设函数f(x,y)在点(0,0)附近有定义,且f’x(0,0)=3,f’y(0,0)=1,则( )

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问题 设函数f(x,y)在点(0,0)附近有定义,且f’x(0,0)=3,f’y(0,0)=1,则(    )

选项 A、dz|(0,0)=3dx+dy.
B、曲面z=f(x,y)在点(0,0,f(0,0))处的法向量为{3,1,1}.
C、曲线,在点(0,0,f(0,0))处的切向量为{1,0,3}.
D、曲线,在点(0,0,f(0,0))处的切向量为{3,0,1}.

答案C

解析 化曲线则该曲线在点(0,0,f(0,0))处的切向量为{1,0,f’x(0,0)}={1,0,3},故选C.
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