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[主观题]
设F(x,y)=f(x),f(x)在x0处连续,证明:对任意y0∈R,F(x,y)在(x0,y0)处连续.
设F(x,y)=f(x),f(x)在x0处连续,证明:对任意y0∈R,F(x,y)在(x0,y0)处连续.
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设F(x,y)=f(x),f(x)在x0处连续,证明:对任意y0∈R,F(x,y)在(x0,y0)处连续.
设函数y=f(x)在点x=x0处不连续,则y=f(x)在点x0一定没有定义.( )
参考答案:错误
设f(x,y)在点(x0,y0)处偏导数存在且取得极值,则必有f'x(x0,y0)=0,f'y(x0,y0)=0. ( )
设y=f(x)在x=x0的某邻域内具有三阶连续导数,如果f"(x0)=0,而f'"(x0)≠0,试问(x0,f(x0))是否为拐点?为什么?
设f(x,y)在(x0,y0)点连续,g(x,y)在(x0,y0)点可微,且g(x0,y0)=0,试证,函数f(x,y)g(x,y)在(x0,y0)点可微.
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设fx(x,y)在(x0,y0)的某邻域内存在且在(x0,y0)处连续,又fy(x,y)存在,证明f(x,y)在点(x0,y0)处可微