逝至肆上 2

 

TO 纳兴 纤鲜饲奄塘

 

阁豉 麸 锺栾泾黹 疳襻腚珉襻祆 a x b, c y d 篝 屦唣邃 f : D R 扉 鲴徙燧礴 篚碥耵珞 (溏脶滢 |f(x, y)| M 汩 贶桢 (x, y) 篝 ).

阁豉 1 = {a = x0 ,x1,...,xk = b} 扉 溟犰蓠轶 麸 [a, b] 2 = {a = x0 ,x1,...,xs = b} 扉 溟犰蓠轶 麸 [c, d]. 燥 簖盹腼 豉 翦赳徙 [xi, xi+1][yj, yj+1] 栳 胼沐翎 溟犰蓠轶 麸 赆 栳 篚焘镫哝弭衢 戾 = 1 2.

阁豉 mij = inf{f(x, y) : x[xi, xi+1] 赆 y[yj, yj+1]} ij = sup{f(x, y) : x[xi, xi+1] 赆 y[yj, yj+1]}. 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:

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

儒珈 1: f 暹磲 篚礤鬓 篝 酎翦 暹磲 镫镪腌颃箝扃 篝 .

甜锺稞戾 磲 狃镤暹铒蹯 翮 疳襻贶豉 沐磉赍躞 麸 桢揿狒矧 1.

儒珈 2: f 暹磲 鲴徙燧礴 赆 篚礤鬓 篝 尻酎 唧 狃 翎 箸戾哚 痫 怦唧觑眙衢 疖睐 箦 蓓 疱疱襻箪蓓 狁殍禳 狃 赆祓弪, 酎翦 暹磲 镫镪腌颃箝扃. [M弭茆狍 篝 赍. 5]

儒珈 3: 阁豉  镩 f, g 暹磲 镫镪腌颃箝戾 篝 赆 , 暹磲 瘃徙灬糸觑. 渣翦

1. f + 暹磲 镫镪腌颃箝扃.

2.

3. f g 酎翦     ([硼轶赳秭] 篝珥 荏赙箸 3 赍.5)

拈徜秣殛 镫镪腌颃灬翎

儒珈 4: 阁豉 = [a, b][c, d] f 扉 镫镪腌颃箝扃 篚碥耵珞 篝 . 另 汩 贶桢 x 篝 [a, b] 麸 镫镪朕聩灬

躔荞麇, 酎翦

阁豉 扉 鲴徙燧礴 疱耖秣 篝 屦唣邃, 蓓 锺栾泾黹 疳襻腚珉襻祆 痫 翮 疱耖蓣彘. 赆 f 扉 篚碥耵珞 锺轶燧礴 篝珥 . O襁骘蹯

隔箝, 犴 fA 暹磲 镫镪腌颃箝扃 篝 , 祓锺稞戾 磲 锺唧秕戾 麸 镫镪朕聩灬 翮 f 篝  孱掾:

剪犴 疱耖秣 疱耖泷荟弭衢 狃 糸 犴轶玺弪 a x b , (x) y (x) 戾 糸 , 脲咤 篚磲耵摅彘 酎翦 蓣秕戾:

儒珈 5: 燥 镫镪朕聩灬 扉狎 篚碥耵珞珧 f 篝珥 疳襻疖睐 疱耖秣 暹磲

 

馏贽箦轵

1. N 躔镫镢轶栾 翎 镫镪腌颃灬翎

   [她箸]

2. 躔镫镢轶桢 麸 镫镪朕聩灬 翮 篚碥耵珞珧 f(x, y) = x2y2 疖睐 篝珥 疱耖秣 痫 疱耖泷荟弭衢 狃 翮 犴轶玺 |x| + |y| 1. [她箸]

3. N 躔镫镢轶桢 麸 屐忉潼 翮 疱耖秣掾 戾翎铨 麸 茴镯 豉 x 赆 翮 y = x2 x = 0 x = 1. [她箸]

 

[绣耖鬻屙]