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3. Let f(x,y) = (x+²)/2 and T be the triangular region cut from the first quadrant by the line x+y=1. Let u (u, u₂) be a unit vector. Find the average value of Duf over the region T. = 4. A flat plate has the shape of the region a² + y² <1. The plate is heated and the temperature at the point (x, y) is given by T(x,y) = x² + 2y²r. Find the temperatures at the hottest and coldest points on the plate.

3. Let f(x,y) = (x+²)/2 and T be the triangular region cut from the first quadrant by the line x+y=1. Let u (u, u₂) be a unit vector. Find the average value of Duf over the region T. = 4. A flat plate has the shape of the region a² + y² <1. The plate is heated and the temperature at the point (x, y) is given by T(x,y) = x² + 2y²r. Find the temperatures at the hottest and coldest points on the plate.

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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3. Let f(x,y) = (x² + y²)/2 and T be the triangular region cut from the first quadrant by the line x+y=1. Let u= (₁, ₂) be a unit vector. Find the average value of Duf over the region T. 4. A flat plate has the shape of the region a² + y² ≤1. The plate is heated and the temperature at the point (x, y) is given by T(x,y) = x² + 2y²r. Find the temperatures at the hottest and coldest points on the plate.
Transcribed Image Text:3. Let f(x,y) = (x² + y²)/2 and T be the triangular region cut from the first quadrant by the line x+y=1. Let u= (₁, ₂) be a unit vector. Find the average value of Duf over the region T. 4. A flat plate has the shape of the region a² + y² ≤1. The plate is heated and the temperature at the point (x, y) is given by T(x,y) = x² + 2y²r. Find the temperatures at the hottest and coldest points on the plate.
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