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Find the maximum and minimum values of f(x, y) = x + 2y on the disk x² + y2² ≤ 1.

Find the maximum and minimum values of f(x, y) = x + 2y on the disk x² + y2² ≤ 1.

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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4. Find the maximum and minimum values of f(x, y) = x + 2y on the disk x² + y² ≤ 1. 5. Find the maximum and minimum values of f(x, y) = xy - x³y2 over the square 0 ≤ x ≤ 1,0 ≤ y ≤ 1. 6. Find the maximum and minimum values of f(x, y) = xy(1-x - y) over the triangle with vertices (0, 0), (1, 0), and (0, 1). 7. Find the maximum and minimum values of f(x, y) = sin x cos y on the closed triangular region bounded by the coordinate axes and the line x + y = 2л. 8. Find the maximum value of f(x, y) = sin x sin y sin(x + y) over the triangle bounded by the coordinate axes and the line x + y = π. 9. The temperature at all points in the disk x² + y2 ≤ 1 is given by T = (x + y) e-x²-y². Find the maximum and minimum temperatures at points of the disk. 10. Find the maximum and minimum values of f(x, y) = x-y 1+ x² + y²
Transcribed Image Text:4. Find the maximum and minimum values of f(x, y) = x + 2y on the disk x² + y² ≤ 1. 5. Find the maximum and minimum values of f(x, y) = xy - x³y2 over the square 0 ≤ x ≤ 1,0 ≤ y ≤ 1. 6. Find the maximum and minimum values of f(x, y) = xy(1-x - y) over the triangle with vertices (0, 0), (1, 0), and (0, 1). 7. Find the maximum and minimum values of f(x, y) = sin x cos y on the closed triangular region bounded by the coordinate axes and the line x + y = 2л. 8. Find the maximum value of f(x, y) = sin x sin y sin(x + y) over the triangle bounded by the coordinate axes and the line x + y = π. 9. The temperature at all points in the disk x² + y2 ≤ 1 is given by T = (x + y) e-x²-y². Find the maximum and minimum temperatures at points of the disk. 10. Find the maximum and minimum values of f(x, y) = x-y 1+ x² + y²
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