{"id":29523,"date":"2024-11-18T02:30:47","date_gmt":"2024-11-18T02:30:47","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=29523"},"modified":"2024-11-18T02:34:53","modified_gmt":"2024-11-18T02:34:53","slug":"%e0%a4%85%e0%a4%b8%e0%a4%bf%e0%a4%ae%e0%a5%8d%e0%a4%aa%e0%a4%9f%e0%a5%8b%e0%a4%9f%e0%a4%be-%e0%a4%b8%e0%a5%80%e0%a4%ae%e0%a4%be%e0%a4%8f%e0%a4%81-%e0%a4%94%e0%a4%b0-%e0%a4%97%e0%a5%8d%e0%a4%b0","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/hi\/%e0%a4%85%e0%a4%b8%e0%a4%bf%e0%a4%ae%e0%a5%8d%e0%a4%aa%e0%a4%9f%e0%a5%8b%e0%a4%9f%e0%a4%be-%e0%a4%b8%e0%a5%80%e0%a4%ae%e0%a4%be%e0%a4%8f%e0%a4%81-%e0%a4%94%e0%a4%b0-%e0%a4%97%e0%a5%8d%e0%a4%b0\/","title":{"rendered":"\u0905\u0938\u093f\u092e\u094d\u092a\u091f\u094b\u091f\u093e, \u0938\u0940\u092e\u093e\u090f\u0901 \u0914\u0930 \u0917\u094d\u0930\u093e\u092b\u093f\u0915 \u092a\u094d\u0930\u0924\u093f\u0928\u093f\u0927\u093f\u0924\u094d\u0935 \u0915\u0940 \u0924\u0915\u0928\u0940\u0915\u0947\u0902"},"content":{"rendered":"<style>\np {\ntext-align:justify;\n}\n<\/style>\n<h1 style=\"text-align:center;\">\u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e, \u0938\u0940\u092e\u093e\u090f\u0901 \u0914\u0930 \u0917\u094d\u0930\u093e\u092b\u093c\u093f\u0915\u0932 \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924\u093f \u0924\u0915\u0928\u0940\u0915\u0947\u0902<\/h1>\n<p style=\"text-align:center;\"><em><strong>\u0938\u093e\u0930\u093e\u0902\u0936:<\/strong><br \/>\n\u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0915\u093e\u0930\u094d\u092f\u094b\u0902 \u0915\u0947 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u092e\u0947\u0902 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e \u0914\u0930 \u092a\u094d\u0930\u092e\u0941\u0916 \u0936\u0930\u094d\u0924\u094b\u0902 \u0915\u0940 \u0905\u0935\u0927\u093e\u0930\u0923\u093e\u0913\u0902 \u0915\u094b \u0938\u092e\u091d\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948\u0964 \u0907\u0938\u092e\u0947\u0902 \u0915\u094d\u0937\u0948\u0924\u093f\u091c \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\u0913\u0902 \u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u091c\u094b \u0924\u092c \u0915\u093e\u0930\u094d\u092f \u0915\u0947 \u0935\u094d\u092f\u0935\u0939\u093e\u0930 \u0915\u093e \u0935\u0930\u094d\u0923\u0928 \u0915\u0930\u0924\u0940 \u0939\u0948\u0902 \u091c\u092c <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0905\u0928\u0902\u0924 \u0915\u0940 \u0913\u0930 \u091c\u093e\u0924\u093e \u0939\u0948; \u090a\u0930\u094d\u0927\u094d\u0935\u093e\u0927\u0930 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\u090f\u0901, \u091c\u094b \u0905\u0928\u0902\u0924 \u0938\u0940\u092e\u093e\u090f\u0901 \u0926\u0930\u094d\u0936\u093e\u0924\u0940 \u0939\u0948\u0902 \u091c\u092c <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0915\u0941\u091b \u092e\u0942\u0932\u094d\u092f\u094b\u0902 \u0915\u0947 \u092a\u093e\u0938 \u092a\u0939\u0941\u0901\u091a\u0924\u093e \u0939\u0948; \u0914\u0930 \u0924\u093f\u0930\u094d\u092f\u0915 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\u090f\u0901, \u091c\u094b \u0924\u092c \u092a\u094d\u0930\u093e\u0938\u0902\u0917\u093f\u0915 \u0939\u094b\u0924\u0940 \u0939\u0948\u0902 \u091c\u092c \u0905\u0902\u0936 \u0915\u093e \u0918\u093e\u0924\u093e\u0902\u0915 \u0939\u0930 \u0915\u0947 \u0918\u093e\u0924\u093e\u0902\u0915 \u0938\u0947 \u0905\u0927\u093f\u0915 \u0939\u094b\u0964 \u0907\u0938\u0915\u0947 \u0905\u0932\u093e\u0935\u093e, \u090f\u0915 \u0915\u093e\u0930\u094d\u092f \u0915\u0947 \u092a\u094d\u0930\u092e\u0941\u0916 \u0936\u0930\u094d\u0924 \u0915\u093e \u092d\u0940 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948, \u091c\u094b \u092c\u0921\u093c\u0947 \u092f\u093e \u0915\u0941\u091b \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u0947 \u092a\u093e\u0938 \u092e\u0942\u0932\u094d\u092f\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u0938\u0928\u094d\u0928\u093f\u0915\u091f\u0928 \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/em><\/p>\n<p style=\"text-align:center;\"><strong>\u0938\u0940\u0916\u0928\u0947 \u0915\u0947 \u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f<\/strong><br \/>\n\u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u0915\u0947 \u0905\u0902\u0924 \u092e\u0947\u0902, \u091b\u093e\u0924\u094d\u0930 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u0938\u0915\u094d\u0937\u092e \u0939\u094b\u0902\u0917\u0947:\n<\/p>\n<ol>\n<li><strong>\u0938\u092e\u091d\u0928\u093e<\/strong> \u0915\u093f \u0915\u094d\u0937\u0948\u0924\u093f\u091c \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\u0913\u0902 \u0915\u093e \u0915\u094d\u092f\u093e \u0905\u0930\u094d\u0925 \u0939\u0948 \u0914\u0930 \u0905\u0928\u0902\u0924 \u0915\u0940 \u0913\u0930 \u091c\u093e\u0924\u0947 \u0938\u092e\u092f \u0915\u093e\u0930\u094d\u092f\u094b\u0902 \u0915\u0947 \u0935\u094d\u092f\u0935\u0939\u093e\u0930 \u0915\u0947 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u092e\u0947\u0902 \u0909\u0928\u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0948\u0938\u0947 \u0915\u0930\u0947\u0902\u0964<\/li>\n<li><strong>\u092a\u0939\u091a\u093e\u0928\u0928\u093e<\/strong> \u0915\u093f \u090a\u0930\u094d\u0927\u094d\u0935\u093e\u0927\u0930 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\u0913\u0902 \u0915\u0940 \u0909\u092a\u0938\u094d\u0925\u093f\u0924\u093f \u0915\u0947 \u0932\u093f\u090f \u0915\u094d\u092f\u093e \u0936\u0930\u094d\u0924\u0947\u0902 \u0939\u094b\u0924\u0940 \u0939\u0948\u0902 \u0914\u0930 \u0905\u0928\u0902\u0924 \u0938\u0940\u092e\u093e\u0913\u0902 \u0935\u093e\u0932\u0947 \u0915\u093e\u0930\u094d\u092f\u094b\u0902 \u0915\u0947 \u0905\u0927\u094d\u092f\u092f\u0928 \u092e\u0947\u0902 \u0909\u0928\u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0948\u0938\u0947 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/li>\n<li><strong>\u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0928\u093e<\/strong> \u0915\u093f \u0924\u093f\u0930\u094d\u092f\u0915 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\u0913\u0902 \u0915\u093e \u092a\u094d\u0930\u0915\u091f \u0939\u094b\u0928\u093e \u0915\u092c \u0939\u094b\u0924\u093e \u0939\u0948, \u0935\u093f\u0936\u0947\u0937\u0915\u0930 \u0924\u092c \u091c\u092c \u0905\u0902\u0936 \u0915\u093e \u0918\u093e\u0924\u093e\u0902\u0915 \u0939\u0930 \u0915\u0947 \u0918\u093e\u0924\u093e\u0902\u0915 \u0938\u0947 \u0905\u0927\u093f\u0915 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/li>\n<li><strong>\u0932\u093e\u0917\u0942 \u0915\u0930\u0928\u093e<\/strong> \u092a\u094d\u0930\u092e\u0941\u0916 \u0936\u0930\u094d\u0924 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u093e\u0930\u094d\u092f\u094b\u0902 \u0915\u0947 \u0935\u094d\u092f\u0935\u0939\u093e\u0930 \u0915\u093e \u0905\u0928\u0941\u092e\u093e\u0928 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u091c\u092c <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0915\u093e \u092e\u093e\u0928 \u092c\u0921\u093c\u093e \u0939\u094b\u0924\u093e \u0939\u0948 \u092f\u093e \u0915\u0941\u091b \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u0947 \u092a\u093e\u0938 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/li>\n<li><strong>\u0938\u092e\u091d\u093e\u0928\u093e<\/strong> \u0915\u093f \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\u0913\u0902 \u0914\u0930 \u092a\u094d\u0930\u092e\u0941\u0916 \u0936\u0930\u094d\u0924\u094b\u0902 \u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u093e\u0930\u094d\u092f\u094b\u0902 \u0915\u0947 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0935\u094d\u092f\u0935\u0939\u093e\u0930 \u0915\u094b \u0938\u092e\u091d\u0928\u0947 \u092e\u0947\u0902 \u0915\u0948\u0938\u0947 \u092f\u094b\u0917\u0926\u093e\u0928 \u0926\u0947\u0924\u093e \u0939\u0948\u0964<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong><u>\u0938\u093e\u092e\u0917\u094d\u0930\u0940 \u0915\u093e \u0938\u0942\u091a\u0915\u093e\u0902\u0915<\/u>:<\/strong><br \/>\n<a href=\"#1\">\u092a\u0930\u093f\u091a\u092f<\/a><br \/>\n<a href=\"#2\">\u0915\u094d\u0937\u0948\u0924\u093f\u091c \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\u090f\u0901 \u0914\u0930 \u0905\u0928\u0902\u0924 \u092a\u0930 \u0938\u0940\u092e\u093e\u090f\u0901<\/a><br \/>\n<a href=\"#3\">\u090a\u0930\u094d\u0927\u094d\u0935\u093e\u0927\u0930 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\u090f\u0901 \u0914\u0930 \u0905\u0928\u0902\u0924 \u0938\u0940\u092e\u093e\u090f\u0901<\/a><br \/>\n<a href=\"#4\">\u0924\u093f\u0930\u094d\u092f\u0915 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\u090f\u0901, \u0935\u0915\u094d\u0930 \u0914\u0930 \u092a\u094d\u0930\u092e\u0941\u0916 \u0936\u0930\u094d\u0924\u0947\u0902<\/a><br \/>\n<a href=\"#5\">\u0938\u092e\u093e\u0927\u093e\u0928\u093e\u0924\u094d\u092e\u0915 \u0905\u092d\u094d\u092f\u093e\u0938<\/a><br \/>\n<a href=\"#6\">\u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935\u093f\u0924 \u0905\u092d\u094d\u092f\u093e\u0938<\/a>\n<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/Ekd0oSvMbfE\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u092a\u0930\u093f\u091a\u092f<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=Ekd0oSvMbfE&amp;t=98s\" target=\"_blank\" rel=\"noopener\"><strong>\u0905\u092c \u0924\u0915 \u091c\u094b \u0938\u0940\u092e\u093e\u090f\u0901 \u0939\u092e\u0928\u0947 \u0926\u0947\u0916\u0940 \u0939\u0948\u0902<\/strong><\/a> \u0935\u0947 \u0939\u092e\u0947\u0902 \u0915\u0941\u091b \u0909\u092a\u092f\u094b\u0917\u0940 \u0905\u0935\u0927\u093e\u0930\u0923\u093e\u0913\u0902 \u0915\u094b \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0940 \u0905\u0928\u0941\u092e\u0924\u093f \u0926\u0947\u0924\u0940 \u0939\u0948\u0902 \u0924\u093e\u0915\u093f \u0915\u093e\u0930\u094d\u092f\u094b\u0902 \u0915\u0947 \u0935\u0948\u0936\u094d\u0935\u093f\u0915 \u0935\u094d\u092f\u0935\u0939\u093e\u0930 \u0915\u094b \u0938\u092e\u091d\u093e \u091c\u093e \u0938\u0915\u0947, \u0907\u0928\u092e\u0947\u0902 \u092a\u094d\u0930\u092e\u0941\u0916 \u0936\u0930\u094d\u0924\u0947\u0902 \u0914\u0930 \u0915\u094d\u0937\u0948\u0924\u093f\u091c \u090f\u0935\u0902 \u090a\u0930\u094d\u0927\u094d\u0935\u093e\u0927\u0930 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\u090f\u0901 \u0936\u093e\u092e\u093f\u0932 \u0939\u0948\u0902; \u092f\u0947, \u092f\u0942\u0901 \u0915\u0939\u0947\u0902 \u0924\u094b, \u0910\u0938\u0940 \u0935\u0915\u094d\u0930 \u0939\u094b\u0924\u0940 \u0939\u0948\u0902 \u091c\u093f\u0928\u0915\u0947 \u0915\u0930\u0940\u092c \u0915\u093e\u0930\u094d\u092f \u0915\u093e \u0917\u094d\u0930\u093e\u092b <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0915\u0947 \u0915\u093f\u0938\u0940 \u092e\u093e\u0928 \u0915\u0940 \u0913\u0930 \u092c\u0922\u093c\u0924\u0947 \u0938\u092e\u092f \u092a\u0939\u0941\u0901\u091a\u0928\u0947 \u0915\u0940 \u0915\u094b\u0936\u093f\u0936 \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u0915\u094d\u0937\u0948\u0924\u093f\u091c \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\u090f\u0901 \u0914\u0930 \u0905\u0928\u0902\u0924 \u092a\u0930 \u0938\u0940\u092e\u093e\u090f\u0901<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=Ekd0oSvMbfE&amp;t=137s\" target=\"_blank\" rel=\"noopener\"><strong>\u092f\u0926\u093f <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u090f\u0915 \u0915\u093e\u0930\u094d\u092f \u0939\u0948<\/strong><\/a> \u091c\u094b <span class=\"katex-eq\" data-katex-display=\"false\">]a,+\\infty[<\/span> \u092a\u0930 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0939\u0948, \u091c\u0939\u093e\u0901 <span class=\"katex-eq\" data-katex-display=\"false\">a\\in\\mathbb{R}<\/span> \u0939\u094b, \u0924\u094b <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u0915\u093e \u0905\u0928\u0902\u0924 \u092a\u0930 \u0938\u0940\u092e\u093e \u0915\u093e \u092e\u0942\u0932\u094d\u092f \u0928\u093f\u0915\u093e\u0932\u0928\u093e \u0938\u0902\u092d\u0935 \u0939\u0948\u0964 \u092f\u0926\u093f \u0910\u0938\u0940 \u0938\u0940\u092e\u093e \u092e\u094c\u091c\u0942\u0926 \u0939\u0948, \u0924\u094b \u0907\u0938 \u0938\u0940\u092e\u093e \u0938\u0947 <strong>\u0926\u093e\u0908\u0902 \u0913\u0930 \u0915\u0940 \u0915\u094d\u0937\u0948\u0924\u093f\u091c \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e<\/strong> \u0928\u093f\u092e\u094d\u0928 \u0938\u092e\u0940\u0915\u0930\u0923 \u0938\u0947 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0939\u094b\u0924\u0940 \u0939\u0948:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">A_+(x) = L^+<\/span>\n<p>\u091c\u0939\u093e\u0901<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to +\\infty}f(x) = L^+<\/span>\n<p>\u0907\u0938\u0940 \u092a\u094d\u0930\u0915\u093e\u0930, <strong>\u092c\u093e\u0908\u0902 \u0913\u0930 \u0915\u0940 \u0915\u094d\u0937\u0948\u0924\u093f\u091c \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e<\/strong> \u0915\u0940 \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0928\u093f\u092e\u094d\u0928 \u0938\u092e\u0940\u0915\u0930\u0923 \u0938\u0947 \u0939\u094b\u0924\u0940 \u0939\u0948:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">A_-(x) = L^-<\/span>\n<p>\u091c\u092c<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to -\\infty}f(x) = L^-<\/span>\n<p>\u0915\u094d\u0937\u0948\u0924\u093f\u091c \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\u090f\u0901 \u0915\u093e\u0930\u094d\u092f <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u0915\u0947 \u0909\u0938 \u0938\u092e\u092f \u0915\u0947 \u0935\u094d\u092f\u0935\u0939\u093e\u0930 \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u0928\u0947 \u092e\u0947\u0902 \u092e\u0926\u0926 \u0915\u0930\u0924\u0940 \u0939\u0948\u0902 \u091c\u092c <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0915\u0947 \u092e\u093e\u0928 \u0905\u0938\u0940\u092e\u093f\u0924 \u0930\u0942\u092a \u0938\u0947 \u092c\u0922\u093c\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-ckBGkFWse2w\/YH1GWClIciI\/AAAAAAAAE6s\/zZ_se7yShqMLiEHKNT_jkgAWuK9cme5wwCLcBGAsYHQ\/s0\/as%25C3%25ADntotahorizontal.PNG\" alt=\"\u0915\u094d\u0937\u0948\u0924\u093f\u091c \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\u090f\u0901\" class=\"aligncenter lazyload\" width=\"478\" height=\"290\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-ckBGkFWse2w\/YH1GWClIciI\/AAAAAAAAE6s\/zZ_se7yShqMLiEHKNT_jkgAWuK9cme5wwCLcBGAsYHQ\/s0\/as%25C3%25ADntotahorizontal.PNG\" alt=\"\u0915\u094d\u0937\u0948\u0924\u093f\u091c \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\u090f\u0901\" class=\"aligncenter lazyload\" width=\"478\" height=\"290\" \/><\/noscript><\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>\u090a\u0930\u094d\u0927\u094d\u0935\u093e\u0927\u0930 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\u090f\u0901 \u0914\u0930 \u0905\u0928\u0902\u0924 \u0938\u0940\u092e\u093e\u090f\u0901<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=Ekd0oSvMbfE&amp;t=277s\" target=\"_blank\" rel=\"noopener\"><strong>\u0915\u094d\u0937\u0948\u0924\u093f\u091c \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\u0913\u0902 \u0915\u0940 \u0924\u0930\u0939 \u0939\u0940,<\/strong><\/a> <strong>\u090a\u0930\u094d\u0927\u094d\u0935\u093e\u0927\u0930 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\u090f\u0901<\/strong> \u092d\u0940 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948\u0902\u0964 \u0915\u093e\u0930\u094d\u092f <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u0915\u0940 <strong>\u090a\u0930\u094d\u0927\u094d\u0935\u093e\u0927\u0930 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e \u090a\u092a\u0930 \u0915\u0940 \u0913\u0930<\/strong> \u0924\u092c \u0939\u094b\u0924\u0940 \u0939\u0948 \u091c\u092c:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to a}f(x) = +\\infty<\/span>\n<p>\u0914\u0930 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e \u0928\u0940\u091a\u0947 \u0915\u0940 \u0913\u0930 \u0939\u094b\u0917\u0940 \u092f\u0926\u093f:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to a}f(x) = -\\infty<\/span>\n<p>\u0938\u0940\u092e\u093e\u0913\u0902 \u0915\u0940 \u0924\u0930\u094d\u0915 \u0915\u094b \u0938\u092e\u091d\u0924\u0947 \u0939\u0941\u090f, \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\u090f\u0901 \u0926\u093e\u0908\u0902 \u092f\u093e \u092c\u093e\u0908\u0902 \u0913\u0930 \u092d\u0940 \u0939\u094b \u0938\u0915\u0924\u0940 \u0939\u0948\u0902\u0964<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-ptEipMpyIhc\/YH1VDclyMxI\/AAAAAAAAE60\/LmzpK2HAU7oLpswJQy5_TLIv9jSf9whDwCLcBGAsYHQ\/s0\/asintotavertical.PNG\" alt=\"\u090a\u0930\u094d\u0927\u094d\u0935\u093e\u0927\u0930 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\" class=\" aligncenter lazyload\" width=\"428\" height=\"283\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-ptEipMpyIhc\/YH1VDclyMxI\/AAAAAAAAE60\/LmzpK2HAU7oLpswJQy5_TLIv9jSf9whDwCLcBGAsYHQ\/s0\/asintotavertical.PNG\" alt=\"\u090a\u0930\u094d\u0927\u094d\u0935\u093e\u0927\u0930 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\" class=\" aligncenter lazyload\" width=\"428\" height=\"283\" \/><\/noscript><\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2>\u0924\u093f\u0930\u094d\u092f\u0915 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\u090f\u0901, \u0935\u0915\u094d\u0930 \u0914\u0930 \u092a\u094d\u0930\u092e\u0941\u0916 \u0936\u0930\u094d\u0924\u0947\u0902<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=Ekd0oSvMbfE&amp;t=400s\" target=\"_blank\" rel=\"noopener\"><strong>\u0924\u093f\u0930\u094d\u092f\u0915 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\u0913\u0902 \u0915\u093e \u0938\u092c\u0938\u0947 \u0938\u0930\u0932 \u0930\u0942\u092a<\/strong><\/a> \u0924\u092c \u0926\u0947\u0916\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u091c\u092c \u0939\u092e \u092d\u093f\u0928\u094d\u0928\u093e\u0924\u094d\u092e\u0915 \u0915\u093e\u0930\u094d\u092f\u094b\u0902 \u0938\u0947 \u0915\u093e\u092e \u0915\u0930 \u0930\u0939\u0947 \u0939\u094b\u0902:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x) = \\dfrac{P(x)}{Q(x)}<\/span>\n<p>\u091c\u0939\u093e\u0901 <span class=\"katex-eq\" data-katex-display=\"false\">P(x)<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">Q(x)<\/span> \u092c\u0939\u0941\u092a\u0926 \u0939\u0948\u0902\u0964 \u091c\u092c <span class=\"katex-eq\" data-katex-display=\"false\">P(x)<\/span> \u0915\u093e \u0918\u093e\u0924\u093e\u0902\u0915 <span class=\"katex-eq\" data-katex-display=\"false\">Q(x)<\/span> \u0938\u0947 \u090f\u0915 \u0905\u0927\u093f\u0915 \u0939\u094b\u0924\u093e \u0939\u0948, \u0924\u094b \u092c\u0939\u0941\u092a\u0926\u094b\u0902 \u0915\u093e \u092d\u093e\u0917 \u0926\u0947\u0915\u0930 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0930\u0942\u092a \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x) = \\dfrac{P(x)}{Q(x)} = C(x) + \\dfrac{r(x)}{Q(x)}<\/span>\n<p>\u091c\u0939\u093e\u0901 <span class=\"katex-eq\" data-katex-display=\"false\">C(x)<\/span> \u092d\u093e\u0917\u092b\u0932 \u0939\u0948 \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">r(x)<\/span> \u0936\u0947\u0937 \u0939\u0948\u0964 \u092f\u0926\u093f <span class=\"katex-eq\" data-katex-display=\"false\">P(x)<\/span> \u0915\u093e \u0918\u093e\u0924\u093e\u0902\u0915 <span class=\"katex-eq\" data-katex-display=\"false\">Q(x)<\/span> \u0938\u0947 \u090f\u0915 \u0905\u0927\u093f\u0915 \u0939\u0948, \u0924\u094b <span class=\"katex-eq\" data-katex-display=\"false\">C(x)<\/span> \u090f\u0915 \u0930\u0947\u0916\u0940\u092f \u0930\u0942\u092a \u092e\u0947\u0902 \u0939\u094b\u0917\u093e \u0914\u0930 \u0907\u0938\u0947 \u0915\u093e\u0930\u094d\u092f <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u0915\u0940 <strong>\u0924\u093f\u0930\u094d\u092f\u0915 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e<\/strong> \u0915\u0939\u093e \u091c\u093e\u090f\u0917\u093e\u0964<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-wRTmSl2Z3HE\/YH1dSl-noDI\/AAAAAAAAE68\/og2lPX_ydUUGlxYnn5hgj2mNCSeAPoQKACLcBGAsYHQ\/s0\/asintotaoblicua.PNG\" alt=\"\u0924\u093f\u0930\u094d\u092f\u0915 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\" class=\" aligncenter lazyload\" width=\"404\" height=\"239\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-wRTmSl2Z3HE\/YH1dSl-noDI\/AAAAAAAAE68\/og2lPX_ydUUGlxYnn5hgj2mNCSeAPoQKACLcBGAsYHQ\/s0\/asintotaoblicua.PNG\" alt=\"\u0924\u093f\u0930\u094d\u092f\u0915 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\" class=\" aligncenter lazyload\" width=\"404\" height=\"239\" \/><\/noscript><\/p>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=Ekd0oSvMbfE&amp;t=633s\" target=\"_blank\" rel=\"noopener\"><strong>\u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0930\u0942\u092a \u0938\u0947, \u092f\u0926\u093f <span class=\"katex-eq\" data-katex-display=\"false\">P(x)<\/span> \u0915\u093e \u0918\u093e\u0924\u093e\u0902\u0915<\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">Q(x)<\/span> \u0938\u0947 \u0915\u094b\u0908 \u092d\u0940 \u092e\u093e\u0924\u094d\u0930\u093e \u0905\u0927\u093f\u0915 \u0939\u0948, \u0924\u094b <span class=\"katex-eq\" data-katex-display=\"false\">C(x)<\/span> \u0915\u093e \u0918\u093e\u0924\u093e\u0902\u0915 <span class=\"katex-eq\" data-katex-display=\"false\">P(x)<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">Q(x)<\/span> \u0915\u0947 \u0918\u093e\u0924\u093e\u0902\u0915\u094b\u0902 \u0915\u0947 \u0905\u0902\u0924\u0930 \u0915\u0947 \u092c\u0930\u093e\u092c\u0930 \u0939\u094b\u0917\u093e, \u0914\u0930 \u092f\u0939 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0930\u0942\u092a \u0938\u0947 \u090f\u0915 \u092c\u0939\u0941\u092a\u0926\u0940\u092f \u0935\u0915\u094d\u0930 \u0939\u094b\u0917\u093e\u0964 \u0907\u0938 \u0938\u094d\u0925\u093f\u0924\u093f \u092e\u0947\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">C(x)<\/span> \u0915\u094b \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e \u0928\u0939\u0940\u0902 \u0915\u0939\u093e \u091c\u093e\u0924\u093e, \u092d\u0932\u0947 \u0939\u0940 \u0915\u093e\u0930\u094d\u092f <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u0915\u093e \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0935\u094d\u092f\u0935\u0939\u093e\u0930 \u00ab<span class=\"katex-eq\" data-katex-display=\"false\">C(x)<\/span>\u00bb \u0915\u0947 \u0915\u0930\u0940\u092c \u092a\u0939\u0941\u0901\u091a\u0928\u093e \u0939\u094b\u0964 \u0910\u0938\u0947 \u092e\u093e\u092e\u0932\u094b\u0902 \u092e\u0947\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">C(x)<\/span> \u0915\u094b <strong><span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0915\u0947 \u092c\u0921\u093c\u0947 \u092e\u0942\u0932\u094d\u092f\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u0915\u093e \u092a\u094d\u0930\u092e\u0941\u0916 \u0936\u0930\u094d\u0924<\/strong> \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-IEYO071tTuY\/YH1fjR-WWnI\/AAAAAAAAE7E\/ga2rZ02i8QU5R1IMvQB9rpgFuDknAGfbACLcBGAsYHQ\/s0\/terminoDominante.PNG\" alt=\"\u092a\u094d\u0930\u092e\u0941\u0916 \u0936\u0930\u094d\u0924 \u0914\u0930 \u090a\u0930\u094d\u0927\u094d\u0935\u093e\u0927\u0930 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\" class=\" aligncenter lazyload\" width=\"479\" height=\"437\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-IEYO071tTuY\/YH1fjR-WWnI\/AAAAAAAAE7E\/ga2rZ02i8QU5R1IMvQB9rpgFuDknAGfbACLcBGAsYHQ\/s0\/terminoDominante.PNG\" alt=\"\u092a\u094d\u0930\u092e\u0941\u0916 \u0936\u0930\u094d\u0924 \u0914\u0930 \u090a\u0930\u094d\u0927\u094d\u0935\u093e\u0927\u0930 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\" class=\" aligncenter lazyload\" width=\"479\" height=\"437\" \/><\/noscript><\/p>\n<p>\u091c\u092c <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0915\u093f\u0938\u0940 <span class=\"katex-eq\" data-katex-display=\"false\">a\\in\\mathbb{R}<\/span> \u0915\u0947 \u092a\u093e\u0938 \u0939\u094b\u0924\u093e \u0939\u0948, \u0924\u092c \u092d\u0940 \u092a\u094d\u0930\u092e\u0941\u0916 \u0936\u0930\u094d\u0924 \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u092c\u093e\u0924 \u0915\u0940 \u091c\u093e \u0938\u0915\u0924\u0940 \u0939\u0948\u0964<\/p>\n<p>\u092f\u0926\u093f <span class=\"katex-eq\" data-katex-display=\"false\">f(x) = P(x)\/Q(x) = C(x) + r(x)\/Q(x),<\/span> \u091c\u0939\u093e\u0901 <span class=\"katex-eq\" data-katex-display=\"false\">P(x),<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">Q(x),<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">r(x)<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">C(x)<\/span> \u092c\u0939\u0941\u092a\u0926 \u0939\u0948\u0902\u0964 \u092f\u0926\u093f <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to a}f(x) = \\infty,<\/span> \u0924\u094b \u092f\u0939 \u0915\u0939\u093e \u091c\u093e\u090f\u0917\u093e \u0915\u093f <span class=\"katex-eq\" data-katex-display=\"false\">r(x)\/Q(x)<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u0915\u093e <strong>\u092a\u094d\u0930\u092e\u0941\u0916 \u0936\u0930\u094d\u0924 \u0939\u0948 \u091c\u092c <span class=\"katex-eq\" data-katex-display=\"false\">x=a.<\/span><\/strong><\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>\u0938\u092e\u093e\u0927\u093e\u0928\u093e\u0924\u094d\u092e\u0915 \u0905\u092d\u094d\u092f\u093e\u0938<\/h2>\n<h3><strong>\u0905\u092d\u094d\u092f\u093e\u0938 1:<\/strong><\/h3>\n<p>\u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0915\u093e\u0930\u094d\u092f \u0915\u0940 \u0915\u094d\u0937\u0948\u0924\u093f\u091c \u0914\u0930 \u090a\u0930\u094d\u0927\u094d\u0935\u093e\u0927\u0930 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\u090f\u0901 \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u0930\u0947\u0902:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x) = \\dfrac{3x + 1}{x - 2}<\/span>\n<p><strong>\u0938\u092e\u093e\u0927\u093e\u0928:<\/strong><\/p>\n<p><strong>\u0915\u094d\u0937\u0948\u0924\u093f\u091c \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e<\/strong> \u0916\u094b\u091c\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u0939\u092e <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u0915\u093e \u0905\u0928\u0902\u0924 \u092a\u0930 \u0938\u0940\u092e\u093e \u0928\u093f\u0915\u093e\u0932\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to\\pm\\infty} \\dfrac{3x + 1}{x - 2} = 3<\/span>\n<p>\u0907\u0938\u0932\u093f\u090f \u0915\u094d\u0937\u0948\u0924\u093f\u091c \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e <span class=\"katex-eq\" data-katex-display=\"false\">y = 3<\/span> \u0939\u0948\u0964<\/p>\n<p><strong>\u090a\u0930\u094d\u0927\u094d\u0935\u093e\u0927\u0930 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e<\/strong> \u0915\u0947 \u0932\u093f\u090f, \u0939\u092e \u0909\u0938 \u092e\u093e\u0928 \u0915\u094b \u092a\u0939\u091a\u093e\u0928\u0924\u0947 \u0939\u0948\u0902 \u091c\u0939\u093e\u0901 \u0939\u0930 \u0936\u0942\u0928\u094d\u092f \u0939\u094b\u0924\u093e \u0939\u0948, \u0905\u0930\u094d\u0925\u093e\u0924\u094d <span class=\"katex-eq\" data-katex-display=\"false\">x = 2<\/span>\u0964<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{z\\to 2^\\pm} \\dfrac{3x + 1}{x - 2} = \\pm\\infty<\/span>\n<p>\u092f\u0939 \u0907\u0902\u0917\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 \u0915\u093f <span class=\"katex-eq\" data-katex-display=\"false\">x = 2<\/span> \u092a\u0930 \u090a\u0930\u094d\u0927\u094d\u0935\u093e\u0927\u0930 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e \u0939\u0948\u0964<\/p>\n<p><strong>\u0905\u0902\u0924\u093f\u092e \u092a\u0930\u093f\u0923\u093e\u092e:<\/strong> \u0915\u093e\u0930\u094d\u092f \u0915\u0940 \u0915\u094d\u0937\u0948\u0924\u093f\u091c \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e <span class=\"katex-eq\" data-katex-display=\"false\">y = 3<\/span> \u0939\u0948 \u0914\u0930 \u090a\u0930\u094d\u0927\u094d\u0935\u093e\u0927\u0930 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e <span class=\"katex-eq\" data-katex-display=\"false\">x = 2<\/span> \u092a\u0930 \u0939\u0948\u0964<\/p>\n<h3><strong>\u0905\u092d\u094d\u092f\u093e\u0938 2:<\/strong><\/h3>\n<p>\u0915\u093e\u0930\u094d\u092f <span class=\"katex-eq\" data-katex-display=\"false\">g(x) =\\dfrac{2x^2 + 3x + 4}{x + 1}<\/span> \u0915\u0940 \u0915\u094d\u0937\u0948\u0924\u093f\u091c \u0914\u0930 \u0924\u093f\u0930\u094d\u092f\u0915 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\u090f\u0901, \u092f\u0926\u093f \u092e\u094c\u091c\u0942\u0926 \u0939\u094b\u0902, \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0947\u0902\u0964<\/p>\n<p><strong>\u0938\u092e\u093e\u0927\u093e\u0928:<\/strong><\/p>\n<p>\u092a\u0939\u0932\u0947 \u0939\u092e \u0905\u0928\u0902\u0924 \u092a\u0930 \u0938\u0940\u092e\u093e \u0928\u093f\u0915\u093e\u0932\u0924\u0947 \u0939\u0948\u0902\u0964 \u091a\u0942\u0902\u0915\u093f \u0905\u0902\u0936 \u0915\u093e \u0918\u093e\u0924\u093e\u0902\u0915 \u0939\u0930 \u0938\u0947 \u0905\u0927\u093f\u0915 \u0939\u0948, \u0915\u094b\u0908 \u0915\u094d\u0937\u0948\u0924\u093f\u091c \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e \u0928\u0939\u0940\u0902 \u0939\u0948\u0964<\/p>\n<p>\u0924\u093f\u0930\u094d\u092f\u0915 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e \u0915\u0947 \u0932\u093f\u090f, \u0939\u092e \u092c\u0939\u0941\u092a\u0926 \u0915\u093e \u092d\u093e\u0917 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{2x^2 + 3x + 4}{x + 1} = 2x + 1 + \\dfrac{3}{x + 1}<\/span>\n<p>\u0907\u0938\u0932\u093f\u090f \u0924\u093f\u0930\u094d\u092f\u0915 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e <span class=\"katex-eq\" data-katex-display=\"false\">y = 2x + 1<\/span> \u0939\u0948\u0964<\/p>\n<p><strong>\u0905\u0902\u0924\u093f\u092e \u092a\u0930\u093f\u0923\u093e\u092e:<\/strong> \u0915\u093e\u0930\u094d\u092f \u0915\u0940 \u0915\u094b\u0908 \u0915\u094d\u0937\u0948\u0924\u093f\u091c \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e \u0928\u0939\u0940\u0902 \u0939\u0948, \u0932\u0947\u0915\u093f\u0928 \u0924\u093f\u0930\u094d\u092f\u0915 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e <span class=\"katex-eq\" data-katex-display=\"false\">y = 2x + 1<\/span> \u0939\u0948\u0964<\/p>\n<h3><strong>\u0905\u092d\u094d\u092f\u093e\u0938 3:<\/strong><\/h3>\n<span class=\"katex-eq\" data-katex-display=\"false\">h(x) =\\dfrac{5}{x^2 - 4}<\/span> \u0915\u0940 \u090a\u0930\u094d\u0927\u094d\u0935\u093e\u0927\u0930 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0947\u0902\u0964<\/p>\n<p><strong>\u0938\u092e\u093e\u0927\u093e\u0928:<\/strong><\/p>\n<p>\u090a\u0930\u094d\u0927\u094d\u0935\u093e\u0927\u0930 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e \u0915\u0947 \u0932\u093f\u090f, \u0939\u092e \u0939\u0930 \u0915\u094b \u0936\u0942\u0928\u094d\u092f \u0915\u0930\u0928\u0947 \u0935\u093e\u0932\u0947 \u092e\u0942\u0932\u094d\u092f\u094b\u0902 \u0915\u094b \u092a\u0939\u091a\u093e\u0928\u0924\u0947 \u0939\u0948\u0902: <span class=\"katex-eq\" data-katex-display=\"false\">x^2 - 4 = 0<\/span>, \u091c\u094b <span class=\"katex-eq\" data-katex-display=\"false\">x = \\pm 2<\/span> \u092a\u0930 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/p>\n<p>\u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092e\u0942\u0932\u094d\u092f \u0915\u0947 \u0932\u093f\u090f \u092a\u093e\u0930\u094d\u0936\u094d\u0935 \u0938\u0940\u092e\u093e\u0913\u0902 \u0915\u093e \u092e\u0942\u0932\u094d\u092f\u093e\u0902\u0915\u0928 \u0915\u0930\u0947\u0902:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to 2^\\pm}\\dfrac{5}{x^2 - 4} = \\pm\\infty<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to -2^\\pm} \\dfrac{5}{x^2 - 4} = \\pm\\infty<\/span>\n<p><strong>\u0905\u0902\u0924\u093f\u092e \u092a\u0930\u093f\u0923\u093e\u092e:<\/strong> \u0915\u093e\u0930\u094d\u092f \u0915\u0940 \u090a\u0930\u094d\u0927\u094d\u0935\u093e\u0927\u0930 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\u090f\u0901 <span class=\"katex-eq\" data-katex-display=\"false\">x = 2<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">x = -2<\/span> \u092a\u0930 \u0939\u0948\u0902\u0964<\/p>\n<p><a name=\"6\"><\/a><\/p>\n<h2>\u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935\u093f\u0924 \u0905\u092d\u094d\u092f\u093e\u0938<\/h2>\n<ol>\n<li>\u0915\u093e\u0930\u094d\u092f <span class=\"katex-eq\" data-katex-display=\"false\">f(x) =\\dfrac{2x^2 - 3x + 1}{x^2 + x - 2}<\/span> \u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0947\u0902\u0964 \u0907\u0938\u0915\u0940 \u0915\u094d\u0937\u0948\u0924\u093f\u091c, \u090a\u0930\u094d\u0927\u094d\u0935\u093e\u0927\u0930 \u0914\u0930 \u0924\u093f\u0930\u094d\u092f\u0915 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\u090f\u0901 \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0947\u0902, \u092f\u0926\u093f \u092e\u094c\u091c\u0942\u0926 \u0939\u094b\u0902\u0964 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u091a\u0930\u0923 \u0915\u094b \u0938\u092e\u091d\u093e\u0924\u0947 \u0939\u0941\u090f \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\u0913\u0902 \u0914\u0930 \u0938\u0940\u092e\u093e\u0913\u0902 \u0915\u0940 \u0905\u0935\u0927\u093e\u0930\u0923\u093e \u0915\u094b \u0938\u0941\u0926\u0943\u0922\u093c \u0915\u0930\u0947\u0902\u0964<\/li>\n<li>\u0915\u093e\u0930\u094d\u092f <span class=\"katex-eq\" data-katex-display=\"false\">g(x) =\\dfrac{3x^3 + 2x}{x^2 + 1}<\/span> \u0915\u093e \u092e\u0942\u0932\u094d\u092f\u093e\u0902\u0915\u0928 \u0915\u0930\u0947\u0902\u0964 \u0905\u0928\u0902\u0924 \u0915\u0940 \u0913\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0915\u0947 \u092c\u0922\u093c\u0928\u0947 \u092a\u0930 \u092a\u094d\u0930\u092e\u0941\u0916 \u0936\u0930\u094d\u0924 \u0915\u0940 \u092a\u0939\u091a\u093e\u0928 \u0915\u0930\u0947\u0902\u0964 \u092b\u093f\u0930 \u091c\u093e\u0902\u091a\u0947\u0902 \u0915\u093f \u0924\u093f\u0930\u094d\u092f\u0915 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e \u0939\u0948 \u092f\u093e \u0928\u0939\u0940\u0902, \u0905\u092a\u0928\u0947 \u0909\u0924\u094d\u0924\u0930 \u0915\u094b \u0909\u091a\u093f\u0924 \u0920\u0939\u0930\u093e\u090f\u0902\u0964<\/li>\n<li>\u0915\u093e\u0930\u094d\u092f <span class=\"katex-eq\" data-katex-display=\"false\">h(x) =\\dfrac{5x - 4}{x + 1}<\/span> \u0915\u093e \u0905\u0928\u0941\u092e\u093e\u0928\u093f\u0924 \u0917\u094d\u0930\u093e\u092b \u0924\u0948\u092f\u093e\u0930 \u0915\u0930\u0947\u0902\u0964 \u0907\u0938\u092e\u0947\u0902 \u0915\u094d\u0937\u0948\u0924\u093f\u091c, \u090a\u0930\u094d\u0927\u094d\u0935\u093e\u0927\u0930 \u0914\u0930 \u0924\u093f\u0930\u094d\u092f\u0915 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\u090f\u0901 (\u092f\u0926\u093f \u092e\u094c\u091c\u0942\u0926 \u0939\u094b\u0902) \u0936\u093e\u092e\u093f\u0932 \u0915\u0930\u0947\u0902 \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">h(x)<\/span> \u0915\u0947 \u091a\u0930\u092e \u092e\u093e\u0928\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0935\u094d\u092f\u0935\u0939\u093e\u0930 \u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0947\u0902\u0964<\/li>\n<li>\u0915\u093e\u0930\u094d\u092f <span class=\"katex-eq\" data-katex-display=\"false\">k(x) =\\dfrac{x^2 - 4x + 3}{x^2 - 1}<\/span> \u0915\u0940 \u090a\u0930\u094d\u0927\u094d\u0935\u093e\u0927\u0930 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\u0913\u0902 \u0915\u0940 \u091c\u093e\u0901\u091a \u0915\u0930\u0947\u0902\u0964 \u0905\u0928\u0902\u0924 \u092a\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">k(x)<\/span> \u0915\u0940 \u0938\u0940\u092e\u093e \u0915\u0947 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u092e\u0947\u0902 \u092a\u094d\u0930\u092e\u0941\u0916 \u0936\u0930\u094d\u0924\u094b\u0902 \u0915\u0940 \u092d\u0942\u092e\u093f\u0915\u093e \u092a\u0930 \u091a\u0930\u094d\u091a\u093e \u0915\u0930\u0947\u0902\u0964<\/li>\n<li>\u0915\u093e\u0930\u094d\u092f <span class=\"katex-eq\" data-katex-display=\"false\">m(x) =\\dfrac{2x^4 + 3x^2 - x + 5}{x^3 - x^2 + 2}<\/span> \u0915\u0947 \u092a\u094d\u0930\u092e\u0941\u0916 \u0936\u0930\u094d\u0924\u094b\u0902 \u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0947\u0902\u0964 \u091c\u092c <span class=\"katex-eq\" data-katex-display=\"false\">x \to \\pm\\infty<\/span> \u0939\u094b \u0924\u094b <span class=\"katex-eq\" data-katex-display=\"false\">m(x)<\/span> \u0915\u0947 \u0935\u094d\u092f\u0935\u0939\u093e\u0930 \u0915\u093e \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u0923 \u0915\u0930\u0947\u0902 \u0914\u0930 \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937 \u0928\u093f\u0915\u093e\u0932\u0947\u0902 \u0915\u093f \u0915\u094d\u092f\u093e \u092f\u0939 \u090f\u0915 \u092c\u0939\u0941\u092a\u0926\u0940\u092f \u0935\u0915\u094d\u0930 \u0915\u0947 \u0915\u0930\u0940\u092c \u092a\u0939\u0941\u0901\u091a\u0924\u093e \u0939\u0948 \u092c\u091c\u093e\u092f \u0915\u093f\u0938\u0940 \u0930\u0947\u0916\u093e \u0915\u0947\u0964<\/li>\n<li>\u0905\u092a\u0928\u0940 \u092a\u0938\u0902\u0926 \u0915\u093e \u0915\u094b\u0908 \u092d\u093f\u0928\u094d\u0928\u093e\u0924\u094d\u092e\u0915 \u0915\u093e\u0930\u094d\u092f \u0924\u0948\u092f\u093e\u0930 \u0915\u0930\u0947\u0902 \u0914\u0930 \u0935\u093f\u0938\u094d\u0924\u093e\u0930\u092a\u0942\u0930\u094d\u0935\u0915 \u0909\u0938\u0915\u0940 \u0915\u094d\u0937\u0948\u0924\u093f\u091c, \u090a\u0930\u094d\u0927\u094d\u0935\u093e\u0927\u0930 \u0914\u0930 \u0924\u093f\u0930\u094d\u092f\u0915 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\u0913\u0902 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0948\u0938\u0947 \u0915\u0930\u0947\u0902, \u0907\u0938\u0915\u093e \u0935\u0930\u094d\u0923\u0928 \u0915\u0930\u0947\u0902, \u0938\u093e\u0925 \u0939\u0940 \u092a\u094d\u0930\u092e\u0941\u0916 \u0936\u0930\u094d\u0924\u094b\u0902 \u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0947\u0902\u0964 \u0905\u092a\u0928\u0947 \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937\u094b\u0902 \u0915\u094b \u0917\u094d\u0930\u093e\u092b\u093f\u0915\u094d\u0938 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0915\u0930\u0947\u0902 \u0924\u093e\u0915\u093f \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u0940 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e \u0915\u093e \u0926\u0943\u0936\u094d\u092f \u092a\u094d\u0930\u0926\u0930\u094d\u0936\u0928 \u0939\u094b \u0938\u0915\u0947\u0964<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e, \u0938\u0940\u092e\u093e\u090f\u0901 \u0914\u0930 \u0917\u094d\u0930\u093e\u092b\u093c\u093f\u0915\u0932 \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924\u093f \u0924\u0915\u0928\u0940\u0915\u0947\u0902 \u0938\u093e\u0930\u093e\u0902\u0936: \u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0915\u093e\u0930\u094d\u092f\u094b\u0902 \u0915\u0947 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u092e\u0947\u0902 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e \u0914\u0930 \u092a\u094d\u0930\u092e\u0941\u0916 \u0936\u0930\u094d\u0924\u094b\u0902 \u0915\u0940 \u0905\u0935\u0927\u093e\u0930\u0923\u093e\u0913\u0902 \u0915\u094b \u0938\u092e\u091d\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948\u0964 \u0907\u0938\u092e\u0947\u0902 \u0915\u094d\u0937\u0948\u0924\u093f\u091c \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\u0913\u0902 \u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u091c\u094b \u0924\u092c \u0915\u093e\u0930\u094d\u092f \u0915\u0947 \u0935\u094d\u092f\u0935\u0939\u093e\u0930 \u0915\u093e \u0935\u0930\u094d\u0923\u0928 \u0915\u0930\u0924\u0940 \u0939\u0948\u0902 \u091c\u092c \u0905\u0928\u0902\u0924 \u0915\u0940 \u0913\u0930 \u091c\u093e\u0924\u093e \u0939\u0948; \u090a\u0930\u094d\u0927\u094d\u0935\u093e\u0927\u0930 \u0906\u0938\u093f\u0902\u091f\u094b\u091f\u093e\u090f\u0901, \u091c\u094b \u0905\u0928\u0902\u0924 \u0938\u0940\u092e\u093e\u090f\u0901 \u0926\u0930\u094d\u0936\u093e\u0924\u0940 \u0939\u0948\u0902 \u091c\u092c [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":29511,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":1,"footnotes":""},"categories":[862,577],"tags":[],"class_list":["post-29523","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-862","category-577"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0905\u0938\u093f\u092e\u094d\u092a\u091f\u094b\u091f\u093e, \u0938\u0940\u092e\u093e\u090f\u0901 \u0914\u0930 \u0917\u094d\u0930\u093e\u092b\u093f\u0915 \u092a\u094d\u0930\u0924\u093f\u0928\u093f\u0927\u093f\u0924\u094d\u0935 \u0915\u0940 \u0924\u0915\u0928\u0940\u0915\u0947\u0902 - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u092f\u0939 \u092e\u093e\u0930\u094d\u0917\u0926\u0930\u094d\u0936\u093f\u0915\u093e 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\/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0905\u0938\u093f\u092e\u094d\u092a\u091f\u094b\u091f\u093e, \u0938\u0940\u092e\u093e\u090f\u0901 \u0914\u0930 \u0917\u094d\u0930\u093e\u092b\u093f\u0915 \u092a\u094d\u0930\u0924\u093f\u0928\u093f\u0927\u093f\u0924\u094d\u0935 \u0915\u0940 \u0924\u0915\u0928\u0940\u0915\u0947\u0902\" \/>\n<meta property=\"og:description\" content=\"\u092f\u0939 \u092e\u093e\u0930\u094d\u0917\u0926\u0930\u094d\u0936\u093f\u0915\u093e \u0906\u092a\u0915\u094b \u0915\u094d\u0937\u0948\u0924\u093f\u091c, \u0932\u0902\u092c\u0935\u0924 \u0914\u0930 \u0924\u093f\u0930\u091b\u0940 \u0905\u0938\u093f\u092e\u094d\u092a\u091f\u094b\u091f\u093e\u0913\u0902 \u0915\u094b \u0938\u092e\u091d\u0928\u0947 \u092e\u0947\u0902 \u092e\u0926\u0926 \u0915\u0930\u0947\u0917\u0940, \u0914\u0930 \u0909\u0928\u094d\u0939\u0947\u0902 \u0938\u0940\u092e\u093e\u0913\u0902 \u0915\u0947 \u0905\u0927\u094d\u092f\u092f\u0928 \u0938\u0947 \u0915\u0948\u0938\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964\" \/>\n<meta property=\"og:url\" content=\"https:\/\/toposuranos.com\/material\/hi\/\u0905\u0938\u093f\u092e\u094d\u092a\u091f\u094b\u091f\u093e-\u0938\u0940\u092e\u093e\u090f\u0901-\u0914\u0930-\u0917\u094d\u0930\/\" \/>\n<meta property=\"og:site_name\" content=\"toposuranos.com\/material\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/groups\/toposuranos\" \/>\n<meta property=\"article:published_time\" content=\"2024-11-18T02:30:47+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-11-18T02:34:53+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/11\/asintotas-1024x550.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"\u0905\u0938\u093f\u092e\u094d\u092a\u091f\u094b\u091f\u093e, \u0938\u0940\u092e\u093e\u090f\u0901 \u0914\u0930 \u0917\u094d\u0930\u093e\u092b\u093f\u0915 \u092a\u094d\u0930\u0924\u093f\u0928\u093f\u0927\u093f\u0924\u094d\u0935 \u0915\u0940 \u0924\u0915\u0928\u0940\u0915\u0947\u0902\" \/>\n<meta name=\"twitter:description\" content=\"\u092f\u0939 \u092e\u093e\u0930\u094d\u0917\u0926\u0930\u094d\u0936\u093f\u0915\u093e \u0906\u092a\u0915\u094b \u0915\u094d\u0937\u0948\u0924\u093f\u091c, \u0932\u0902\u092c\u0935\u0924 \u0914\u0930 \u0924\u093f\u0930\u091b\u0940 \u0905\u0938\u093f\u092e\u094d\u092a\u091f\u094b\u091f\u093e\u0913\u0902 \u0915\u094b \u0938\u092e\u091d\u0928\u0947 \u092e\u0947\u0902 \u092e\u0926\u0926 \u0915\u0930\u0947\u0917\u0940, \u0914\u0930 \u0909\u0928\u094d\u0939\u0947\u0902 \u0938\u0940\u092e\u093e\u0913\u0902 \u0915\u0947 \u0905\u0927\u094d\u092f\u092f\u0928 \u0938\u0947 \u0915\u0948\u0938\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 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