未分类题
设f(x，y，z)=xy+zx+yz-x-y-z+6，试问函数f(x，y，z)在点M(3，4，0)沿哪个方向的变化率最大?并求此最大变化率。
【参考答案】
l={3，2，6}；7
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设方程F(x2+y2，y2+z2，z2+x2)=0确定了函数z=z(x，y)，其中F有连续一阶偏导数，求 style='FONT-SIZE: 16px; FONT-FAMILY: zuoyeFont_mathFont, Microsoft Yahei, 宋体, sans-serif; WHITE-SPACE: normal; TEXT-TRANSFORM: none; WORD-SPACING: 0px; FLOAT: none; FONT-WEIGHT: normal; COLOR: rgb(51,51,51); FONT-STYLE: normal; ORPHANS: 2; WIDOWS: 2; DISPLAY: inline !important; LETTER-SPACING: normal; BACKGROUND-COLOR: rgb(255,255,255); TEXT-INDENT: 0px; font-variant-ligatures: normal; font-variant-caps: normal; -webkit-text-stroke-width: 0px'>函数z = z( x,y)在点(1,0,-1)处的全微分dz, style='FONT-SIZE: 16px; FONT-FAMILY: zuoyeFont_mathFont, Microsoft Yahei, 宋体, sans-serif; WHITE-SPACE: normal; TEXT-TRANSFORM: none; WORD-SPACING: 0px; FLOAT: none; FONT-WEIGHT: normal; COLOR: rgb(51,51,51); FONT-STYLE: normal; ORPHANS: 2; WIDOWS: 2; DISPLAY: inline !important; LETTER-SPACING: normal; BACKGROUND-COLOR: rgb(255,255,255); TEXT-INDENT: 0px; font-variant-ligatures: normal; font-variant-caps: normal; -webkit-text-stroke-width: 0px'>是xyz + （x2 + y2 + z2）^(1 2) =2^(1 2)