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7) Use a tangent line approximation with the function g(x)= Jx to estimate V9.2

7) Use a tangent line approximation with the function g(x)= Jx to estimate V9.2

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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Question
**Problem 7:** Use a tangent line approximation with the function \( g(x) = \sqrt{x} \) to estimate \( \sqrt{9.2} \). **Explanation:** - **Tangent Line Approximation:** This technique involves finding the equation of the tangent line to a curve at a specific point. The equation of this line can be used to approximate values of the function near that point. - **Function:** The given function is \( g(x) = \sqrt{x} \). - **Objective:** Estimate the value of \( \sqrt{9.2} \) using the tangent line to the function \( g(x) \) at a point close to \( x = 9.2 \).
Transcribed Image Text:**Problem 7:** Use a tangent line approximation with the function \( g(x) = \sqrt{x} \) to estimate \( \sqrt{9.2} \). **Explanation:** - **Tangent Line Approximation:** This technique involves finding the equation of the tangent line to a curve at a specific point. The equation of this line can be used to approximate values of the function near that point. - **Function:** The given function is \( g(x) = \sqrt{x} \). - **Objective:** Estimate the value of \( \sqrt{9.2} \) using the tangent line to the function \( g(x) \) at a point close to \( x = 9.2 \).
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