求曲面的切平面方程及法线方程 怎么求切平面方程和法线方程
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\u628a\u70b9P\u5e26\u5165\u5f97\u5230n=(1, -2, 2/3)
\u53ef\u4ee5\u53d6n0=(3, -6, 2)
\u6240\u4ee5\u5207\u5e73\u9762\u4e3a3(x-2)-6(y+1)+2(z-3)=0
\u6574\u7406\u540e3x-6y+2z=18
\u6cd5\u7ebf\u4e3a(x-2)/3=(y+1)/(-6)=(z-3)/2
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绛旓細Fx=-1/x Fy=-1+1/y Fz=1 灏哅锛1锛1锛1锛夊垎鍒唬鍏ュ緱娉曞悜閲忥紙-1锛0锛1锛夌敤鐐规硶寮廇(X-1)+B(Y-1)+C(Z-1)=0灏辫兘鐩存帴鍐欏嚭璇鍒囧钩闈㈢殑鏂圭▼浜嗭紒(A,B,C)灏辨槸浣犳眰鍑烘潵鐨勬硶鍚戦噺 浠ｅ叆寰梲-x=0 娉曠嚎鏂圭▼锛氾紙x-1锛/锛-1锛=(z-1)/(1)绫诲瀷 涓銆佹埅璺濆紡 璁骞抽潰鏂圭▼涓篈x+By+Cz+D=...
绛旓細娉曠嚎涓庡垏闈㈢殑瀹氫箟</娉曠嚎锛屽氨鍍忕毊鐞冧笂鐨勭粡绾嚎锛屾槸鍨傜洿浜庢洸闈㈠湪鏌愮偣P鐨勭洿绾匡紝瀹冪殑鏂瑰悜鎸囧悜鏇查潰鐨鏈闄″抄澶勩傚湪鏁板涓婏紝娉曞悜閲N鍙互閫氳繃鍑芥暟鐨勬搴︽潵璁＄畻锛屽嵆锛歂 = ∇F(P)鑰鍒囧钩闈鍒欐槸杩欎釜娉曠嚎鍦ㄧ偣P澶勭殑鎶曞奖锛屽畠鏄笌鏇查潰鍦ㄧ偣P澶勬渶鎺ヨ繎鐨勫钩闈傚垏骞抽潰鐨鏂圭▼鍙互鍐欎负锛欶(x, y, z) - F(...
绛旓細zx=2x/(x²+y²)zy=2y/(x²+y²)鍦ㄥ垏鐐瑰锛寊x=2锛寊y=0 鎵浠ワ紝娉曞悜閲忎负 n=(2锛0锛-1)鍒囧钩闈㈡柟绋涓 2(x-1)-x=0 鍗筹紝2x-z-2=0 娉曠嚎鏂圭▼涓 (x-1)/2=y/0=z/(-1)
绛旓細∂F/∂y,∂F/∂z} 鍗 {x/2,2y/9,-1}锛涚偣 (-2,-3,2) 澶鐨勫垏骞抽潰娉曠嚎鏂瑰悜鏁帮細{-1,-2/3,-1} 锛堟垨{1,2/3,1}锛夛紱鎸囧畾鐐瑰鍒囧钩闈㈡柟绋锛(x+2)+2(y+3)/3+(z-2)=0锛屽寲绠鍚庯細3x+2y+3z+6=0锛涘搴娉曠嚎鏂圭▼锛(x+2)=3(y+3)/2=(z-2)锛
绛旓細鎵浠ュ叾娉曞悜閲忎负杩欎袱涓悜閲忕殑鍙夌Н锛屾墍浠ヤ负閭ｄ釜琛屽垪寮 Xu=cosv Yu=sinv Zu=0锛孹v=-usinv锛孻v=ucosv Zv=a锛屾墍浠ヨ鍒楀紡缁撴灉涓 锛坅sinv锛宎cosv锛寀锛夛紝灏唘=1锛寁=蟺/2锛屼唬鍏ュ緱锛1锛0锛1锛夛紝鍒囩偣鍧愭爣涓猴紙0锛1锛屜/2锛夛紝鈭鍒囧钩闈㈡柟绋涓猴紙鐐规硶鎷級x+z-蟺/2=0锛娉曠嚎鏂圭▼鍒欎笉蹇呭璇 ...
绛旓細F(x銆亂銆亃)=x²+2y²+3z²-21 n=锛團x銆丗y銆丗z锛=锛2x銆4y銆6z锛塶|(1銆-2銆2)=锛2銆-8銆12锛鍒囧钩闈㈡柟绋锛2锛坸-1锛-8锛坹+2锛+12锛坺-2锛=0 2x-8y+12z-42=0 娉曠嚎鏂圭▼锛氾紙x-1锛/2=锛坹+2锛/锛-8锛=锛坺-2锛/12 ...
绛旓細浠 f(x锛寉锛寊)=z-e^z+2xy-3 锛屽垯 f 瀵 x銆亂銆亃 鐨勫亸瀵兼暟鍒嗗埆涓 2y銆2x銆1-e^z 锛岀敱姝ゅ緱鐐癸紙1锛2锛0锛夊鐨勫垏骞抽潰鐨勬硶鍚戦噺涓 n=锛4锛2锛0锛夛紝鍥犳鍒囧钩闈㈡柟绋涓 4(x-1)+2(y-2)=0 锛屽嵆 2x+y-4=0 锛娉曠嚎鏂圭▼涓 (x-1)/4=(y-2)/2=(z-0)/0 銆
绛旓細绠鍗曞垎鏋愪竴涓嬶紝璇︽儏濡傚浘鎵绀
绛旓細瀵逛簬鏇查潰鍦ㄦ煇鐐鐨勫垏骞抽潰鍜屾硶绾挎柟绋嬬殑姹傝В锛屽彲浠ラ噰鍙栦互涓嬫楠わ細1銆侀鍏堬紝璁惧畾鏇查潰鐨勬柟绋涓簓^2+z^2=2x銆傝嫢浠ヨ鏂圭▼涓哄熀纭锛屽洿缁昘杞存棆杞竴鍛紝鎵褰㈡垚鐨勬棆杞鏇查潰鏂圭▼涓篎=0锛寉=0銆傚悓鐞嗭紝鍥寸粫Z杞存棆杞竴鍛紝鎵褰㈡垚鐨勬棆杞洸闈㈡柟绋嬩负F=卤鈭(0)銆2銆佸湪鏃嬭浆杩囩▼涓紝鍥哄畾涓涓彉閲忥紝鑰屽皢鍙︿竴涓彉閲忕殑...
绛旓細璁綟锛坸,y,z)=x2-y2-3z 鍒橣x(x,y,z)=2x,Fy(x,y,z)=-2y,Fz(x,y,z)=-3 Fx(2,-1,1)=4,Fy(2,-1,1)=2,Fxz(2,-1,1)=-3 鏇查潰x2-y2-3z=0涓婄偣锛2锛-1,1锛夊鐨勫垏骞抽潰鏂圭▼涓4锛坸-2)+2(y+2)-3(z-1)=0 娉曠嚎鏂圭▼鏄紙x-2)/4=(y+2)/2=(z-1)/(-3)
