1.计算二重积分∫∫(x/1+y^2)dxdy,D由0

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1.计算二重积分∫∫(x/1+y^2)dxdy,D由0
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1.计算二重积分∫∫(x/1+y^2)dxdy,D由0
1.计算二重积分∫∫(x/1+y^2)dxdy,D由0

1.计算二重积分∫∫(x/1+y^2)dxdy,D由0
答案如图



1:∫∫(x/1+y^2)dxdy=∫[x^2/2(1+y^2)]dy,(0<=x<=2, 0<=y<=1)
=∫[4/2(1+y^2)]dy, (0<=y<=1)
=2arctany, (0<=y<=1)
...

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1:∫∫(x/1+y^2)dxdy=∫[x^2/2(1+y^2)]dy,(0<=x<=2, 0<=y<=1)
=∫[4/2(1+y^2)]dy, (0<=y<=1)
=2arctany, (0<=y<=1)
=2arctan1
=2*pi/4=pi/2
2:lim{[根号(1+xy)]-1}/x (x,y)→(0,1)
=lim[(1+xy)-1]/x{[根号(1+xy)]+1}
=limy/{[根号(1+xy)]+1}
=lim1/{[根号(1+0*1)]+1}
=1/2
OK么?O(∩_∩)O

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