1、简述二元函数z=f(x,y)在点(x0,y0)连续，可偏导，可微及有一阶连续偏导数彼此之间的关 函数z=f(x,y)在点（x0.y0)处偏导数连续，则z=f...
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1、二元函数z=f(x,y)在点(x0,y0)连续，可偏导，可微及有一阶连续偏导数彼此之间的关系：
有一阶连续偏导数 ==>可微 ==> 连续；
可微 ==> 可偏导；
可偏导 =≠> 连续。
2、如果 f(x,y) 在 (x0,y0) 处可微，则(x0,y0)为f(x,y)极值点的必要条件是：fx(x0,y0) = fy(x0,y0) = 0。
绛旓細1銆浜屽厓鍑芥暟z=f(x,y)鍦ㄧ偣(x0,y0)杩炵画锛屽彲鍋忓锛屽彲寰強鏈変竴闃惰繛缁亸瀵兼暟褰兼涔嬮棿鐨勫叧绯伙細鏈変竴闃惰繛缁亸瀵兼暟 ==>鍙井 ==> 杩炵画锛涘彲寰 ==> 鍙亸瀵硷紱鍙亸瀵 =鈮> 杩炵画銆2銆佸鏋 f(x,y) 鍦 (x0,y0) 澶勫彲寰紝鍒(x0,y0)涓篺(x,y)鏋佸肩偣鐨勫繀瑕佹潯浠舵槸锛fx(x0,y0) = fy(x0,y0...
绛旓細鍑芥暟Z=f(x,y)鍦(0,0)鐐瑰彲寰==>鍑芥暟Z=f(x,y)鍦(0,0)鐐硅繛缁==>鍑芥暟Z=f(x,y)鍦(0,0)鐐归偦鍩熷唴鏈夊畾涔夛紱鍑芥暟Z=f(x,y)鍦(0,0)鐐瑰彲寰==>鍑芥暟Z=f(x,y)鍦(0,0)鐐瑰亸瀵兼暟瀛樺湪锛涘嚱鏁癦=f(x,y)鍦(0,0)鐐瑰亸瀵兼暟瀛樺湪鈮>鍑芥暟Z=f(x,y)鍦(0,0)鐐硅繛缁紱鍑芥暟Z=f(x,y)鍦(0...
绛旓細鍑芥暟Z=f(x,y)鍦(0,0)鐐瑰亸瀵兼暟瀛樺湪鈮>鍑芥暟Z=f(x,y)鍦(0,0)鐐瑰彲寰紱鍑芥暟Z=f(x,y)鍦(0,0)鐐归偦鍩熷唴鍋忓鏁板瓨鍦ㄤ笖鍦(0,0)鐐硅繛缁==>鍑芥暟Z=f(x,y)鍦(0,0)鐐瑰彲寰
绛旓細浜屽厓鍑芥暟z=f锛坸锛寉锛夌殑浜岄樁鍋忓鏁板叡鏈夊洓绉嶆儏鍐碉細锛1锛∂z²/∂x²=[∂锛∂z/∂x锛塢/ ∂x锛涳紙2锛∂z²/∂y ²=[∂锛∂z/∂y锛塢/ ∂y锛涳紙3锛∂z²/锛∂y ∂...
绛旓細浜屻佸亸瀵煎叕寮忕殑鍑犱綍鎰忎箟 鍋忓鏁扮殑鍑犱綍鎰忎箟鏄〃绀哄浐瀹氶潰涓婁竴鐐圭殑鍒囩嚎鏂滅巼銆傚浜浜屽厓鍑芥暟z=f(x,y)锛屽湪鐐(x0,y0)澶勭殑鍋忓鏁癴'x(x0,y0)琛ㄧず鍥哄畾闈笂璇ョ偣瀵箈杞寸殑鍒囩嚎鏂滅巼锛宖'y(x0,y0)琛ㄧず鍥哄畾闈笂璇ョ偣瀵箉杞寸殑鍒囩嚎鏂滅巼銆備笁銆佸亸瀵兼暟鐨勫畾涔 鍋忓鏁版槸澶氬厓鍑芥暟姹傚鐨勪竴绉嶅舰寮忥紝瀹冭〃绀哄綋鍑芥暟鐨勬煇...
绛旓細鍋忓鏁 f'x(x0,y0) 琛ㄧず鍥哄畾闈笂涓鐐瑰 x 杞寸殑鍒囩嚎鏂滅巼锛涘亸瀵兼暟 f'y(x0,y0) 琛ㄧず鍥哄畾闈笂涓鐐瑰 y 杞寸殑鍒囩嚎鏂滅巼銆傞珮闃跺亸瀵兼暟锛氬鏋浜屽厓鍑芥暟 z=f(x,y) 鐨勫亸瀵兼暟 f'x(x,y) 涓 f'y(x,y) 浠嶇劧鍙锛岄偅涔堣繖涓や釜鍋忓鍑芥暟鐨勫亸瀵兼暟绉颁负 z=f(x,y) 鐨勪簩闃跺亸瀵兼暟銆備簩鍏冨嚱鏁扮殑浜岄樁...
绛旓細xy+z = arctan(x+z)涓よ竟瀵 x 姹傚亸瀵锛寉 + ∂z/∂x = (1+∂z/∂x)/[1+(x+z)^2]y[1+(x+z)^2] + [1+(x+z)^2]∂z/∂x = 1+∂z/∂x ∂z/∂x = {1 - y[1+(x+z)^2]}/(x+z)^2;涓よ竟瀵 y ...
绛旓細浜屽厓鍑芥暟z=f(x,y)琛ㄧず涓涓┖闂存洸闈紱鍏充簬x鍋忓鍑芥暟,鍦ㄦ眰鐨勬椂鍊檡鏆傛椂涓嶅彉锛屽垯鐩稿綋鍙栦换鎰y=y0涓烘埅闈㈡椂锛屽湪璇ユ埅闈笂鐨勬洸绾縵=g(x) 鐨勫鏁般傛敞鎰忥紝姝ゆ椂y鐪嬩綔甯告暟
绛旓細锛1锛夊厛鍒ゆ柇杩炵画鎬э紝鍗宠璁(x,y)鈫(x0,y0)鏃锛孎(x,y)鐨勬瀬闄愬兼槸鍚︾瓑浜鍑芥暟鍊糉(x0,y0)銆傝嫢涓嶈繛缁紝鍒欎笉鍙井锛涜嫢杩炵画锛岀户缁笅涓姝 锛2锛夋眰(x0,y0)澶勭殑鍋忓鏁般傝嫢鍋忓鏁拌嚦灏戞湁涓涓笉瀛樺湪锛屽垯涓嶅彲寰紱鑻ヤ袱涓亸瀵兼暟閮藉瓨鍦紝缁х画涓嬩竴姝 锛3锛夎鏄庘柍z锛Fx(x0,y0)鈻硏锛Fy(x0,y0)鈻...
