{"id":35275,"date":"2024-12-20T13:00:27","date_gmt":"2024-12-20T13:00:27","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=35275"},"modified":"2025-12-11T17:07:24","modified_gmt":"2025-12-11T17:07:24","slug":"%e0%a4%b5%e0%a4%be%e0%a4%af%e0%a4%b0%e0%a4%b8%e0%a5%8d%e0%a4%9f%e0%a5%8d%e0%a4%b0%e0%a4%be%e0%a4%b8-%e0%a4%95%e0%a4%be-%e0%a4%9a%e0%a4%b0%e0%a4%ae-%e0%a4%ae%e0%a4%be%e0%a4%a8-%e0%a4%aa%e0%a5%8d","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/hi\/%e0%a4%b5%e0%a4%be%e0%a4%af%e0%a4%b0%e0%a4%b8%e0%a5%8d%e0%a4%9f%e0%a5%8d%e0%a4%b0%e0%a4%be%e0%a4%b8-%e0%a4%95%e0%a4%be-%e0%a4%9a%e0%a4%b0%e0%a4%ae-%e0%a4%ae%e0%a4%be%e0%a4%a8-%e0%a4%aa%e0%a5%8d\/","title":{"rendered":"\u0935\u093e\u092f\u0930\u0938\u094d\u091f\u094d\u0930\u093e\u0938 \u0915\u093e \u091a\u0930\u092e \u092e\u093e\u0928 \u092a\u094d\u0930\u092e\u0947\u092f"},"content":{"rendered":"<style>\np, ul, ol{\ntext-align: justify;\n}\nh1{\ntext-align:center;\ntext-transform: uppercase;\n}\nh2{\ntext-align:center;\ntext-transform: uppercase;\nfont-size:24pt;\n}\nh3 { \n    text-align: center;\n    text-transform: uppercase;\n    font-size: 24px !important;\n}\n<\/style>\n<h1>\u0935\u093e\u092f\u0930\u0938\u094d\u091f\u094d\u0930\u093e\u0938 \u0915\u0947 \u091a\u0930\u092e \u092e\u093e\u0928 \u092a\u094d\u0930\u092e\u0947\u092f<\/h1>\n<p style=\"text-align:center;\"><em>\u0915\u094d\u092f\u094b\u0902 \u0905\u0928\u0941\u0915\u0942\u0932\u0928 \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0907\u0924\u0928\u0947 \u0905\u0927\u093f\u0915 \u0938\u092e\u0938\u094d\u092f\u093e\u0913\u0902 \u092e\u0947\u0902 \u092a\u094d\u0930\u093e\u092f\u0903 \u092f\u0939 \u092e\u093e\u0928 \u0932\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u201c\u0905\u0927\u093f\u0915\u0924\u092e \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u092e\u0947\u0902 \u0939\u0948\u201d \u092f\u093e \u201c\u0928\u094d\u092f\u0942\u0928\u0924\u092e \u0905\u0935\u0936\u094d\u092f \u092e\u094c\u091c\u0942\u0926 \u0939\u0948\u201d \u0915\u093f\u0938\u0940 \u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0905\u0902\u0924\u0930\u093e\u0932 \u092e\u0947\u0902, \u091c\u092c\u0915\u093f \u0935\u093e\u0938\u094d\u0924\u0935 \u092e\u0947\u0902 \u0910\u0938\u093e \u0939\u094b\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u094b\u0908 \u0905\u0928\u093f\u0935\u093e\u0930\u094d\u092f\u0924\u093e \u0928\u0939\u0940\u0902 \u0939\u0948? <strong>\u0935\u093e\u092f\u0930\u0938\u094d\u091f\u094d\u0930\u093e\u0938 \u092a\u094d\u0930\u092e\u0947\u092f<\/strong> \u0935\u0939 \u0915\u0921\u093c\u0940 \u0939\u0948 \u091c\u094b \u0907\u0938 \u092a\u0939\u0947\u0932\u0940 \u092e\u0947\u0902 \u0915\u092e\u0940 \u0925\u0940: \u092f\u0939 \u0938\u0941\u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 \u0915\u093f \u090f\u0915 \u092c\u0902\u0926 \u0914\u0930 \u092a\u0930\u093f\u092c\u0926\u094d\u0927 \u0905\u0902\u0924\u0930\u093e\u0932 \u092a\u0930 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u090f\u0915 \u0938\u0924\u0924 \u092b\u0932\u0928 \u0928 \u0915\u0947\u0935\u0932 \u092a\u0930\u093f\u092c\u0926\u094d\u0927 \u0939\u094b\u0924\u093e \u0939\u0948, \u092c\u0932\u094d\u0915\u093f \u0905\u092a\u0928\u0947 \u091a\u0930\u092e \u092e\u093e\u0928\u094b\u0902 \u0915\u094b \u0935\u093e\u0938\u094d\u0924\u0935 \u092e\u0947\u0902 \u0917\u094d\u0930\u0939\u0923 \u092d\u0940 \u0915\u0930\u0924\u093e \u0939\u0948\u0964 \u0907\u0938 \u0932\u0947\u0916 \u092e\u0947\u0902 \u0939\u092e \u0907\u0938\u0915\u0947 \u0915\u0925\u0928 \u0915\u0940 \u0938\u092e\u0940\u0915\u094d\u0937\u093e \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e, \u0938\u0902\u092a\u0940\u0921\u094d\u092f\u0924\u093e \u0914\u0930 \u0938\u0941\u092a\u094d\u0930\u0940\u092e\u094b \u0915\u0947 \u0938\u094d\u0935\u092f\u0902\u0938\u093f\u0926\u094d\u0927 \u092a\u0930 \u0906\u0927\u093e\u0930\u093f\u0924 \u090f\u0915 \u0915\u0920\u094b\u0930 \u092a\u094d\u0930\u092e\u093e\u0923 \u0915\u094b \u0935\u093f\u0938\u094d\u0924\u093e\u0930 \u0938\u0947 \u0928\u093f\u0930\u094d\u092e\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u0924\u0925\u093e \u0938\u0902\u0915\u094d\u0937\u093f\u092a\u094d\u0924 \u0938\u092e\u0941\u091a\u094d\u091a\u092f\u094b\u0902 \u092a\u0930 \u0938\u0924\u0924 \u092b\u0932\u0928\u094b\u0902 \u0915\u0940 \u0906\u0927\u0941\u0928\u093f\u0915 \u0935\u094d\u092f\u093e\u0916\u094d\u092f\u093e \u092a\u0930 \u091f\u093f\u092a\u094d\u092a\u0923\u0940 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964 \u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f \u092f\u0939 \u0939\u0948 \u0915\u093f \u0905\u0902\u0924 \u092e\u0947\u0902 \u0906\u092a \u0928 \u0915\u0947\u0935\u0932 \u0907\u0938 \u092a\u094d\u0930\u092e\u0947\u092f \u0915\u094b \u090f\u0915 \u0935\u093e\u0915\u094d\u092f \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u092f\u093e\u0926 \u0930\u0916\u0947\u0902, \u092c\u0932\u094d\u0915\u093f \u092f\u0939 \u092d\u0940 \u0938\u092e\u091d\u0947\u0902 \u0915\u093f \u092f\u0939 \u0938\u0924\u094d\u092f \u0915\u094d\u092f\u094b\u0902 \u0939\u0948 \u0914\u0930 \u092f\u0939 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923, \u0905\u0928\u0941\u0915\u0942\u0932\u0928 \u0914\u0930 \u0905\u0928\u0941\u092a\u094d\u0930\u092f\u0941\u0915\u094d\u0924 \u092e\u0949\u0921\u0932\u094b\u0902 \u092e\u0947\u0902 \u092c\u093e\u0930 \u092c\u093e\u0930 \u0915\u094d\u092f\u094b\u0902 \u092a\u094d\u0930\u0915\u091f \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/em><\/p>\n<p style=\"text-align:center;\"><b>\u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0947 \u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f<\/b><\/p>\n<ol>\n<li>\n    <strong>\u0935\u093e\u092f\u0930\u0938\u094d\u091f\u094d\u0930\u093e\u0938 \u092a\u094d\u0930\u092e\u0947\u092f \u0915\u0947 \u0915\u0925\u0928 \u0915\u094b \u0938\u092e\u091d\u0928\u093e\u0964<\/strong><br \/>\n    \u092a\u094d\u0930\u092e\u0947\u092f \u0915\u0940 \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e\u0913\u0902 (\u0938\u0924\u0924 \u092b\u0932\u0928 \u090f\u0915 \u092c\u0902\u0926 \u0914\u0930 \u092a\u0930\u093f\u092c\u0926\u094d\u0927 \u0905\u0902\u0924\u0930\u093e\u0932 <span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span> \u092e\u0947\u0902) \u0914\u0930 \u0907\u0938\u0915\u0940 \u092e\u0941\u0916\u094d\u092f \u092a\u0930\u093f\u0923\u0924\u093f\u092f\u094b\u0902: \u092a\u0930\u093f\u092c\u0926\u094d\u0927\u0924\u093e \u0924\u0925\u093e \u0905\u0927\u093f\u0915\u0924\u092e \u0914\u0930 \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u092e\u093e\u0928\u094b\u0902 \u0915\u0947 \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u0915\u0940 \u0938\u091f\u0940\u0915 \u092a\u0939\u091a\u093e\u0928 \u0915\u0930\u0928\u093e\u0964\n  <\/li>\n<li>\n    <strong>\u0938\u0902\u092a\u0940\u0921\u094d\u092f\u0924\u093e \u0915\u0947 \u0938\u0902\u0926\u0930\u094d\u092d \u092e\u0947\u0902 \u0935\u093e\u092f\u0930\u0938\u094d\u091f\u094d\u0930\u093e\u0938 \u092a\u094d\u0930\u092e\u0947\u092f \u0915\u0940 \u0935\u094d\u092f\u093e\u0916\u094d\u092f\u093e \u0915\u0930\u0928\u093e\u0964<\/strong><br \/>\n    \u0906\u0927\u0941\u0928\u093f\u0915 \u092d\u093e\u0937\u093e \u092e\u0947\u0902 \u092a\u0930\u093f\u0923\u093e\u092e \u0915\u094b \u0938\u0942\u0924\u094d\u0930\u092c\u0926\u094d\u0927 \u0915\u0930\u0928\u093e: \u0938\u0924\u0924 \u092b\u0932\u0928 \u0938\u0902\u0915\u094d\u0937\u093f\u092a\u094d\u0924 \u0938\u092e\u0941\u091a\u094d\u091a\u092f\u094b\u0902 \u0915\u094b \u0910\u0938\u0947 \u0938\u092e\u0941\u091a\u094d\u091a\u092f\u094b\u0902 \u092e\u0947\u0902 \u092a\u094d\u0930\u0924\u093f\u091a\u093f\u0924\u094d\u0930\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902 \u091c\u0939\u093e\u0901 \u091a\u0930\u092e \u092e\u093e\u0928 \u0909\u092a\u0932\u092c\u094d\u0927 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902, \u091c\u093f\u0938\u0938\u0947 <span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span> \u0915\u0947 \u092e\u093e\u092e\u0932\u0947 \u0915\u094b \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0947 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0922\u093e\u0901\u091a\u0947 \u0938\u0947 \u091c\u094b\u0921\u093c\u093e \u091c\u093e \u0938\u0915\u0947\u0964\n  <\/li>\n<li>\n    <strong>\u0935\u093e\u092f\u0930\u0938\u094d\u091f\u094d\u0930\u093e\u0938 \u092a\u094d\u0930\u092e\u0947\u092f \u0915\u094b \u0905\u0928\u0941\u0915\u0942\u0932\u0928 \u0938\u092e\u0938\u094d\u092f\u093e\u0913\u0902 \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0915\u0930\u0928\u093e\u0964<\/strong><br \/>\n    \u090f\u0915 \u091a\u0930 \u0915\u0940 \u0905\u0928\u0941\u0915\u0942\u0932\u0928 \u0938\u092e\u0938\u094d\u092f\u093e\u0913\u0902 \u092e\u0947\u0902, \u091a\u093e\u0939\u0947 \u0938\u0948\u0926\u094d\u0927\u093e\u0902\u0924\u093f\u0915 \u0939\u094b\u0902 \u092f\u093e \u0905\u0928\u0941\u092a\u094d\u0930\u092f\u0941\u0915\u094d\u0924, \u0905\u0927\u093f\u0915\u0924\u092e \u0914\u0930 \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u0915\u0947 \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u0915\u0947 \u0932\u093f\u090f \u0907\u0938 \u092a\u094d\u0930\u092e\u0947\u092f \u0915\u0940 \u092e\u094c\u0932\u093f\u0915 \u092d\u0942\u092e\u093f\u0915\u093e \u0915\u094b \u092a\u0939\u091a\u093e\u0928\u0928\u093e\u0964\n  <\/li>\n<\/ol>\n<p style=\"text-align:center;\"><b><u>\u0935\u093f\u0937\u092f-\u0938\u0942\u091a\u0940<\/u>:<\/b><br \/>\n<a href=\"#1\"><b>\u092a\u0930\u093f\u091a\u092f<\/b><\/a><br \/>\n<a href=\"#2\"><b>\u0935\u093e\u092f\u0930\u0938\u094d\u091f\u094d\u0930\u093e\u0938 \u092a\u094d\u0930\u092e\u0947\u092f \u0915\u093e \u0915\u0925\u0928<\/b><\/a><br \/>\n<a href=\"#3\">\u092a\u094d\u0930\u092e\u093e\u0923<\/a><br \/>\n<a href=\"#4\">\u091a\u0930\u0923 1: <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span> \u092a\u0930 \u092c\u093f\u0902\u0926\u0941-\u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e<\/a><br \/>\n<a href=\"#5\">\u091a\u0930\u0923 2: \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0916\u0941\u0932\u093e \u0906\u0935\u0930\u0923<\/a><br \/>\n<a href=\"#6\">\u091a\u0930\u0923 3: <span dir=\"ltr\">[a,b]<\/span> \u0915\u0940 \u0938\u0902\u092a\u0940\u0921\u094d\u092f\u0924\u093e \u0914\u0930 \u0938\u0940\u092e\u093f\u0924 \u0909\u092a-\u0906\u0935\u0930\u0923<\/a><br \/>\n<a href=\"#7\">\u091a\u0930\u0923 4: \u090f\u0915 \u0910\u0938\u093e <span class=\"katex-eq\" data-katex-display=\"false\">\\delta<\/span> \u0928\u093f\u0930\u094d\u092e\u093f\u0924 \u0915\u0930\u0928\u093e \u091c\u094b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u092a\u0930 \u0928\u093f\u0930\u094d\u092d\u0930 \u0928 \u0939\u094b (\u0938\u092e\u093e\u0928 \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e)<\/a><br \/>\n<a href=\"#8\">\u091a\u0930\u0923 5: \u0938\u092e\u093e\u0928 \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e \u0938\u0947 <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u0915\u0940 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span> \u092a\u0930 \u092a\u0930\u093f\u092c\u0926\u094d\u0927\u0924\u093e<\/a><br \/>\n<a href=\"#9\">\u091a\u0930\u0923 6: \u0905\u0927\u093f\u0915\u0924\u092e \u0914\u0930 \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u092e\u093e\u0928\u094b\u0902 \u0915\u093e \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935<\/a><br \/>\n<a href=\"#10\"><b>\u0938\u0902\u092a\u0940\u0921\u094d\u092f\u0924\u093e \u0915\u0947 \u0938\u0902\u0926\u0930\u094d\u092d \u092e\u0947\u0902 \u0935\u094d\u092f\u093e\u0916\u094d\u092f\u093e \u0914\u0930 \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937<\/b><\/a>\n<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/N5mSrhJgCds\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><br \/>\n<a name=\"1\"><\/a><\/br><\/p>\n<h2>\u092a\u0930\u093f\u091a\u092f<\/h2>\n<p>\n<strong>\u0935\u093e\u092f\u0930\u0938\u094d\u091f\u094d\u0930\u093e\u0938 \u0915\u0947 \u091a\u0930\u092e \u092e\u093e\u0928 \u092a\u094d\u0930\u092e\u0947\u092f<\/strong> \u0909\u0928 \u092a\u0930\u093f\u0923\u093e\u092e\u094b\u0902 \u092e\u0947\u0902 \u0938\u0947 \u090f\u0915 \u0939\u0948 \u091c\u094b \u092f\u0926\u094d\u092f\u092a\u093f \u0938\u093e\u092e\u093e\u0928\u094d\u092f\u0924\u0903 \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0940 \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u0907\u0915\u093e\u0907\u092f\u094b\u0902 \u092e\u0947\u0902 \u092a\u094d\u0930\u0915\u091f \u0939\u094b\u0924\u093e \u0939\u0948, \u0935\u093e\u0938\u094d\u0924\u0935 \u092e\u0947\u0902 \u0905\u0928\u0941\u092a\u094d\u0930\u092f\u0941\u0915\u094d\u0924 \u0917\u0923\u093f\u0924 \u0915\u0947 \u090f\u0915 \u092c\u0921\u093c\u0947 \u092d\u093e\u0917 \u0915\u094b \u092e\u094c\u0928 \u0930\u0942\u092a \u0938\u0947 \u0938\u0939\u093e\u0930\u093e \u0926\u0947\u0924\u093e \u0939\u0948\u0964 \u091c\u092c \u092d\u0940 \u092d\u094c\u0924\u093f\u0915\u0940, \u0905\u0930\u094d\u0925\u0936\u093e\u0938\u094d\u0924\u094d\u0930 \u092f\u093e \u0938\u093e\u0902\u0916\u094d\u092f\u093f\u0915\u0940 \u092e\u0947\u0902 \u0939\u092e \u0915\u093f\u0938\u0940 \u092e\u093e\u0924\u094d\u0930\u093e \u0915\u094b \u0915\u0941\u091b \u092a\u094d\u0930\u0924\u093f\u092c\u0902\u0927\u094b\u0902 \u0915\u0947 \u0905\u0927\u0940\u0928 \u00ab\u0905\u0927\u093f\u0915\u0924\u092e\u00bb \u092f\u093e \u00ab\u0928\u094d\u092f\u0942\u0928\u0924\u092e\u00bb \u0915\u0930\u0928\u0947 \u0915\u0940 \u092c\u093e\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u092e\u0942\u0932 \u0930\u0942\u092a \u0938\u0947 \u0939\u092e \u090f\u0915 \u0910\u0938\u0940 \u0905\u0935\u0927\u093e\u0930\u0923\u093e \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930 \u0930\u0939\u0947 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902 \u091c\u094b \u0907\u0938 \u092a\u094d\u0930\u092e\u0947\u092f \u0915\u0940 \u0917\u093e\u0930\u0902\u091f\u0940 \u0915\u0947 \u092c\u0939\u0941\u0924 \u0928\u093f\u0915\u091f \u0939\u0948: \u0915\u093f \u090f\u0915 \u092c\u0902\u0926 \u0914\u0930 \u092a\u0930\u093f\u092c\u0926\u094d\u0927 \u0905\u0902\u0924\u0930\u093e\u0932 \u092a\u0930 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0938\u0924\u0924 \u092b\u0932\u0928 <strong>\u0938\u093f\u0930\u094d\u092b \u092a\u0930\u093f\u092c\u0926\u094d\u0927 \u0928\u0939\u0940\u0902 \u0939\u094b\u0924\u093e, \u092c\u0932\u094d\u0915\u093f \u0905\u092a\u0928\u0947 \u091a\u0930\u092e \u092e\u093e\u0928\u094b\u0902 \u0915\u094b \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0930\u0942\u092a \u0938\u0947 \u0917\u094d\u0930\u0939\u0923 \u092d\u0940 \u0915\u0930\u0924\u093e \u0939\u0948<\/strong>\u0964\n<\/p>\n<p>\n\u0938\u0939\u091c \u0930\u0942\u092a \u0938\u0947 \u092f\u0939 \u201c\u0938\u094d\u092a\u0937\u094d\u091f\u201d \u0932\u0917 \u0938\u0915\u0924\u093e \u0939\u0948 \u0915\u093f \u092f\u0926\u093f \u0939\u092e \u090f\u0915 \u0938\u0924\u0924 \u0935\u0915\u094d\u0930 \u0915\u094b \u0916\u0902\u0921 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u092a\u0930 \u091a\u093f\u0924\u094d\u0930\u093f\u0924 \u0915\u0930\u0947\u0902, \u0924\u094b \u0905\u0935\u0936\u094d\u092f \u0939\u0940 \u0915\u094b\u0908 \u0938\u092c\u0938\u0947 \u090a\u0901\u091a\u093e \u0914\u0930 \u0915\u094b\u0908 \u0938\u092c\u0938\u0947 \u0928\u0940\u091a\u093e \u092c\u093f\u0902\u0926\u0941 \u0939\u094b\u0917\u093e\u0964 \u0939\u093e\u0932\u093e\u0902\u0915\u093f, \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e\u0913\u0902 \u092e\u0947\u0902 \u091b\u094b\u091f\u0947 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0939\u0940 \u0907\u0938 \u0905\u0902\u0924\u0930\u094d\u091c\u094d\u091e\u093e\u0928 \u0915\u094b \u092a\u0942\u0930\u094d\u0923\u0924\u0903 \u0935\u093f\u092b\u0932 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092a\u0930\u094d\u092f\u093e\u092a\u094d\u0924 \u0939\u0948\u0902: \u092f\u0926\u093f \u0939\u092e \u0905\u0902\u0924\u0930\u093e\u0932 \u0915\u094b \u0916\u094b\u0932 \u0926\u0947\u0902, \u092f\u0926\u093f \u092b\u0932\u0928 \u0938\u0924\u0924 \u0928 \u0930\u0939\u0947 \u092f\u093e \u092f\u0926\u093f \u092a\u0930\u093f\u092d\u093e\u0937\u093e-\u0915\u094d\u0937\u0947\u0924\u094d\u0930 \u092a\u0930\u093f\u092c\u0926\u094d\u0927 \u0928 \u0939\u094b, \u0924\u094b \u0905\u0927\u093f\u0915\u0924\u092e \u0914\u0930 \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u0938\u0930\u0932\u0924\u093e \u0938\u0947 \u0917\u093e\u092f\u092c \u0939\u094b \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u0935\u093e\u092f\u0930\u0938\u094d\u091f\u094d\u0930\u093e\u0938 \u092a\u094d\u0930\u092e\u0947\u092f \u0907\u0938 \u0905\u0902\u0924\u0930\u094d\u091c\u094d\u091e\u093e\u0928 \u092e\u0947\u0902 \u0935\u094d\u092f\u0935\u0938\u094d\u0925\u093f\u0924\u0924\u093e \u0932\u093e\u0924\u093e \u0939\u0948 \u0914\u0930 \u0939\u092e\u0947\u0902 \u0938\u091f\u0940\u0915 \u0930\u0942\u092a \u0938\u0947 \u092c\u0924\u093e\u0924\u093e \u0939\u0948 \u0915\u093f <em>\u0915\u092c<\/em> \u0939\u092e \u0907\u0938 \u092a\u0930 \u092d\u0930\u094b\u0938\u093e \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 <em>\u0915\u094d\u092f\u094b\u0902<\/em>\u0964\n<\/p>\n<p>\n\u0938\u0948\u0926\u094d\u0927\u093e\u0902\u0924\u093f\u0915 \u0926\u0943\u0937\u094d\u091f\u093f\u0915\u094b\u0923 \u0938\u0947 \u092f\u0939 \u092a\u094d\u0930\u092e\u0947\u092f <strong>\u0938\u0902\u092a\u0940\u0921\u094d\u092f\u0924\u093e<\/strong> \u0915\u0940 \u0905\u0935\u0927\u093e\u0930\u0923\u093e \u0938\u0947 \u0917\u0902\u092d\u0940\u0930 \u092a\u094d\u0930\u0925\u092e \u092a\u0930\u093f\u091a\u092f \u0939\u0948: \u0906\u0927\u0941\u0928\u093f\u0915 \u092d\u093e\u0937\u093e \u092e\u0947\u0902 \u092f\u0939 \u0915\u0939\u0924\u093e \u0939\u0948 \u0915\u093f \u0938\u0924\u0924 \u092b\u0932\u0928 \u0938\u0902\u0915\u094d\u0937\u093f\u092a\u094d\u0924 \u0938\u092e\u0941\u091a\u094d\u091a\u092f\u094b\u0902 \u0915\u094b \u0938\u0902\u0915\u094d\u0937\u093f\u092a\u094d\u0924 \u0938\u092e\u0941\u091a\u094d\u091a\u092f\u094b\u0902 \u092e\u0947\u0902 \u092a\u094d\u0930\u0924\u093f\u091a\u093f\u0924\u094d\u0930\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964 \u0935\u094d\u092f\u093e\u0935\u0939\u093e\u0930\u093f\u0915 \u0926\u0943\u0937\u094d\u091f\u093f\u0915\u094b\u0923 \u0938\u0947, \u0907\u0938\u0915\u093e \u0905\u0930\u094d\u0925 \u092f\u0939 \u0939\u0948 \u0915\u093f \u090f\u0915 \u0906\u092f\u093e\u092e \u092e\u0947\u0902 \u0915\u0908 \u0905\u0928\u0941\u0915\u0942\u0932\u0928 \u0938\u092e\u0938\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u0938\u092e\u093e\u0927\u093e\u0928 \u0935\u093e\u0938\u094d\u0924\u0935 \u092e\u0947\u0902 \u092e\u094c\u091c\u0942\u0926 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902, \u0914\u0930 \u092f\u0939 \u092c\u093e\u0926 \u0915\u0947 \u092a\u0930\u093f\u0923\u093e\u092e\u094b\u0902 \u091c\u0948\u0938\u0947 <b>\u092e\u0927\u094d\u092f\u092e\u093e\u0928 \u092a\u094d\u0930\u092e\u0947\u092f<\/b> \u0924\u0925\u093e \u0905\u0902\u0924\u0924\u0903 \u0915\u0932\u0928 \u0915\u0947 \u092e\u0942\u0932 \u092a\u094d\u0930\u092e\u0947\u092f \u0915\u094b \u0936\u093e\u0902\u0924\u093f \u0938\u0947 \u0938\u092e\u091d\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0915\u0921\u093c\u0940 \u092c\u0928 \u091c\u093e\u0924\u093e \u0939\u0948\u0964\n<\/p>\n<p>\n\u0907\u0938 \u0916\u0902\u0921 \u092e\u0947\u0902 \u0939\u092e \u0935\u093e\u092f\u0930\u0938\u094d\u091f\u094d\u0930\u093e\u0938 \u092a\u094d\u0930\u092e\u0947\u092f \u0915\u093e \u0915\u0925\u0928 \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0915\u0930\u0947\u0902\u0917\u0947 \u0914\u0930 \u0909\u0938\u0915\u0940 \u0935\u093f\u0938\u094d\u0924\u0943\u0924 \u092a\u094d\u0930\u092e\u093e\u0923-\u0935\u093f\u0915\u093e\u0938 \u0915\u0930\u0947\u0902\u0917\u0947, \u091c\u093f\u0938\u092e\u0947\u0902 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u092a\u0930 \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e \u0924\u0925\u093e \u0938\u0941\u092a\u094d\u0930\u0940\u092e\u094b \u0915\u0947 \u0938\u094d\u0935\u092f\u0902\u0938\u093f\u0926\u094d\u0927 \u0915\u0940 \u0905\u0935\u0927\u093e\u0930\u0923\u093e\u090f\u0901 \u0906\u0927\u093e\u0930 \u0939\u094b\u0902\u0917\u0940\u0964 \u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f \u092f\u0939 \u0939\u0948 \u0915\u093f \u092f\u0939 \u092a\u093e\u0920 \u0906\u092a\u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u0920\u094b\u0938 \u0938\u0902\u0926\u0930\u094d\u092d \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0909\u092a\u092f\u094b\u0917\u0940 \u0939\u094b: \u091a\u093e\u0939\u0947 \u0938\u094d\u0935\u092f\u0902 \u092a\u094d\u0930\u092e\u0947\u092f \u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0930\u0928\u093e \u0939\u094b, \u092f\u093e \u0905\u0928\u094d\u092f \u092a\u094d\u0930\u092e\u0947\u092f\u094b\u0902 \u0915\u094b \u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0924\u0947 \u0938\u092e\u092f \u0905\u0925\u0935\u093e \u0935\u093f\u0936\u093f\u0937\u094d\u091f \u0938\u092e\u0938\u094d\u092f\u093e\u0913\u0902 \u092e\u0947\u0902 \u0905\u0927\u093f\u0915\u0924\u092e \u0914\u0930 \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u0915\u0947 \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u0915\u094b \u0915\u0920\u094b\u0930 \u0930\u0942\u092a \u0938\u0947 \u0909\u091a\u093f\u0924 \u0920\u0939\u0930\u093e\u0924\u0947 \u0938\u092e\u092f \u0907\u0938\u0915\u0940 \u0913\u0930 \u0932\u094c\u091f\u0928\u093e \u0939\u094b\u0964\n<\/p>\n<p><a name=\"2\"><\/a><\/br><\/p>\n<h2>\u0935\u093e\u092f\u0930\u0938\u094d\u091f\u094d\u0930\u093e\u0938 \u092a\u094d\u0930\u092e\u0947\u092f \u0915\u093e \u0915\u0925\u0928<\/h2>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: justify; background-color: #e0e0ff;\">\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=N5mSrhJgCds&amp;t=439s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092b\u0932\u0928 <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924<\/span><\/strong><\/a> \u0924\u0925\u093e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b],<\/span><\/span> \u092a\u0930 \u0938\u0924\u0924 \u0939\u094b\u0924\u093e \u0939\u0948, \u0935\u0939 \u092a\u0930\u093f\u092c\u0926\u094d\u0927 \u0939\u094b\u0924\u093e \u0939\u0948 \u0914\u0930 \u0909\u0938\u0915\u0947 \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u0924\u0925\u093e \u0905\u0927\u093f\u0915\u0924\u092e \u092e\u093e\u0928 <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">M<\/span> \u0939\u094b\u0924\u0947 \u0939\u0948\u0902, \u0910\u0938\u0947 \u0915\u093f \u092f\u0926\u093f <span class=\"katex-eq\" data-katex-display=\"false\">x\\in[a,b]<\/span>, \u0924\u092c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)\\in[m,M]<\/span><\/span>\u0964<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"3\"><\/a><\/br><\/p>\n<h3>\u092a\u094d\u0930\u092e\u093e\u0923<\/h3>\n<p>\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0947\u0902 \u0915\u093f \u092f\u0926\u093f <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f:[a,b]\\to\\mathbb{R}<\/span><\/span><\/strong> \u0905\u0902\u0924\u0930\u093e\u0932 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u092a\u0930 \u0938\u0924\u0924 \u0939\u0948, \u0924\u094b <strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u092a\u0930\u093f\u092c\u0926\u094d\u0927 \u0939\u0948 \u0914\u0930 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u092e\u0947\u0902 \u090f\u0915 \u0905\u0927\u093f\u0915\u0924\u092e \u0924\u0925\u093e \u090f\u0915 \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u092e\u093e\u0928 \u0917\u094d\u0930\u0939\u0923 \u0915\u0930\u0924\u0940 \u0939\u0948\u0964 \u0939\u092e \u092a\u094d\u0930\u092e\u093e\u0923 \u0915\u094b \u0926\u094b \u092e\u0941\u0916\u094d\u092f \u092d\u093e\u0917\u094b\u0902 \u092e\u0947\u0902 \u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0947\u0902\u0917\u0947:\n<\/p>\n<ul>\n<li>\u092a\u0939\u0932\u0947, \u0939\u092e \u0926\u093f\u0916\u093e\u090f\u0901\u0917\u0947 \u0915\u093f <strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u0915\u0940 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u092a\u0930 \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e \u0938\u0947 \u092f\u0939 \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937 \u0928\u093f\u0915\u0932\u0924\u093e \u0939\u0948 \u0915\u093f <strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> <em>\u0938\u092e\u093e\u0928 \u0930\u0942\u092a \u0938\u0947 \u0938\u0924\u0924<\/em> \u0939\u0948, \u0914\u0930 \u0907\u0938\u0938\u0947 \u0939\u092e \u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0947\u0902\u0917\u0947 \u0915\u093f \u092f\u0939 <strong>\u092a\u0930\u093f\u092c\u0926\u094d\u0927<\/strong> \u0939\u0948\u0964<\/li>\n<li>\u0907\u0938\u0915\u0947 \u092c\u093e\u0926, \u0938\u0941\u092a\u094d\u0930\u0940\u092e\u094b \u0915\u0947 \u0938\u094d\u0935\u092f\u0902\u0938\u093f\u0926\u094d\u0927 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f \u0939\u092e \u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0947\u0902\u0917\u0947 \u0915\u093f <strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u0905\u092a\u0928\u0947 \u0905\u0927\u093f\u0915\u0924\u092e \u0914\u0930 \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u092e\u093e\u0928\u094b\u0902 \u0915\u094b \u0905\u0902\u0924\u0930\u093e\u0932 \u092e\u0947\u0902 \u0917\u094d\u0930\u0939\u0923 \u0915\u0930\u0924\u0940 \u0939\u0948\u0964<\/li>\n<\/ul>\n<p><a name=\"4\"><\/a><\/br><\/p>\n<h4><b>\u091a\u0930\u0923 1:<\/b> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span> \u092a\u0930 \u092c\u093f\u0902\u0926\u0941-\u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e<\/h4>\n<p>\n\u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930, <strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092c\u093f\u0902\u0926\u0941 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in[a,b]<\/span><\/span><\/strong> \u092a\u0930 \u0938\u0924\u0924 \u0939\u0948\u0964 <span class=\"katex-eq\" data-katex-display=\"false\">\\epsilon<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">\\delta<\/span> \u0915\u0940 \u0936\u0930\u094d\u0924\u094b\u0902 \u092e\u0947\u0902 \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e \u0915\u0940 \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930 \u0907\u0938\u0915\u093e \u0905\u0930\u094d\u0925 \u0939\u0948:\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n(\\forall x_0\\in[a,b])(\\forall \\epsilon\\gt 0)(\\exists \\delta(x_0)\\gt 0)\n\n\\big(|x-x_0|\\lt\\delta(x_0)\\Rightarrow |f(x)-f(x_0)|\\lt\\epsilon\\big).\n\n<\/span>\n<\/p>\n<p>\n\u0907\u0938 \u092c\u093f\u0902\u0926\u0941 \u092a\u0930, \u0938\u0902\u0916\u094d\u092f\u093e <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta(x_0)<\/span><\/span><\/strong> \u092c\u093f\u0902\u0926\u0941 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span><\/strong> \u092a\u0930 \u0928\u093f\u0930\u094d\u092d\u0930 \u0915\u0930 \u0938\u0915\u0924\u0940 \u0939\u0948\u0964 \u0939\u092e\u093e\u0930\u093e \u0924\u0924\u094d\u0915\u093e\u0932 \u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f \u0907\u0928 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta(x_0)<\/span><\/span><\/strong> \u0938\u0947 \u090f\u0915 \u0910\u0938\u0940 \u090f\u0915\u0932 \u0938\u0902\u0916\u094d\u092f\u093e <strong><span class=\"katex-eq\" data-katex-display=\"false\">\\delta<\/span><\/strong> \u0915\u093e \u0928\u093f\u0930\u094d\u092e\u093e\u0923 \u0915\u0930\u0928\u093e \u0939\u0948 \u091c\u094b <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span><\/strong> \u092a\u0930 \u0928\u093f\u0930\u094d\u092d\u0930 \u0928 \u0939\u094b \u0914\u0930 \u092a\u0942\u0930\u0947 \u0905\u0902\u0924\u0930\u093e\u0932 \u0915\u0947 \u0938\u092d\u0940 \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u0947 \u0932\u093f\u090f \u0915\u093e\u092e \u0915\u0930\u0947\u0964\n<\/p>\n<p><a name=\"5\"><\/a><\/br><\/p>\n<h4><b>\u091a\u0930\u0923 2:<\/b> \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0916\u0941\u0932\u093e \u0906\u0935\u0930\u0923<\/h4>\n<p>\n\u0915\u094b\u0908 \u092d\u0940 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\epsilon\\gt 0<\/span><\/span><\/strong> \u0928\u093f\u092f\u0924 \u0915\u0930\u0947\u0902\u0964 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in[a,b]<\/span><\/span><\/strong> \u0915\u0947 \u0932\u093f\u090f, <strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u0915\u0940 \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e \u0939\u092e\u0947\u0902 \u090f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta(x_0)\\gt 0<\/span><\/span><\/strong> \u091a\u0941\u0928\u0928\u0947 \u0926\u0947\u0924\u0940 \u0939\u0948, \u0910\u0938\u0940 \u0915\u093f\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n|x-x_0|\\lt\\delta(x_0)\\Rightarrow |f(x)-f(x_0)|\\lt\\frac{\\epsilon}{2}.\n\n<\/span>\n<\/p>\n<p>\n\u0907\u0928 \u092e\u093e\u0928\u094b\u0902 \u0938\u0947 \u0939\u092e \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in[a,b]<\/span><\/span><\/strong> \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u0916\u0941\u0932\u093e \u0905\u0902\u0924\u0930\u093e\u0932 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902:\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\nI_{x_0}=\\left(x_0-\\frac{\\delta(x_0)}{2},\\,x_0+\\frac{\\delta(x_0)}{2}\\right).\n\n<\/span>\n<\/p>\n<p>\n\u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I_{x_0}<\/span><\/span><\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}<\/span> \u092e\u0947\u0902 \u090f\u0915 \u0916\u0941\u0932\u093e \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0939\u0948 \u0914\u0930 \u0906\u0917\u0947, \u092f\u0939 \u092a\u0930\u093f\u0935\u093e\u0930\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n\\{I_{x_0}\\}_{x_0\\in[a,b]}\n\n<\/span>\n<\/p>\n<p>\n<strong>\u0916\u0941\u0932\u093e \u0906\u0935\u0930\u0923<\/strong> \u092c\u0928\u093e\u0924\u093e \u0939\u0948 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u0915\u093e\u0964 \u0935\u093e\u0938\u094d\u0924\u0935 \u092e\u0947\u0902, \u0915\u094b\u0908 \u092d\u0940 \u092c\u093f\u0902\u0926\u0941 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y\\in[a,b]<\/span><\/span><\/strong> \u0932\u0947\u0902\u0964 \u092c\u0938 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0=y<\/span><\/span><\/strong> \u091a\u0941\u0928\u0947\u0902; \u0928\u093f\u0930\u094d\u092e\u093e\u0923 \u0938\u0947 \u0938\u094d\u092a\u0937\u094d\u091f \u0939\u0948 \u0915\u093f <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y\\in I_y<\/span><\/span><\/strong>\u0964 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930, \u0905\u0902\u0924\u0930\u093e\u0932 \u0915\u093e \u0939\u0930 \u092c\u093f\u0902\u0926\u0941 \u0915\u092e \u0938\u0947 \u0915\u092e \u090f\u0915 \u0916\u0941\u0932\u0947 \u0938\u092e\u0941\u091a\u094d\u091a\u092f <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I_{x_0}<\/span><\/span><\/strong> \u092e\u0947\u0902 \u0938\u092e\u094d\u092e\u093f\u0932\u093f\u0924 \u0939\u0948\u0964\n<\/p>\n<p>\n\u092f\u0939 \u0916\u0941\u0932\u0947 \u0938\u092e\u0941\u091a\u094d\u091a\u092f\u094b\u0902 \u0915\u093e \u092a\u0930\u093f\u0935\u093e\u0930 \u0938\u093e\u092e\u093e\u0928\u094d\u092f\u0924\u0903 <strong>\u0905\u0928\u0928\u094d\u0924<\/strong> \u0939\u094b\u0924\u093e \u0939\u0948 (\u0915\u094d\u092f\u094b\u0902\u0915\u093f \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in[a,b]<\/span><\/span><\/strong> \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0939\u0948)\u0964 \u092f\u0939\u0940\u0902 \u092a\u0930 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u0915\u0940 \u0938\u0902\u092a\u0940\u0921\u094d\u092f\u0924\u093e \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u092d\u0942\u092e\u093f\u0915\u093e \u0928\u093f\u092d\u093e\u0924\u0940 \u0939\u0948\u0964\n<\/p>\n<p><a name=\"6\"><\/a><\/br><\/p>\n<h4><b>\u091a\u0930\u0923 3:<\/b> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span> \u0915\u0940 \u0938\u0902\u092a\u0940\u0921\u094d\u092f\u0924\u093e \u0914\u0930 \u0938\u0940\u092e\u093f\u0924 \u0909\u092a-\u0906\u0935\u0930\u0923<\/h4>\n<p>\n\u0939\u093e\u0907\u0928\u2013\u092c\u094b\u0930\u0932 \u092a\u094d\u0930\u092e\u0947\u092f \u0938\u0947 \u091c\u094d\u091e\u093e\u0924 \u0939\u0948 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}<\/span><\/span> \u0915\u093e \u0915\u094b\u0908 \u0909\u092a\u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0924\u092d\u0940 \u0914\u0930 \u0915\u0947\u0935\u0932 \u0924\u092d\u0940 \u0938\u0902\u0915\u094d\u0937\u093f\u092a\u094d\u0924 (compact) \u0939\u094b\u0924\u093e \u0939\u0948 \u091c\u092c \u0935\u0939 \u092c\u0902\u0926 \u0914\u0930 \u092a\u0930\u093f\u092c\u0926\u094d\u0927 \u0939\u094b\u0964 \u0905\u0902\u0924\u0930\u093e\u0932 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u092c\u0902\u0926 \u0914\u0930 \u092a\u0930\u093f\u092c\u0926\u094d\u0927 \u0939\u0948, \u0905\u0924\u0903 \u092f\u0939 \u0938\u0902\u0915\u094d\u0937\u093f\u092a\u094d\u0924 \u0939\u0948\u0964 \u0938\u0902\u092a\u0940\u0921\u094d\u092f\u0924\u093e \u0915\u0940 \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930 \u0907\u0938\u0915\u093e \u0905\u0930\u094d\u0925 \u0939\u0948:\n<\/p>\n<p>\n<strong>\u0915\u093f\u0938\u0940 \u092d\u0940<\/strong> \u0916\u0941\u0932\u093e \u0906\u0935\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> (\u091a\u093e\u0939\u0947 \u0909\u0938\u092e\u0947\u0902 \u0905\u0928\u0928\u094d\u0924 \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0939\u094b\u0902) \u090f\u0915 <strong>\u0938\u0940\u092e\u093f\u0924 \u0909\u092a-\u0906\u0935\u0930\u0923<\/strong> \u0928\u093f\u0915\u093e\u0932\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964\n<\/p>\n<p>\n\u0907\u0938 \u0917\u0941\u0923 \u0915\u094b \u0916\u0941\u0932\u0947 \u0906\u0935\u0930\u0923 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{I_{x_0}\\}_{x_0\\in[a,b]}<\/span><\/span><\/strong> \u092a\u0930 \u0932\u093e\u0917\u0942 \u0915\u0930\u0928\u0947 \u0938\u0947 \u092f\u0939 \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937 \u0928\u093f\u0915\u0932\u0924\u093e \u0939\u0948 \u0915\u093f \u0910\u0938\u0947 \u092c\u093f\u0902\u0926\u0941 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_1,\\dots,x_N\\in[a,b]<\/span><\/span><\/strong> \u092e\u094c\u091c\u0942\u0926 \u0939\u0948\u0902 \u091c\u093f\u0928\u0915\u0947 \u0932\u093f\u090f \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0905\u0902\u0924\u0930\u093e\u0932\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\nI_{x_1},\\, I_{x_2},\\,\\dots,\\,I_{x_N}\n\n<\/span>\n<\/p>\n<p>\n\u092f\u0939 \u092a\u0942\u0930\u0947 \u0905\u0902\u0924\u0930\u093e\u0932 \u0915\u094b \u0905\u092c \u092d\u0940 \u0906\u0935\u0943\u0924\u094d\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902:\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n[a,b]\\subset I_{x_1}\\cup I_{x_2}\\cup\\cdots\\cup I_{x_N}.\n\n<\/span>\n<\/p>\n<p>\n\u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0939\u092e\u0928\u0947 \u0916\u0941\u0932\u0947 \u0905\u0902\u0924\u0930\u093e\u0932\u094b\u0902 \u0915\u0947 \u090f\u0915 \u0905\u0928\u0928\u094d\u0924 \u092a\u0930\u093f\u0935\u093e\u0930 \u0938\u0947 \u0915\u0947\u0935\u0932 <strong>\u0938\u0940\u092e\u093f\u0924 \u0938\u0902\u0916\u094d\u092f\u093e<\/strong> \u0935\u093e\u0932\u0947 \u0909\u092a-\u0906\u0935\u0930\u0923 \u092e\u0947\u0902 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u093f\u092f\u093e \u0939\u0948, \u092c\u093f\u0928\u093e <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u0915\u094b \u0906\u0935\u0943\u0924\u094d\u0924 \u0915\u0930\u0928\u0947 \u0915\u093e \u0917\u0941\u0923 \u0916\u094b\u090f\u0964\n<\/p>\n<p><a name=\"7\"><\/a><\/br><\/p>\n<h4><b>\u091a\u0930\u0923 4:<\/b> \u090f\u0915 \u0910\u0938\u093e <span class=\"katex-eq\" data-katex-display=\"false\">\\delta<\/span> \u0928\u093f\u0930\u094d\u092e\u093f\u0924 \u0915\u0930\u0928\u093e \u091c\u094b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u092a\u0930 \u0928\u093f\u0930\u094d\u092d\u0930 \u0928 \u0939\u094b (\u0938\u092e\u093e\u0928 \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e)<\/h4>\n<p>\n\u0938\u0940\u092e\u093f\u0924 \u0909\u092a-\u0906\u0935\u0930\u0923 \u0938\u0947 \u0939\u092e \u0928\u093f\u092e\u094d\u0928 \u0938\u0902\u0916\u094d\u092f\u093e \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902:\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n\\delta=\\min\\left\\{\\frac{\\delta(x_1)}{2},\\frac{\\delta(x_2)}{2},\\dots,\\frac{\\delta(x_N)}{2}\\right\\}.\n\n<\/span>\n<\/p>\n<p>\n\u091a\u0942\u0901\u0915\u093f \u092f\u0939 \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u090f\u0915 \u0938\u0940\u092e\u093f\u0924 \u0938\u092e\u0942\u0939 \u0915\u093e \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u0939\u0948, \u0907\u0938\u0932\u093f\u090f <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta\\gt 0<\/span><\/span><\/strong> \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0939\u092e \u0926\u0947\u0916\u0947\u0902\u0917\u0947 \u0915\u093f \u092f\u0939 <strong><span class=\"katex-eq\" data-katex-display=\"false\">\\delta<\/span><\/strong> <strong>\u0938\u092d\u0940<\/strong> \u092c\u093f\u0902\u0926\u0941\u0913\u0902 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in[a,b]<\/span><\/span><\/strong> \u0915\u0947 \u0932\u093f\u090f \u0915\u093e\u092e \u0915\u0930\u0924\u093e \u0939\u0948, \u0905\u0930\u094d\u0925\u093e\u0924 \u092f\u0939 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span><\/strong> \u0915\u0940 \u092a\u0938\u0902\u0926 \u092a\u0930 \u0928\u093f\u0930\u094d\u092d\u0930 \u0928\u0939\u0940\u0902 \u0939\u0948\u0964\n<\/p>\n<p>\n\u0905\u092c \u0932\u0947\u0902:\n<\/p>\n<ul>\n<li>\u0915\u094b\u0908 \u092d\u0940 \u092c\u093f\u0902\u0926\u0941 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in[a,b]<\/span><\/span><\/strong>, \u0914\u0930<\/li>\n<li>\u0915\u094b\u0908 \u092c\u093f\u0902\u0926\u0941 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in[a,b]<\/span><\/span><\/strong> \u0910\u0938\u093e \u0915\u093f <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|x-x_0|\\lt\\delta<\/span><\/span><\/strong>\u0964<\/li>\n<\/ul>\n<p>\n\u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0905\u0902\u0924\u0930\u093e\u0932 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I_{x_1},\\dots,I_{x_N}<\/span><\/span><\/strong> <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u0915\u094b \u0906\u0935\u0943\u0924\u094d\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u0907\u0938\u0932\u093f\u090f \u092c\u093f\u0902\u0926\u0941 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span><\/strong> \u0915\u092e \u0938\u0947 \u0915\u092e \u0909\u0928\u092e\u0947\u0902 \u0938\u0947 \u0915\u093f\u0938\u0940 \u090f\u0915 \u092e\u0947\u0902 \u0905\u0935\u0936\u094d\u092f \u0939\u094b\u0917\u093e, \u092e\u093e\u0928 \u0932\u0947\u0902 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I_{x_j}<\/span><\/span><\/strong>, \u091c\u0939\u093e\u0901 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">j\\in\\{1,\\dots,N\\}<\/span><\/span><\/strong>\u0964 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">I_{x_j}<\/span><\/span><\/strong> \u0915\u0940 \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930, \u0907\u0938\u0915\u093e \u0905\u0930\u094d\u0925 \u0939\u0948:\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n|x_0-x_j|\\lt\\frac{\\delta(x_j)}{2}.\n\n<\/span>\n<\/p>\n<p>\n\u0907\u0938\u0915\u0947 \u0905\u0924\u093f\u0930\u093f\u0915\u094d\u0924, <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta<\/span><\/span><\/strong> \u0915\u0940 \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0938\u0947 \u0939\u092e\u0947\u0902 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948 \u0915\u093f <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta\\le\\frac{\\delta(x_j)}{2}<\/span><\/span><\/strong>, \u0905\u0924\u0903 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|x-x_0|\\lt\\delta<\/span><\/span><\/strong> \u0938\u0947 \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937 \u0928\u093f\u0915\u0932\u0924\u093e \u0939\u0948:\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n|x-x_0|\\lt\\frac{\\delta(x_j)}{2}.\n\n<\/span>\n<\/p>\n<p>\n\u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0905\u0938\u092e\u093e\u0928\u0924\u093e \u0932\u093e\u0917\u0942 \u0915\u0930\u0928\u0947 \u092a\u0930:\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n|x-x_j|\\le |x-x_0|+|x_0-x_j|\n\n\\lt \\frac{\\delta(x_j)}{2}+\\frac{\\delta(x_j)}{2}\n\n=\\delta(x_j).\n\n<\/span>\n<\/p>\n<p>\n<strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta(x_j)<\/span><\/span><\/strong> \u0915\u0940 \u092a\u0938\u0902\u0926 (\u092f\u093e\u0928\u0940 <strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u0915\u0940 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_j<\/span><\/span><\/strong> \u092a\u0930 \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e \u091c\u092c <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\epsilon\/2<\/span><\/span><\/strong> \u0926\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u094b) \u0915\u0947 \u0915\u093e\u0930\u0923, \u0905\u0938\u092e\u093e\u0928\u0924\u093e\u090f\u0901 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|x_0-x_j|\\lt\\delta(x_j)<\/span><\/span><\/strong> \u0914\u0930 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|x-x_j|\\lt\\delta(x_j)<\/span><\/span><\/strong> \u092f\u0939 \u0938\u0941\u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0915\u0930\u0924\u0940 \u0939\u0948\u0902:\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n|f(x_0)-f(x_j)|\\lt\\frac{\\epsilon}{2}\n\n\\quad\\text{y}\\quad\n\n|f(x)-f(x_j)|\\lt\\frac{\\epsilon}{2}.\n\n<\/span>\n<\/p>\n<p>\n\u092b\u093f\u0930 \u0938\u0947 \u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0905\u0938\u092e\u093e\u0928\u0924\u093e \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f \u0939\u092e\u0947\u0902 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948:\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n|f(x)-f(x_0)|\n\n\\le |f(x)-f(x_j)| + |f(x_j)-f(x_0)|\n\n\\lt \\frac{\\epsilon}{2}+\\frac{\\epsilon}{2}\n\n=\\epsilon.\n\n<\/span>\n<\/p>\n<p>\n\u091a\u0942\u0901\u0915\u093f <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span><\/strong> \u0914\u0930 <strong><span class=\"katex-eq\" data-katex-display=\"false\">x<\/span><\/strong> \u0926\u094b\u0928\u094b\u0902 \u092e\u0928\u092e\u093e\u0928\u0947 \u0925\u0947, \u0939\u092e\u0928\u0947 \u0938\u093f\u0926\u094d\u0927 \u0915\u0930 \u0926\u093f\u092f\u093e \u0939\u0948 \u0915\u093f \u092a\u094d\u0930\u093e\u0930\u0902\u092d \u092e\u0947\u0902 \u091a\u0941\u0928\u0947 \u0917\u090f <strong><span class=\"katex-eq\" data-katex-display=\"false\">\\epsilon<\/span><\/strong> \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta\\gt 0<\/span><\/span><\/strong> \u092e\u094c\u091c\u0942\u0926 \u0939\u0948, \u091c\u094b <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span><\/strong> \u092a\u0930 \u0928\u093f\u0930\u094d\u092d\u0930 \u0928\u0939\u0940\u0902 \u0915\u0930\u0924\u093e, \u0914\u0930 \u091c\u093f\u0938\u0915\u0947 \u0932\u093f\u090f\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n(\\forall x_0\\in[a,b])(\\forall x\\in[a,b])\n\n\\big(|x-x_0|\\lt\\delta\\Rightarrow |f(x)-f(x_0)|\\lt\\epsilon\\big).\n\n<\/span>\n<\/p>\n<p>\n\u092f\u0926\u093f \u0939\u092e <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span><\/strong> \u0915\u093e \u0928\u093e\u092e \u092c\u0926\u0932\u0915\u0930 <strong><span class=\"katex-eq\" data-katex-display=\"false\">y<\/span><\/strong> \u0915\u0930 \u0926\u0947\u0902, \u0924\u094b \u0907\u0938\u0947 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0932\u093f\u0916\u093e \u091c\u093e\u0924\u093e \u0939\u0948:\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n(\\forall \\epsilon\\gt 0)(\\exists \\delta\\gt 0)(\\forall x,y\\in[a,b])\n\n\\big(|x-y|\\lt\\delta\\Rightarrow |f(x)-f(y)|\\lt\\epsilon\\big),\n\n<\/span>\n<\/p>\n<p>\n\u091c\u094b \u0920\u0940\u0915 \u0935\u0939\u0940 \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0939\u0948 \u091c\u094b <strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u0915\u0940 <strong>\u0938\u092e\u093e\u0928 \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e<\/strong> \u0915\u094b <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u092a\u0930 \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u0930\u0924\u0940 \u0939\u0948\u0964 \u0906\u0917\u0947 \u0939\u092e \u0915\u0947\u0935\u0932 \u0907\u0938 \u092a\u0930\u093f\u0923\u093e\u092e \u0915\u094b \u0935\u093f\u0936\u0947\u0937 caso <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\epsilon=1<\/span><\/span><\/strong> \u092e\u0947\u0902 \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0947\u0902\u0917\u0947\u0964\n<\/p>\n<p><a name=\"8\"><\/a><\/br><\/p>\n<h4><b>\u091a\u0930\u0923 5:<\/b> \u0938\u092e\u093e\u0928 \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e \u0938\u0947 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span> \u092a\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u0915\u0940 \u092a\u0930\u093f\u092c\u0926\u094d\u0927\u0924\u093e<\/h4>\n<p>\n\u0905\u092c \u0938\u092e\u093e\u0928 \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e \u0915\u094b <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\epsilon=1<\/span><\/span><\/strong> \u0915\u0947 \u0938\u093e\u0925 \u0932\u093e\u0917\u0942 \u0915\u0930\u0947\u0902\u0964 \u0924\u092c \u090f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta_1\\gt 0<\/span><\/span><\/strong> \u092e\u094c\u091c\u0942\u0926 \u0939\u0948, \u0910\u0938\u0940 \u0915\u093f \u0938\u092d\u0940 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x,y\\in[a,b]<\/span><\/span><\/strong> \u0915\u0947 \u0932\u093f\u090f\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n|x-y|\\lt\\delta_1\\Rightarrow |f(x)-f(y)|\\lt 1.\n\n<\/span>\n<\/p>\n<p>\n\u0905\u092c \u0905\u0902\u0924\u0930\u093e\u0932 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u0915\u094b \u0938\u0940\u092e\u093f\u0924 \u0938\u0902\u0916\u094d\u092f\u093e \u092e\u0947\u0902 \u0909\u092a-\u0905\u0902\u0924\u0930\u093e\u0932\u094b\u0902 \u092e\u0947\u0902 \u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0947\u0902, \u091c\u093f\u0928\u0915\u0940 \u0932\u0902\u092c\u093e\u0908 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta_1<\/span><\/span><\/strong> \u0938\u0947 \u091b\u094b\u091f\u0940 \u0939\u094b\u0964 \u0905\u0930\u094d\u0925\u093e\u0924, \u090f\u0915 \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915 <strong><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/strong> \u0924\u0925\u093e \u092c\u093f\u0902\u0926\u0941\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\na = x_0 \\lt x_1 \\lt \\cdots \\lt x_n = b\n\n<\/span>\n<\/p>\n<p>\n\u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u091a\u0941\u0928\u0947\u0902 \u0915\u093f \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k=0,1,\\dots,n-1<\/span><\/span><\/strong> \u0915\u0947 \u0932\u093f\u090f\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\nx_{k+1}-x_k\\lt\\delta_1.\n\n<\/span>\n<\/p>\n<p>\n\u0905\u092c \u0938\u0940\u092e\u093f\u0924 \u0938\u092e\u0941\u091a\u094d\u091a\u092f\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n\\{f(x_0),f(x_1),\\dots,f(x_{n-1})\\}.\n\n<\/span>\n<\/p>\n<p>\n\u092a\u0930 \u0935\u093f\u091a\u093e\u0930 \u0915\u0930\u0947\u0902\u0964 \u091a\u0942\u0901\u0915\u093f \u092f\u0939 \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u093e \u090f\u0915 \u0938\u0940\u092e\u093f\u0924 \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0939\u0948, \u0939\u092e \u092c\u093f\u0928\u093e \u0938\u092e\u0938\u094d\u092f\u093e \u0928\u093f\u092e\u094d\u0928 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\nC = \\max\\{|f(x_k)| \\;|\\; k=0,1,\\dots,n-1\\}.\n\n<\/span>\n<\/p>\n<p>\n\u0939\u092e \u0926\u093f\u0916\u093e\u090f\u0901\u0917\u0947 \u0915\u093f <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C+1<\/span><\/span><\/strong> \u092a\u0942\u0930\u0947 \u0905\u0902\u0924\u0930\u093e\u0932 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u092a\u0930 <strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u0915\u0947 \u0932\u093f\u090f \u092e\u093e\u0928\u2212\u092a\u0930\u093f\u092e\u093e\u0923 \u0915\u0940 \u090f\u0915 \u090a\u092a\u0930\u0940 \u0938\u0940\u092e\u093e \u0939\u0948\u0964 \u0915\u094b\u0908 \u092d\u0940 \u092c\u093f\u0902\u0926\u0941 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in[a,b]<\/span><\/span><\/strong> \u0932\u0947\u0902\u0964 \u0924\u092c \u0910\u0938\u093e \u090f\u0915 \u0938\u0942\u091a\u0915\u093e\u0902\u0915 <strong><span class=\"katex-eq\" data-katex-display=\"false\">k<\/span><\/strong> \u092e\u094c\u091c\u0942\u0926 \u0939\u0948 \u091c\u093f\u0938\u0915\u0947 \u0932\u093f\u090f <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in[x_k,x_{k+1}]<\/span><\/span><\/strong>\u0964 \u0935\u093f\u0936\u0947\u0937 \u0930\u0942\u092a \u0938\u0947:\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n|x-x_k|\\le x_{k+1}-x_k\\lt\\delta_1.\n\n<\/span>\n<\/p>\n<p>\n\u0938\u092e\u093e\u0928 \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e (con <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\epsilon=1<\/span><\/span><\/strong>) \u0915\u0947 \u0926\u094d\u0935\u093e\u0930\u093e, <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|x-x_k|\\lt\\delta_1<\/span><\/span><\/strong> \u0938\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948:\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n|f(x)-f(x_k)|\\lt 1.\n\n<\/span>\n<\/p>\n<p>\n\u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0905\u0938\u092e\u093e\u0928\u0924\u093e \u092a\u094d\u0930\u092f\u094b\u0917 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f:\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n|f(x)|\\le |f(x)-f(x_k)| + |f(x_k)| \\lt 1 + |f(x_k)| \\le 1 + C.\n\n<\/span>\n<\/p>\n<p>\n\u091a\u0942\u0901\u0915\u093f <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in[a,b]<\/span><\/span><\/strong> \u092e\u0928\u092e\u093e\u0928\u093e \u0925\u093e, \u0907\u0938\u0938\u0947 \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937 \u0928\u093f\u0915\u0932\u0924\u093e \u0939\u0948:\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n|f(x)|\\le C+1 \\quad \\text{para todo } x\\in[a,b],\n\n<\/span>\n<\/p>\n<p>\n\u0905\u0930\u094d\u0925\u093e\u0924\u094d, \u092b\u0932\u0928 <strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u092a\u0930 <strong>\u092a\u0930\u093f\u092c\u0926\u094d\u0927<\/strong> \u0939\u0948\u0964\n<\/p>\n<p><a name=\"9\"><\/a><\/br><\/p>\n<h4><b>\u091a\u0930\u0923 6:<\/b> \u0905\u0927\u093f\u0915\u0924\u092e \u0914\u0930 \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u092e\u093e\u0928\u094b\u0902 \u0915\u093e \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935<\/b><\/h4>\n<p>\n\u0905\u092c \u0909\u0938 \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0915\u094b \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0930\u0947\u0902 \u091c\u094b \u0905\u0902\u0924\u0930\u093e\u0932 \u092e\u0947\u0902 \u092b\u0932\u0928 \u0915\u0947 \u0938\u092d\u0940 \u092e\u093e\u0928\u094b\u0902 \u0915\u094b \u090f\u0915\u0924\u094d\u0930\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948:\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\nH=\\{f(x)\\;|\\;x\\in[a,b]\\}\\subset\\mathbb{R}.\n\n<\/span>\n<\/p>\n<p>\n\u0939\u092e \u092a\u0939\u0932\u0947 \u0938\u0947 \u091c\u093e\u0928\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f <strong><span class=\"katex-eq\" data-katex-display=\"false\">H<\/span><\/strong> \u0930\u093f\u0915\u094d\u0924 \u0928\u0939\u0940\u0902 \u0939\u0948 (\u0915\u094d\u092f\u094b\u0902\u0915\u093f <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u0930\u093f\u0915\u094d\u0924 \u0928\u0939\u0940\u0902 \u0939\u0948) \u0914\u0930 \u092f\u0939 \u092a\u0930\u093f\u092c\u0926\u094d\u0927 \u0939\u0948\u0964 \u0905\u0924\u0903 \u0938\u0941\u092a\u094d\u0930\u0940\u092e\u094b \u0915\u0947 \u0938\u094d\u0935\u092f\u0902\u0938\u093f\u0926\u094d\u0927 \u0926\u094d\u0935\u093e\u0930\u093e \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\nM=\\sup H,\\qquad m=\\inf H.\n\n<\/span>\n<\/p>\n<p>\n\u0938\u0941\u0938\u0902\u0917\u0924 \u0930\u0942\u092a \u0938\u0947 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0939\u0948\u0902\u0964 \u0905\u092c \u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f <strong><span class=\"katex-eq\" data-katex-display=\"false\">M<\/span><\/strong> \u0935\u093e\u0938\u094d\u0924\u0935 \u092e\u0947\u0902 \u092b\u0932\u0928 \u0915\u093e \u092e\u093e\u0928 \u0939\u0948, \u0905\u0930\u094d\u0925\u093e\u0924 \u0910\u0938\u093e <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_1\\in[a,b]<\/span><\/span><\/strong> \u092e\u094c\u091c\u0942\u0926 \u0939\u0948 \u091c\u093f\u0938\u0915\u0947 \u0932\u093f\u090f <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x_1)=M<\/span><\/span><\/strong>\u0964 \u0939\u092e \u0935\u093f\u0930\u094b\u0927\u093e\u092d\u093e\u0938 \u0926\u094d\u0935\u093e\u0930\u093e \u0938\u093f\u0926\u094d\u0927\u093f \u0905\u092a\u0928\u093e\u090f\u0901\u0917\u0947\u0964\n<\/p>\n<p>\n\u092e\u093e\u0928 \u0932\u0947\u0902 \u0915\u093f <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span><\/strong> \u0915\u092d\u0940 \u092d\u0940 \u092e\u093e\u0928 <strong><span class=\"katex-eq\" data-katex-display=\"false\">M<\/span><\/strong> \u0928\u0939\u0940\u0902 \u0932\u0947\u0924\u093e\u0964 \u0905\u0930\u094d\u0925\u093e\u0924\u094d:\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n(\\forall x\\in[a,b])\\big(f(x)\\lt M\\big).\n\n<\/span>\n<\/p>\n<p>\n\u0907\u0938 \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u0915\u0947 \u0924\u0939\u0924, \u092b\u0932\u0928\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\ng(x)=\\frac{1}{M-f(x)}\n\n<\/span>\n<\/p>\n<p>\n\u0938\u0941\u0938\u094d\u092a\u0937\u094d\u091f \u0930\u0942\u092a \u0938\u0947 \u0938\u092d\u0940 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in[a,b]<\/span><\/span><\/strong> \u0915\u0947 \u0932\u093f\u090f \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0939\u0948 \u0914\u0930 \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0939\u0948, \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u0938\u0947 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">M-f(x)\\gt 0<\/span><\/span><\/strong> \u092e\u093f\u0932\u0924\u093e \u0939\u0948\u0964 \u0938\u093e\u0925 \u0939\u0940, <strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u0938\u0924\u0924 \u0939\u0948 \u0914\u0930 <strong><span class=\"katex-eq\" data-katex-display=\"false\">M<\/span><\/strong> \u0938\u094d\u0925\u093f\u0930 \u0939\u0948, \u0905\u0924\u0903 <strong><span class=\"katex-eq\" data-katex-display=\"false\">g<\/span><\/strong> \u092d\u0940 \u0938\u0924\u0924 \u0939\u0948\u0964 \u092a\u0939\u0932\u0940 \u092d\u093e\u0917 \u092e\u0947\u0902 \u0938\u093f\u0926\u094d\u0927 \u0915\u093f\u090f \u0917\u090f \u092a\u0930\u093f\u0923\u093e\u092e \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930, \u0915\u094b\u0908 \u092d\u0940 \u0938\u0924\u0924 \u092b\u0932\u0928 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u092a\u0930 \u092a\u0930\u093f\u092c\u0926\u094d\u0927 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0905\u0924\u0903 \u0915\u094b\u0908 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">N\\gt 0<\/span><\/span><\/strong> \u092e\u094c\u091c\u0942\u0926 \u0939\u0948, \u0910\u0938\u093e \u0915\u093f:\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n(\\forall x\\in[a,b])\\big(g(x)\\le N\\big).\n\n<\/span>\n<\/p>\n<p>\n\u0935\u093f\u0936\u0947\u0937 \u0930\u0942\u092a \u0938\u0947, \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\in[a,b]<\/span><\/span><\/strong> \u0915\u0947 \u0932\u093f\u090f \u092f\u0939 \u0938\u0924\u094d\u092f \u0939\u0948 \u0915\u093f\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n\\frac{1}{M-f(x)} = g(x)\\le N,\n\n<\/span>\n<\/p>\n<p>\n\u091c\u094b \u0938\u092e\u0924\u0941\u0932\u094d\u092f \u0939\u0948:\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\nM-f(x)\\ge \\frac{1}{N}\n\n\\quad\\Rightarrow\\quad\n\nf(x)\\le M-\\frac{1}{N}.\n\n<\/span>\n<\/p>\n<p>\n\u0907\u0938\u0915\u093e \u0905\u0930\u094d\u0925 \u0939\u0948 \u0915\u093f <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u092e\u0947\u0902 \u092b\u0932\u0928 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span><\/strong> \u0915\u0947 \u0938\u092d\u0940 \u092e\u093e\u0928 \u0905\u0927\u093f\u0915 \u0938\u0947 \u0905\u0927\u093f\u0915 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">M-\\frac{1}{N}<\/span><\/span><\/strong> \u0939\u0948\u0902\u0964 \u0935\u093f\u0936\u0947\u0937 \u0930\u0942\u092a \u0938\u0947, <strong><span class=\"katex-eq\" data-katex-display=\"false\">H<\/span><\/strong> \u0915\u0947 \u0938\u0941\u092a\u094d\u0930\u0940\u092e\u094b \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u0939\u092e\u0947\u0902 \u092e\u093f\u0932\u0924\u093e \u0939\u0948:\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n\\sup H\\le M-\\frac{1}{N}\\lt M,\n\n<\/span>\n<\/p>\n<p>\n\u091c\u094b <strong><span class=\"katex-eq\" data-katex-display=\"false\">M<\/span><\/strong> \u0915\u0940 \u092a\u0930\u093f\u092d\u093e\u0937\u093e (\u090f\u0915 \u0938\u0941\u092a\u094d\u0930\u0940\u092e\u094b \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902) \u0915\u0947 \u0938\u093e\u0925 \u0935\u093f\u0930\u094b\u0927\u093e\u092d\u093e\u0938 \u092e\u0947\u0902 \u0939\u0948\u0964 \u0905\u0924\u0903 \u0939\u092e\u093e\u0930\u0940 \u092a\u094d\u0930\u093e\u0930\u092e\u094d\u092d\u093f\u0915 \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u0917\u0932\u0924 \u0925\u0940, \u0914\u0930 \u0905\u0935\u0936\u094d\u092f \u0939\u0940 \u0915\u094b\u0908 \u092c\u093f\u0902\u0926\u0941 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_1\\in[a,b]<\/span><\/span><\/strong> \u092e\u094c\u091c\u0942\u0926 \u0939\u0948 \u091c\u093f\u0938\u0915\u0947 \u0932\u093f\u090f\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\nf(x_1)=M.\n\n<\/span>\n<\/p>\n<p>\n\u092a\u0942\u0930\u0940 \u0924\u0930\u0939 \u0938\u092e\u093e\u0928 \u0924\u0930\u094d\u0915, \u091c\u092c <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">m=\\inf H<\/span><\/span><\/strong> \u092a\u0930 \u0932\u093e\u0917\u0942 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 (\u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, \u092b\u0932\u0928 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">h(x)=-f(x)<\/span><\/span><\/strong> \u092a\u0930 \u0935\u093f\u091a\u093e\u0930 \u0915\u0930\u0915\u0947), \u092f\u0939 \u0926\u093f\u0916\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u0915\u094b\u0908 \u092c\u093f\u0902\u0926\u0941 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_2\\in[a,b]<\/span><\/span><\/strong> \u092e\u094c\u091c\u0942\u0926 \u0939\u0948 \u091c\u093f\u0938\u0915\u0947 \u0932\u093f\u090f\n<\/p>\n<p style=\"text-align: center;\" dir=\"ltr\">\n<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\nf(x_2)=m.\n\n<\/span>\n<\/p>\n<p><a name=\"10\"><\/a><\/br><\/p>\n<h2>\u0938\u0902\u092a\u0940\u0921\u094d\u092f\u0924\u093e \u0915\u0947 \u0938\u0902\u0926\u0930\u094d\u092d \u092e\u0947\u0902 \u0935\u094d\u092f\u093e\u0916\u094d\u092f\u093e \u0914\u0930 \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937<\/h2>\n<p>\n\u0939\u092e\u0928\u0947 \u0938\u093f\u0926\u094d\u0927 \u0915\u093f\u092f\u093e \u0939\u0948 \u0915\u093f \u0939\u0930 \u0938\u0924\u0924 \u092b\u0932\u0928 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f:[a,b]\\to\\mathbb{R}<\/span><\/span><\/strong> \u092a\u0930\u093f\u092c\u0926\u094d\u0927 \u0939\u094b\u0924\u093e \u0939\u0948 \u0914\u0930 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong> \u092e\u0947\u0902 \u0905\u092a\u0928\u0947 \u0905\u0927\u093f\u0915\u0924\u092e \u0924\u0925\u093e \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u092e\u093e\u0928 \u0917\u094d\u0930\u0939\u0923 \u0915\u0930\u0924\u093e \u0939\u0948\u0964 \u0906\u0927\u0941\u0928\u093f\u0915 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0940 \u092d\u093e\u0937\u093e \u092e\u0947\u0902 \u0907\u0938\u0915\u093e \u0905\u0930\u094d\u0925 \u0939\u0948 \u0915\u093f <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}<\/span><\/span><\/strong> \u092e\u0947\u0902 \u092c\u0902\u0926 \u0914\u0930 \u092a\u0930\u093f\u092c\u0926\u094d\u0927 \u0905\u0902\u0924\u0930\u093e\u0932, \u091c\u0948\u0938\u0947 <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,b]<\/span><\/span><\/strong>, \u0938\u0902\u0915\u094d\u0937\u093f\u092a\u094d\u0924 (compact) \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0939\u094b\u0924\u0947 \u0939\u0948\u0902, \u0914\u0930 \u0938\u0924\u0924 \u092b\u0932\u0928 \u0938\u0902\u0915\u094d\u0937\u093f\u092a\u094d\u0924 \u0938\u092e\u0941\u091a\u094d\u091a\u092f\u094b\u0902 \u0915\u094b \u0938\u0902\u0915\u094d\u0937\u093f\u092a\u094d\u0924 \u0938\u092e\u0941\u091a\u094d\u091a\u092f\u094b\u0902 \u092e\u0947\u0902 \u092a\u094d\u0930\u0924\u093f\u091a\u093f\u0924\u094d\u0930\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964\n<\/p>\n<p>\n\u0935\u093f\u0936\u0947\u0937 \u0930\u0942\u092a \u0938\u0947, \u092f\u0926\u093f <strong><span class=\"katex-eq\" data-katex-display=\"false\">I<\/span><\/strong> \u0938\u0902\u0915\u094d\u0937\u093f\u092a\u094d\u0924 (compacto) \u0939\u0948 \u0914\u0930 <strong><span class=\"katex-eq\" data-katex-display=\"false\">f<\/span><\/strong> \u0909\u0938 \u092a\u0930 \u0938\u0924\u0924 \u0939\u0948, \u0924\u094b \u091b\u0935\u093f <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(I)<\/span><\/span><\/strong> <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}<\/span><\/span><\/strong> \u0915\u093e \u090f\u0915 \u0938\u0902\u0915\u094d\u0937\u093f\u092a\u094d\u0924 \u0909\u092a\u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 \u092f\u0939 \u0938\u0941\u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 \u0915\u093f <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(I)<\/span><\/span><\/strong> \u092a\u0930\u093f\u092c\u0926\u094d\u0927 \u0939\u0948 \u0914\u0930 \u0909\u0938\u092e\u0947\u0902 \u0935\u093e\u0938\u094d\u0924\u0935 \u092e\u0947\u0902 \u0905\u0927\u093f\u0915\u0924\u092e \u0924\u0925\u093e \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u092e\u093e\u0928 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902, \u091c\u094b \u0920\u0940\u0915 \u0909\u0938\u0940 \u0915\u0925\u0928 \u0915\u093e \u0938\u093e\u0930 \u0939\u0948 \u091c\u093f\u0938\u0947 \u0935\u093e\u092f\u0930\u0938\u094d\u091f\u094d\u0930\u093e\u0938 \u0915\u0947 \u092a\u094d\u0930\u092e\u0947\u092f \u092e\u0947\u0902 \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948\u0964<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0935\u093e\u092f\u0930\u0938\u094d\u091f\u094d\u0930\u093e\u0938 \u0915\u0947 \u091a\u0930\u092e \u092e\u093e\u0928 \u092a\u094d\u0930\u092e\u0947\u092f \u0915\u094d\u092f\u094b\u0902 \u0905\u0928\u0941\u0915\u0942\u0932\u0928 \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0907\u0924\u0928\u0947 \u0905\u0927\u093f\u0915 \u0938\u092e\u0938\u094d\u092f\u093e\u0913\u0902 \u092e\u0947\u0902 \u092a\u094d\u0930\u093e\u092f\u0903 \u092f\u0939 \u092e\u093e\u0928 \u0932\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u201c\u0905\u0927\u093f\u0915\u0924\u092e \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u092e\u0947\u0902 \u0939\u0948\u201d \u092f\u093e \u201c\u0928\u094d\u092f\u0942\u0928\u0924\u092e \u0905\u0935\u0936\u094d\u092f \u092e\u094c\u091c\u0942\u0926 \u0939\u0948\u201d \u0915\u093f\u0938\u0940 \u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0905\u0902\u0924\u0930\u093e\u0932 \u092e\u0947\u0902, \u091c\u092c\u0915\u093f \u0935\u093e\u0938\u094d\u0924\u0935 \u092e\u0947\u0902 \u0910\u0938\u093e \u0939\u094b\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u094b\u0908 \u0905\u0928\u093f\u0935\u093e\u0930\u094d\u092f\u0924\u093e \u0928\u0939\u0940\u0902 \u0939\u0948? \u0935\u093e\u092f\u0930\u0938\u094d\u091f\u094d\u0930\u093e\u0938 \u092a\u094d\u0930\u092e\u0947\u092f \u0935\u0939 \u0915\u0921\u093c\u0940 \u0939\u0948 \u091c\u094b \u0907\u0938 \u092a\u0939\u0947\u0932\u0940 \u092e\u0947\u0902 \u0915\u092e\u0940 \u0925\u0940: [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":35255,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":5,"footnotes":""},"categories":[862,577],"tags":[],"class_list":["post-35275","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-862","category-577"],"yoast_head":"<!-- This site is optimized with the 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