding the point (3,9) on which both f (x, y) and ƒy (x, y) are continuous.
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