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5) Find the absolute maximum and absolute minimum values of ƒ (x, y) = e-x². and all points (x,y) at which they occur on the set D = {(x,y): x² + y² ≤ 4}. ²(x² + 2y²)

5) Find the absolute maximum and absolute minimum values of ƒ (x, y) = e-x². and all points (x,y) at which they occur on the set D = {(x,y): x² + y² ≤ 4}. ²(x² + 2y²)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Problem 5:** Find the absolute maximum and absolute minimum values of the function \( f(x, y) = e^{-x^2 - y^2}(x^2 + 2y^2) \) and all points \((x, y)\) at which they occur on the set \( D = \{(x, y): x^2 + y^2 \leq 4\} \). **Problem 6:** Use Lagrange multipliers to find the maximum and minimum values and points \((x, y, z)\) at which they occur, of the function \( f(x, y, z) = x^2 + 2y^2 + 3z^2 \) subject to the constraints \( x + y + z = 1 \) and \( x - y + 2z = 2 \).
Transcribed Image Text:**Problem 5:** Find the absolute maximum and absolute minimum values of the function \( f(x, y) = e^{-x^2 - y^2}(x^2 + 2y^2) \) and all points \((x, y)\) at which they occur on the set \( D = \{(x, y): x^2 + y^2 \leq 4\} \). **Problem 6:** Use Lagrange multipliers to find the maximum and minimum values and points \((x, y, z)\) at which they occur, of the function \( f(x, y, z) = x^2 + 2y^2 + 3z^2 \) subject to the constraints \( x + y + z = 1 \) and \( x - y + 2z = 2 \).
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