高等数学（二）练习题

y=e^(x+y) y'=(1+y')e^(x+y) [1-e^(x+y)]y'=e^(x+y) y'=e^(x+y)/[1-e^(x+y)] 选C
f(x,y)=xy^3-x^2y^6 f'(x)=y^3-2xy^6|(1,1)=-1 f'(y)=3xy^2-6x^2y^5|(1,1)=-3 df=-dx-3dy 选A
∫∫[x^2+y^2<=2](x^2+y^2)dxdy=∫[0,2pi]dt∫[0,√2]r^3dr=2pi*r^4/4[0,√2]=2pi 选B
选D
x^2+y^2-4>0 x^2+y^2≠5 选 D