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25. f(x, y) = sin x + sin y + sin(x + y), 0 ≤ x ≤ 2π, 0≤ y ≤ 2π

25. f(x, y) = sin x + sin y + sin(x + y), 0 ≤ x ≤ 2π, 0≤ y ≤ 2π

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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23-26 Use a graph or level curves or both to estimate the local maximum and minimum values and saddle point(s) of the function. Then use calculus to find these values precisely. 1030089 -2 23. f(x, y) = x² + y² + x²²y=² TRAR EM3R03HT NO 24. f(x, y) = (x - y)e-x²-y² 25. f(x, y) = sin x + sin y + sin(x + y), 0≤x≤ 2π, 0≤ y ≤ 2T 26. f(x, y) = sin x + sin y + cos(x + y), 0≤x≤ π/4, 0≤ y ≤ π/4 valu 27-30 Use a graphing device as in Example 4 (or Newton's method or solve numerically using a calculator or computer) to find the critical points of f correct to three decimal places. Then classify the critical points and find the highest or lowest points on the graph, if any. 27. f(x, y) = x² + y4 - 4x²y + 2y 2 28. f(x, y) = y6 - 2y + x² - y² + y 2 29. f(x, y) = x² + y³ - 3x² + y² + x - 2y + 1 ctangle TOTOON | 30. f(x, y) = 20e-x²-y² sin 3x cos 3y, x≤ 1, |y|<1 31-38 Find the absolute maximum and minimum values of fon the set D. 31. f(x, y) = x² + y² - 2x, D is the closed triangular region
Transcribed Image Text:23-26 Use a graph or level curves or both to estimate the local maximum and minimum values and saddle point(s) of the function. Then use calculus to find these values precisely. 1030089 -2 23. f(x, y) = x² + y² + x²²y=² TRAR EM3R03HT NO 24. f(x, y) = (x - y)e-x²-y² 25. f(x, y) = sin x + sin y + sin(x + y), 0≤x≤ 2π, 0≤ y ≤ 2T 26. f(x, y) = sin x + sin y + cos(x + y), 0≤x≤ π/4, 0≤ y ≤ π/4 valu 27-30 Use a graphing device as in Example 4 (or Newton's method or solve numerically using a calculator or computer) to find the critical points of f correct to three decimal places. Then classify the critical points and find the highest or lowest points on the graph, if any. 27. f(x, y) = x² + y4 - 4x²y + 2y 2 28. f(x, y) = y6 - 2y + x² - y² + y 2 29. f(x, y) = x² + y³ - 3x² + y² + x - 2y + 1 ctangle TOTOON | 30. f(x, y) = 20e-x²-y² sin 3x cos 3y, x≤ 1, |y|<1 31-38 Find the absolute maximum and minimum values of fon the set D. 31. f(x, y) = x² + y² - 2x, D is the closed triangular region
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