多元函数微分法及其应用答案.pdf
第九章 多元函数微分法及其应用一、填空题1.若22(,)tanxf x yxyxyy,则(,)f tx ty222222tan(,)xt xt yt xyt f x yy.2.若22()(0)xyxfyyy,则()f x21u.3.函数arcsinyzx的定义域为(,)|10yx yxx且.4.1sin00lim(1)xyxyxye.5.若2xyzeyx,则zy2xyxex.6.若23(,)5f x yx y,则(0,1)xf3(0,1)10|0 xy.7.若222ln(1)uxyz,则 du2222()xdxydyzdzxyz.8.设yxze,则 dz21yyxxye dxe dyxx.9.已知sin()xzye,而3yx,则dzdx23(3)cos()xxxexe.10.已知2xyze,而3sin,xt yt,则dzdt3sin22(cos6).ttett11.设)1ln(22yxz,则21yxdz1233dxdy.12.设vuz2,而yxvyxusin,cos,则xz223cossinxyy,yz322cos(cos2sin)xyyy.13.若(,)zf x y在区域D上的两个混合偏导数22,zzx yy x连续，则在D上22zzx yy x.14.函数(,)zf x y在点00(,)xy处可微的必要 条件是(,)zf x y在点00(,)xy处的偏导数存在.(填“充分”、“必要”或“充分必要”)15.函数(,)zf x y在点00(,)xy可微是(,)zf x y在点00(,)xy处连续的充分 条件.(填“充分”、“必要”或“充分必要”)16设23(,)f x y zxy z，其中(,)zz x y是由方程22230 xyzxyz所确定的隐函数，则(1,1,1)xf2.二、选择题1.二元函数222241lnarcsinzxyxy的定义域是(A)（A）22(,)|14x yxy;（B）22(,)|14x yxy;（C）22(,)|14x yxy;（D）22(,)|14x yxy.2.设函数ln()zxy,则zx(C)（A）1y;（B）xy;（C）1x;（D）yx.3.设函数2sin()zxy,则zx(D)（A）2cos()xyxy;（B）2cos()xyxy;（C）22cos()yxy;（D）22cos()yxy.4.设函数3xyz,则zx(D)（A）3xyy;（B）3ln3xy;（C）13xyxy;（D）3ln 3xyy.5.设函数1zxy,则zy(C)（A）21x y;（B）21x y;（C）21xy;（D）21xy.6.设函数sinzxy,则22zx(A)（A）2sinyxy;（B）2sinyxy;（C）2sinxxy;（D）2sinxxy.7.设二元函数xyzxy,则 dz(B)（A）22()()xdxydyxy;（B）22()()xdyydxxy;（C）22()()ydyxdxxy;（D）22()()ydxxdyxy.8.设函数()yf x是由方程0yyxex确定,则dydx(B)文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5（A）1yyexe;（B）11yyexe;（C）11yyexe;（D）1yyexe.9.设函数(,)zf x y是由方程2320 xyxyz确定,则zx(B)（A）222xyzxyz;（B）222xyzxyz;（C）2232yxzxyz;（D）2232yxzxyz.10.若函数(,)f x y在点00(,)xy处不连续，则(C)（A）00lim(,)xxyyf x y 必不存在；（B）00(,)f xy必不存在；（C）(,)f x y在点00(,)xy必不可微；（D）0000(,),(,)xyfxyfxy必不存在.11.考虑二元函数(,)f x y的下面 4 条性质：函数(,)f x y在点00(,)xy处连续；函数(,)f x y在点00(,)xy处两个偏导数连续；函数(,)f x y在点00(,)xy处可微；函数(,)f x y在点00(,)xy处两个偏导数存在.则下面结论正确的是（A）（A）；（B）；（C）；D）。12.设函数2224222,0(,)0,0 x yxyxyf x yxy，则在(0,0)点处（C）（A）连续，偏导数存在；（B）连续，偏导数不存在；（C）不连续，偏导数存在；（D）不连续，偏导数不存在。三、是非题1.设2lnzxy，则12zxxy（）2.若函数(,)zf x y在00(,)P xy处的两个偏导数00(,)xfxy与00(,)yfxy均存在，则该函数在P点处一定连续（）3.函数(,)zfx y在00(,)P xy处一定有0000(,)(,)xyyxfxyfxy.（）4.函数222222,0(,)0,0 xyxyxyf x yxy在点(0,0)处有(0,0)(0,0)0 xyff.（）5.函数22zxy在点(0,0)处连续，但在点(0,0)处的两个偏导数(0,0),(0,0)xyzz均不存在。（）文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 HZ7R5R10K2C2 ZU4I5L10L1B5文档编码:CY1A1R10S8W4 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