KE至肆上 5

 

TO T焉兴 纤鲜饲奄塘

 

溟徜殛狍哚 锺轶祜 麸 赳轲腼 镫镪腌颃灬麸 暹磲 镩 戾 狨艮 麸 溟痣稞 镫镪腌颃灬麸. 五觊碥戾 戾 蓓 锺栾泾黹 疳襻腚珉屦唣邃 R3 :

= [, 鈃 [, 鋆 [, 鎉,

溏脶滢 麸 簖盹腼 豉 箸戾啭 (x, y, z) R3

x ,     y ,    z ,

赆 扉 篚碥耵珞 f : R 镳镞 暹磲 鲴徙燧礴 篝 .

阁豉 1 ={ = x0 < x1... < xn = } 溟犰蓠轶 麸 [, 鈃, 2 = { = y0 < y1... < ym = } 扉 溟犰蓠轶 麸 [, 鋆 赆 3 ={ = z0 < z1... < zs = } 扉 溟犰蓠轶 [, 鎉. 溟犰蓠轶 , 篚焘镫殒屙 戾 = 1 2 3 , 狃雉咫暹翎 狃  翎 锺栾泾黹 疳襻腚珉屦唣邃 祜聆掾 ijk = [xi-1, xi] [yj-1, yj] [zk-1, zk], i = 1,..., n, j = 1,..., m, k = 1,..., s.

阁豉 mijk = inf{f(x, y, z) : (x, y, z) ijk} ijk = sup{{f(x, y, z) : (x, y, z) ijk}. 拣 篝珥 疱襁痿 豉 篚磲耵摅妁 扉狎 戾翎怆玺掾 锺哝秕戾 麸 贶豉 赆 麸 茼 荑耧轶灬 翮 f  瘃矧 翮 溟犰蓠轶  孱掾:

秕 vol (ijk) 觑 ijk.

f 栳 胼沐翎 镫镪腌颃箝扃 篝 犴 躔荞麇 祜磲溟挈 狁殍禳 ..

L(f, P) O U(f, Q)

汩 弪 糸 溟犰羼唧彘 P, Q 麸 .

另 f 暹磲 镫镪腌颃箝扃, 狁殍禳 栳 胼沐翎 镫镪朕聩灬 f 篝 赆 栳 篚焘镫哝弭衢 戾

溟痣 镫镪朕聩灬 暹溽戾  犴 f 暹磲 篚礤鬓 篝 尻酎 唧 狃 蓓 疱疱襻箪蓓 狁殍禳 狃 赆祓弪 酎翦 暹磲 镫镪腌颃箝扃. 郁 赳轲朦 镫镪朕聩灬 蓣秕戾 麸 咪轱 狃雉蓦弩灬 犴 犴糸赆翎篝摅秕戾 糸 赆祓弪 戾 屦轹茼彘弪. (溴唪 翎 桢揿狒 篝 赍鲕脶轱 2 [M弭茆狍 篝 赍. 2]).

响镞 祓锺稞戾 磲 躔镫镢唧秕戾 蓓 赳轲朦 镫镪朕聩灬 戾 翮 黢摅 屦茈腌膣 镫镪腌聩燔豉:

儒珈: 阁豉 , : [, 鈃 R 潺 脲咤 篚磲耵摅彘 .. (x) (x) ,x [, 鈃 赆 , 潺 瘃徙灬糸贻 脲咤 篚磲耵摅彘 锺轶燧礤 篝 簖盹腼 豉 (x, y) R2

x ,         (x) y (x).

阁豉 麸 簖盹腼 豉 箸戾啭 (x, y, z) R3 ..

x ,     (x) y (x)     赆     (x) z (x)

f: A R 扉 篚礤鬓 篚碥耵珞. 渣翦

馏贽箦轵

1. 歪 躔镫镢唧弭 麸 镫镪朕聩灬

    戾 = [0, 2] [0, 2] [0, 2]. [她箸]

2. 埋暹翦 麸 觑 翮 疱耖秣掾 痫 疱耖觌暹弭衢 戾翎铨 豉

           z = x2 + 3y2 z = 12 2x2. [她箸]

3. 阁豉 f 扉 篚礤鬓 篚碥耵珞, 祓茈脶 戾 贻眙耧 麸 箸戾唢 (a, b, c) 赆 彡暨磲 > 0 Vol() 觑 . 歪 狃镤暹铄翦 

[她箸]

4. N 躔镫镢唧桢 觑 疱耖秣掾 痫 疱耖觌暹弭衢 戾翎铨 豉

          x2 + y2 = 2, x + y + z = 4, z = 0 . [她箸]

 

[绣耖鬻屙]