设$z=y^2+\ln(xy)$, 则$\displaystyle \frac{\partial^2{z}}{\partial{y^2}}=$.
A. $\displaystyle 2-\frac{1}{y^2}$
B. $\displaystyle 2y+\frac{1}{y}$
C. $\displaystyle 2-\frac{1}{x^2}$
D. $\displaystyle 2y+\frac{1}{x}$
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将二次积分$\displaystyle I=\int_0^1\int_y^{\sqrt{y}}\frac{sinx}{x}dxdy$，交换积分次序，则$I=$
A. $\displaystyle I=\int_0^1\int_{x^2}^x\frac{sinx}{x}dydx$
B. $\displaystyle I=\int_0^1\int_x^{x^2}\frac{sinx}{x}dydx$
C. $\displaystyle I=\int_{-1}^0\int_{x^2}^x\frac{sinx}{x}dydx$
D. $\displaystyle I=\int_{-1}^0\int^{x^2}_x\frac{sinx}{x}dydx$
$\displaystyle\lim\limits_{(x,y)\to(0,0)}\frac{3xy}{x^2+y^2}=$
A. $\displaystyle\frac{3}{2}$
B. $0$
C. $\displaystyle\frac{6}{5}$
D. 不存在
二重积分$\displaystyle I=\iint_Dx\sqrt{y}dxdy$,其中$D$是由两条抛物线$y=\sqrt{x},y=x^2$所围成的闭区域, 则积分值$I=$
A. $\displaystyle -\frac{6}{55}$
B. $\displaystyle\frac{6}{55}$
C. $\displaystyle-\frac{3}{11}$
D. $\displaystyle \frac{3}{11}$
曲线$x=t,y=t^2,z=t^3$在点$(1,1,1)$处的切线方程为
A. $\displaystyle x+2y+3z-6=0$
B. $\displaystyle\frac{x-1}{3}=\frac{y-1}{2}=\frac{z-1}{1}$
C. $\displaystyle 3x+2y+z-6=0$
D. $\displaystyle\frac{x-1}{1}=\frac{y-1}{2}=\frac{z-1}{3}$
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