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Find the linearization L(x,y) of the function at each point. f(x,y)=x² + y² + 1 a. (0,4) b. (4,1)

Find the linearization L(x,y) of the function at each point. f(x,y)=x² + y² + 1 a. (0,4) b. (4,1)

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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**Problem Statement: Linearization of a Function** Find the linearization \( L(x, y) \) of the function at each point. **Function:** \[ f(x, y) = x^2 + y^2 + 1 \] **Points for Linearization:** a. \((0,4)\) b. \((4,1)\) --- **Solution Step:** a. \( L(x, y) = \) [Type an exact answer, using \(\pi\) as needed.]
Transcribed Image Text:**Problem Statement: Linearization of a Function** Find the linearization \( L(x, y) \) of the function at each point. **Function:** \[ f(x, y) = x^2 + y^2 + 1 \] **Points for Linearization:** a. \((0,4)\) b. \((4,1)\) --- **Solution Step:** a. \( L(x, y) = \) [Type an exact answer, using \(\pi\) as needed.]
Expert Solution
Step 1: Given function f(x,y)

Given, f left parenthesis x comma y right parenthesis equals x squared plus y squared plus 1

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