課程名稱︰微積分甲下
課程性質︰微積分
課程教師︰官彥良
開課學院：工管、生工
試題 :
(1)Find all critical points of the function f(x,y) = xye^(-x^2-y^2)
and classifiy them.
(2)Evaluate the folloing intergrals:
(a)∫(0,1)∫(x^2,1) sqrt(y)sin(y) dy dx
(b)∫(1,sqrt(2))∫(0,sqrt(2-y^2)) (x+y) / (x^2+y^2) dx dy+
∫(0,1)∫(1-y,1) (x+y) / (x^2+y^2) dx dy +
∫(1,sqrt(2))∫(0,sqrt(2-x^2)) (x+y) / (x^2+y^2) dx dy
(3)Find points on the intersection of plane x + y + 2z = 2 and
the paraboloid z = x^2 + y^2 that are nearest and farthest from the origin.