9第九章 多元函數(shù)微分學(xué)及其應(yīng)用

1、第九章多元函數(shù)微分學(xué)及其應(yīng)用1第九章第九章多元函數(shù)微分學(xué)及其多元函數(shù)微分學(xué)及其應(yīng)用第一節(jié)第一節(jié)多元函數(shù)的基本概念多元函數(shù)的基本概念1、求下列各函數(shù)的定義域，并作出其草圖.(1)；2211yxz????解:定義域圖略??1111)(???????yxyxD(2)；)1ln(4222yxyxz????解:由得:?????????????11010422222yxyxyx定義域圖略??xyyxyxD410)(222?????(3)）（12ar

2、csin22???yxz解:由得:112122?????yx定義域圖略??22)(22???yxyxD２設(shè)，求22)(yxxyyxf???)(yxf解:令得：????????sxytyx?????????stsystx11代入得sststf???1)1()(2故yyxyxf???1)1()(23、求下列極限：(1)；32210)(1limyxexyxyx?????解:(直接代入)原式=210101????(2)；11)(cos1lim2

3、200?????yxxyyx第九章多元函數(shù)微分學(xué)及其應(yīng)用3第二節(jié)第二節(jié)偏導(dǎo)數(shù)偏導(dǎo)數(shù)１填空題：(1)在處均存在是在該點連續(xù)的既非充分也非yxff)(00yx)(yxf必要條件；(2)曲線在點處的切線與軸正向所成?????????1122xyxz)311(y的角是；6?(3)設(shè)，則，；xyzln????xzx1????yzy1(4)設(shè)，則，，xyzef(xyz)??)(fx1000?)(fy1000?)(f100z12求下列函數(shù)的一階偏導(dǎo)數(shù)

4、：(1)；yxxyz??解:，22y)(xyxz????22y)(xxyz????(2)xxy)(z??1解:，]xyxyxy)([xy)(xzx???????11ln1121?????xxy)(xyz(3)；zyxu?解:1zz????yxyxu，，xxzyyuzyzln1????xxyyzuzyzlnln????3求下列函數(shù)的二階偏導(dǎo)數(shù)：(1)y)(xxz??ln解:，，yxxy)(xxz??????lnyxxyz????，，222