填空题 12.二元函数f(x,y)=xy在点(e,0)处的二阶(即n=2)泰勒展开式(不要求写余项)为________.
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【正确答案】 1、    
【答案解析】f(e,0)=1,fx'(x,y)=yxy-1,fx'(e,0)=0,fy'(x,y)=xylnx,fy''(e,0)=1,fxx''(x,y)=y(y一1)xy-2,fxx''(e,0)=0,fxy''(x,y)=xy-1+yxy-1lnx,fxy''(e,0)=e-1,fyy''(x,y)=xy(lnx)2,fyy''(e,0)=1.代入n=2,点(e,0)处展开的泰勒公式为