課程名稱︰微積分甲下 課程性質︰理工學院必修 課程教師︰官彥良 開課學院：理學院 開課系所︰數學系 考試日期（年月日）︰108.04.11 考試時限（分鐘）：30 試題 : -x^2-y^2 1. (30%) Find all critical points of the function f(x,y)=xye^ and clas- ify them. 2. Evaluate the following integrals. 1 1 (a) (20%)∫∫√(y)sinydydx 0 x^2 √2 √(2-y^2) 1 1 (b) (20%)∫ ∫ (x+y)/(x^2+y^2)dxdy + ∫∫ (x+y)/(x^2+y^2)dxdy 1 0 0 1-y √2 √(2-x^2) +∫ ∫ (x+y)/(x^2+y^2)dydx. 1 0 3. (30%) Find the points on the intersections of the plane x+y+2z=2 and the paraboloid z = x^2 + y^2 that are nearest to and farthest from the origin. --

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