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4. Suppose that y = y(x) is a differentiable function which is defined near x = 2, satisfies y(2) = -1 and x' + 3xy +y =9. Use the linear approximation to the change in y to approximate the value of y(1.91).

4. Suppose that y = y(x) is a differentiable function which is defined near x = 2, satisfies y(2) = -1 and x' + 3xy +y =9. Use the linear approximation to the change in y to approximate the value of y(1.91).

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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**Linear Approximation in Calculus** **Problem 4:** Consider a function \( y = y(x) \) that is differentiable and defined near \( x = 2 \). The function satisfies the conditions \( y(2) = -1 \) and \( x^2 + 3xy^2 + y^3 = 9 \). **Objective:** Use the linear approximation to estimate the value of \( y(1.91) \). This involves finding the change in \( y \) using the given function and conditions.
Transcribed Image Text:**Linear Approximation in Calculus** **Problem 4:** Consider a function \( y = y(x) \) that is differentiable and defined near \( x = 2 \). The function satisfies the conditions \( y(2) = -1 \) and \( x^2 + 3xy^2 + y^3 = 9 \). **Objective:** Use the linear approximation to estimate the value of \( y(1.91) \). This involves finding the change in \( y \) using the given function and conditions.
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