Question

A flat circular plate has the shape of the region a2 + y2 ≤ 1. The plate, including the boundary where ² + y² = 1, is heated so that the temperature at the point (x, y) is T(x, y) = x² + 2y² coldest point on the plate.

Answer 1

A flat circular plate has the shape of the region x2+y2 ≤1 . The plate, including the boundary where 2 2 x y + =1, is heated so that the temperature at the point ( x ,y) is 2 2 T(x,y) = x2+2y2-x . Find the temperatures at the hottest and coldest points of the plate.