{"id":29568,"date":"2024-11-18T17:33:45","date_gmt":"2024-11-18T17:33:45","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=29568"},"modified":"2024-11-18T17:33:45","modified_gmt":"2024-11-18T17:33:45","slug":"%e0%a4%b8%e0%a5%80%e0%a4%ae%e0%a4%be-%e0%a4%94%e0%a4%b0-%e0%a4%a8%e0%a4%bf%e0%a4%b0%e0%a4%82%e0%a4%a4%e0%a4%b0%e0%a4%a4%e0%a4%be","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/hi\/%e0%a4%b8%e0%a5%80%e0%a4%ae%e0%a4%be-%e0%a4%94%e0%a4%b0-%e0%a4%a8%e0%a4%bf%e0%a4%b0%e0%a4%82%e0%a4%a4%e0%a4%b0%e0%a4%a4%e0%a4%be\/","title":{"rendered":"\u0938\u0940\u092e\u093e \u0914\u0930 \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e"},"content":{"rendered":"<style>\np {\ntext-align:justify;\n}\n<\/style>\n<p><center><\/p>\n<h1>\u0938\u0940\u092e\u093e \u0914\u0930 \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e<\/h1>\n<p><\/center><\/p>\n<p style=\"text-align:center;\"><em><strong>\u0938\u093e\u0930\u093e\u0902\u0936:<\/strong><\/em><br \/>\n\u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0939\u092e \u090f\u0915 \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0915\u0940 \u0938\u0940\u092e\u093e \u0914\u0930 \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e \u0915\u0947 \u092c\u0940\u091a \u0915\u0947 \u0938\u0902\u092c\u0902\u0927 \u092a\u0930 \u091a\u0930\u094d\u091a\u093e \u0915\u0930\u0947\u0902\u0917\u0947, \u091c\u093f\u0938\u0947 \u090f\u0915 \u0938\u0939\u091c \u0914\u0930 \u0914\u092a\u091a\u093e\u0930\u093f\u0915 \u0938\u094d\u092a\u0937\u094d\u091f\u0940\u0915\u0930\u0923 \u0915\u0947 \u0938\u093e\u0925 \u0936\u0941\u0930\u0942 \u0915\u093f\u092f\u093e \u091c\u093e\u090f\u0917\u093e\u0964 \u0915\u093f\u0938\u0940 \u092c\u093f\u0902\u0926\u0941 \u0914\u0930 \u0915\u093f\u0938\u0940 \u0938\u0947\u091f \u092a\u0930 \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e \u0915\u093e \u092a\u0924\u093e \u0932\u0917\u093e\u092f\u093e \u091c\u093e\u090f\u0917\u093e, \u092f\u0939 \u0938\u092e\u091d\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f \u090f\u0915 \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0915\u0947 \u0928\u093f\u0930\u0902\u0924\u0930 \u0939\u094b\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f\u0928 \u0936\u0930\u094d\u0924\u094b\u0902 \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 \u0928\u093f\u0930\u0902\u0924\u0930 \u092b\u093c\u0902\u0915\u094d\u0936\u0928\u094b\u0902 \u0915\u0947 \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u0917\u0941\u0923\u094b\u0902 \u0915\u094b \u092d\u0940 \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u090f\u0917\u093e, \u091c\u093f\u0928\u092e\u0947\u0902 \u091c\u094b\u0921\u093c, \u0917\u0941\u0923\u0928, \u0935\u093f\u092d\u093e\u091c\u0928 \u0914\u0930 \u0938\u0902\u092f\u094b\u091c\u0928 \u0936\u093e\u092e\u093f\u0932 \u0939\u0948\u0902\u0964 \u0905\u0902\u0924 \u092e\u0947\u0902, \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0915\u093e\u0930\u094d\u092f\u094b\u0902 \u0915\u0940 \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e \u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0928\u0947 \u0914\u0930 \u0938\u0940\u092e\u093e \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0935\u094d\u092f\u093e\u0935\u0939\u093e\u0930\u093f\u0915 \u0909\u0926\u093e\u0939\u0930\u0923 \u0939\u0932 \u0915\u093f\u090f \u091c\u093e\u090f\u0902\u0917\u0947, \u091c\u093f\u0928\u094d\u0939\u0947\u0902 \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e \u0915\u0940 \u0905\u0935\u0927\u093e\u0930\u0923\u093e \u0938\u0947 \u091c\u094b\u0921\u093c\u093e \u091c\u093e\u090f\u0917\u093e\u0964\n<\/p>\n<p style=\"text-align:center;\"><strong>\u0905\u0927\u094d\u092f\u092f\u0928 \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 \u0924\u0915, \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:<\/p>\n<ol>\n<li><strong>\u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0928\u093e<\/strong> \u0915\u093f \u0915\u093f\u0938\u0940 \u092c\u093f\u0902\u0926\u0941 \u092a\u0930 \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0928\u093f\u0930\u0902\u0924\u0930 \u0939\u0948 \u092f\u093e \u0928\u0939\u0940\u0902, \u0914\u0930 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0940 \u0917\u0908 \u0936\u0930\u094d\u0924\u094b\u0902 \u0915\u094b \u0938\u0924\u094d\u092f\u093e\u092a\u093f\u0924 \u0915\u0930\u0928\u093e\u0964<\/li>\n<li><strong>\u092e\u0942\u0932\u094d\u092f\u093e\u0902\u0915\u0928 \u0915\u0930\u0928\u093e<\/strong> \u0915\u093f \u0915\u094b\u0908 \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0915\u093f\u0938\u0940 \u0928\u093f\u0930\u094d\u0926\u093f\u0937\u094d\u091f \u0938\u0947\u091f \u092e\u0947\u0902 \u0928\u093f\u0930\u0902\u0924\u0930 \u0939\u0948 \u092f\u093e \u0928\u0939\u0940\u0902, \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e \u0915\u0940 \u0914\u092a\u091a\u093e\u0930\u093f\u0915 \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947\u0964<\/li>\n<li><strong>\u092a\u094d\u0930\u0926\u0930\u094d\u0936\u093f\u0924 \u0915\u0930\u0928\u093e<\/strong> \u0915\u093f \u090f\u0915 \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0905\u092a\u0928\u0940 \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u0917\u0941\u0923\u094b\u0902 \u0915\u0947 \u0906\u0927\u093e\u0930 \u092a\u0930 \u0928\u093f\u0930\u0902\u0924\u0930 \u0939\u0948\u0964<\/li>\n<li><strong>\u0935\u0930\u094d\u0917\u0940\u0915\u0943\u0924 \u0915\u0930\u0928\u093e<\/strong> \u0905\u0938\u0902\u0932\u0917\u094d\u0928\u0924\u093e \u0915\u0947 \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u094b, \u0909\u0928 \u0936\u0930\u094d\u0924\u094b\u0902 \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930 \u091c\u094b \u092a\u0942\u0930\u0940 \u0928\u0939\u0940\u0902 \u0939\u094b\u0924\u0940\u0902\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\u093f\u0938\u0940 \u092c\u093f\u0902\u0926\u0941 \u092a\u0930 \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e<\/a><br \/>\n<a href=\"#3\">\u090f\u0915 \u0938\u0947\u091f \u092a\u0930 \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e<\/a><br \/>\n<a href=\"#4\">\u0928\u093f\u0930\u0902\u0924\u0930 \u0915\u093e\u0930\u094d\u092f\u094b\u0902 \u0915\u0947 \u0917\u0941\u0923<\/a><br \/>\n<a href=\"#5\">\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\/4kehfJcyPRg\" title=\"YouTube \u0935\u0940\u0921\u093f\u092f\u094b \u092a\u094d\u0932\u0947\u092f\u0930\" 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=4kehfJcyPRg&amp;t=109s\" target=\"_blank\" rel=\"noopener\"><strong>\u0938\u0939\u091c \u0930\u0942\u092a \u092e\u0947\u0902, \u090f\u0915 \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0915\u0940 \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e<\/strong><\/a> \u0915\u094b \u0907\u0938 \u0924\u0930\u0939 \u0938\u092e\u091d\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u0907\u0938\u0915\u093e \u0917\u094d\u0930\u093e\u092b \u00ab\u092c\u093f\u0928\u093e \u092a\u0947\u0902\u0938\u093f\u0932 \u0909\u0920\u093e\u090f\u00bb \u092c\u0928\u093e\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u092f\u0939 \u0935\u093f\u091a\u093e\u0930 \u091c\u094b \u0915\u093f \u0905\u092a\u0928\u0947 \u0906\u092a \u092e\u0947\u0902 \u0938\u092e\u091d\u0928\u0947 \u092e\u0947\u0902 \u0915\u093e\u092b\u0940 \u0906\u0938\u093e\u0928 \u0939\u0948, \u0935\u0939 \u092a\u0930\u094d\u092f\u093e\u092a\u094d\u0924 \u0928\u0939\u0940\u0902 \u0939\u0948 \u0905\u0917\u0930 \u0917\u0923\u093f\u0924\u0940\u092f \u0924\u0930\u094d\u0915 \u0915\u0940 \u0938\u0916\u094d\u0924\u0940 \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0915\u0947 \u0932\u093f\u090f \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u0914\u092a\u091a\u093e\u0930\u093f\u0915\u0924\u093e \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0939\u094b\u0924\u0940 \u0939\u0948\u0964 \u0914\u092a\u091a\u093e\u0930\u093f\u0915 \u0930\u0942\u092a \u0938\u0947, \u092b\u093c\u0902\u0915\u094d\u0936\u0928\u094b\u0902 \u0915\u0940 \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e \u0915\u093e \u0938\u0902\u092c\u0902\u0927 \u0938\u0940\u092e\u093e \u0915\u0940 \u0905\u0935\u0927\u093e\u0930\u0923\u093e \u0938\u0947 \u0939\u094b\u0924\u093e \u0939\u0948, \u0914\u0930 \u0939\u092e \u0907\u0938\u0947 \u0935\u093f\u0938\u094d\u0924\u093e\u0930 \u0938\u0947 \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0930\u0947\u0902\u0917\u0947\u0964<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h3>\u0915\u093f\u0938\u0940 \u092c\u093f\u0902\u0926\u0941 \u092a\u0930 \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e<\/h3>\n<p ><a href=\"https:\/\/www.youtube.com\/watch?v=4kehfJcyPRg&amp;t=152s\" target=\"_blank\" rel=\"noopener\"><strong>\u0915\u094b\u0908 \u092b\u093c\u0902\u0915\u094d\u0936\u0928 <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u0915\u093f\u0938\u0940 \u092c\u093f\u0902\u0926\u0941 \u092a\u0930<\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">x=x_0<\/span> \u0928\u093f\u0930\u0902\u0924\u0930 \u0939\u0948, \u0905\u0917\u0930 \u0914\u0930 \u0915\u0947\u0935\u0932 \u0905\u0917\u0930 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0936\u0930\u094d\u0924\u0947\u0902 \u092a\u0942\u0930\u0940 \u0939\u094b\u0902:<\/p>\n<ul >\n<li><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span> \u092a\u0930 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0939\u0948<\/li>\n<li>\u0938\u0940\u092e\u093e <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to x_0} f(x)<\/span> \u092e\u094c\u091c\u0942\u0926 \u0939\u0948<\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to x_0} f(x) = f(x_0)<\/span><\/li>\n<\/ul>\n<p >\u0907\u0928 \u0938\u092d\u0940 \u0915\u094b \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0917\u0923\u093f\u0924\u0940\u092f \u0905\u092d\u093f\u0935\u094d\u092f\u0915\u094d\u0924\u093f \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u0938\u0902\u0915\u094d\u0937\u0947\u092a\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(\\forall \\epsilon \\gt 0 \\right) \\left(\\exists \\delta \\gt 0 \\right) \\left(0\\lt |x-x_0|\\lt \\delta \\rightarrow |f(x) - f(x_0)|\\lt \\epsilon\\right)<\/span>\n<p >\u092f\u0939 \u0938\u0940\u092e\u093e \u0915\u0940 \u0917\u0923\u093f\u0924\u0940\u092f \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0939\u0948, \u091c\u093f\u0938\u092e\u0947\u0902 \u092e\u0942\u0932\u094d\u092f \u00abL\u00bb \u0915\u094b \u00abf(<span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span>)\u00bb \u0938\u0947 \u092c\u0926\u0932 \u0926\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h3>\u090f\u0915 \u0938\u0947\u091f \u092a\u0930 \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e<\/h3>\n<p ><a href=\"https:\/\/www.youtube.com\/watch?v=4kehfJcyPRg&amp;t=462s\" target=\"_blank\" rel=\"noopener\"><strong>\u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e \u0915\u0940 \u092a\u0930\u093f\u092d\u093e\u0937\u093e<\/strong><\/a> \u0915\u093f\u0938\u0940 \u090f\u0915 \u092c\u093f\u0902\u0926\u0941 \u0938\u0947 \u0938\u092d\u0940 \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u0947 \u0932\u093f\u090f \u0935\u093f\u0938\u094d\u0924\u093e\u0930\u093f\u0924 \u0915\u0940 \u091c\u093e \u0938\u0915\u0924\u0940 \u0939\u0948 \u091c\u094b \u0915\u093f\u0938\u0940 \u0935\u093f\u0936\u0947\u0937 \u0938\u0947\u091f \u0915\u0947 \u092d\u0940\u0924\u0930 \u0939\u0948\u0902\u0964 \u0939\u092e \u0915\u0939\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u0915\u093f\u0938\u0940 \u0938\u0947\u091f <span class=\"katex-eq\" data-katex-display=\"false\">I\\subseteq Dom(f)<\/span> \u092e\u0947\u0902 \u0928\u093f\u0930\u0902\u0924\u0930 \u0939\u0948 \u0905\u0917\u0930 \u0935\u0939 \u0938\u0947\u091f \u0915\u0947 \u0938\u092d\u0940 \u092c\u093f\u0902\u0926\u0941\u0913\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">x_0\\in I.<\/span> \u092a\u0930 \u0928\u093f\u0930\u0902\u0924\u0930 \u0939\u094b\u0964 \u0907\u0938\u0947 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0917\u0923\u093f\u0924\u0940\u092f \u0905\u092d\u093f\u0935\u094d\u092f\u0915\u094d\u0924\u093f \u0926\u094d\u0935\u093e\u0930\u093e \u0938\u0902\u0915\u094d\u0937\u0947\u092a\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left(\\forall x_0 \\in I\\subseteq Dom(f) \\right)\\left(\\forall \\epsilon \\gt 0 \\right) \\left(\\exists \\delta \\gt 0 \\right) \\left(0\\lt |x-x_0|\\lt \\delta \\rightarrow |f(x) - f(x_0)|\\lt \\epsilon\\right)<\/span>\n<p><a name=\"4\"><\/a><\/p>\n<h3>\u0928\u093f\u0930\u0902\u0924\u0930 \u0915\u093e\u0930\u094d\u092f\u094b\u0902 \u0915\u0947 \u0917\u0941\u0923<\/h3>\n<h4>\u0928\u093f\u0930\u0902\u0924\u0930 \u0915\u093e\u0930\u094d\u092f\u094b\u0902 \u0915\u093e \u092c\u0940\u091c\u0917\u0923\u093f\u0924<\/h4>\n<p ><a href=\"https:\/\/www.youtube.com\/watch?v=4kehfJcyPRg&amp;t=575s\" target=\"_blank\" rel=\"noopener\"><strong>\u092f\u0926\u093f <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">g<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">I\\subseteq Dom(f)\\cap Dom(g)<\/span> \u092a\u0930 \u0928\u093f\u0930\u0902\u0924\u0930 \u0915\u093e\u0930\u094d\u092f \u0939\u0948\u0902<\/strong><\/a>, \u0924\u094b \u0939\u092e \u092f\u0939 \u0915\u0939 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<ul >\n<li><span class=\"katex-eq\" data-katex-display=\"false\">f\\pm g<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">I<\/span> \u092a\u0930 \u0928\u093f\u0930\u0902\u0924\u0930 \u0939\u0948<\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">f\\cdot g<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">I<\/span> \u092a\u0930 \u0928\u093f\u0930\u0902\u0924\u0930 \u0939\u0948<\/li>\n<li>\u092f\u0926\u093f <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha\\in\\mathbb{R}<\/span>, \u0924\u094b <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha f<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">I<\/span> \u092a\u0930 \u0928\u093f\u0930\u0902\u0924\u0930 \u0939\u0948<\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">f\/g<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">I<\/span> \u092a\u0930 \u0928\u093f\u0930\u0902\u0924\u0930 \u0939\u0948 \u091c\u092c <span class=\"katex-eq\" data-katex-display=\"false\">g\\neq 0<\/span><\/li>\n<li>\u092f\u0926\u093f <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha,\\beta\\in\\mathbb{R}<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">\\beta\\neq 0<\/span>, \u0924\u094b <span class=\"katex-eq\" data-katex-display=\"false\">f^{\\alpha\/\\beta}<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">I<\/span> \u092a\u0930 \u0928\u093f\u0930\u0902\u0924\u0930 \u0939\u0948, \u091c\u092c \u0924\u0915 \u0915\u093f <span class=\"katex-eq\" data-katex-display=\"false\">f^{\\alpha\/\\beta}<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">I<\/span> \u092a\u0930 \u0905\u091a\u094d\u091b\u0940 \u0924\u0930\u0939 \u0938\u0947 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0939\u094b\u0964<\/li>\n<\/ul>\n<p >\u092f\u0947 \u0938\u092d\u0940 \u0917\u0941\u0923 \u091c\u094b \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e \u0915\u0940 \u0914\u092a\u091a\u093e\u0930\u093f\u0915 \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0938\u0947 \u092a\u094d\u0930\u092e\u093e\u0923\u093f\u0924 \u0915\u0930\u0928\u093e \u0915\u0920\u093f\u0928 \u092a\u094d\u0930\u0924\u0940\u0924 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902, \u0935\u093e\u0938\u094d\u0924\u0935 \u092e\u0947\u0902 \u092c\u0939\u0941\u0924 \u0906\u0938\u093e\u0928 \u0939\u0948\u0902, \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0935\u0947 \u0932\u0917\u092d\u0917 \u0938\u0940\u092e\u093e \u0915\u0940 \u092c\u0940\u091c\u0917\u0923\u093f\u0924 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0939\u0940 \u0939\u0948\u0902 \u091c\u093f\u0938\u0947 \u0939\u092e <a href=\"https:\/\/toposuranos.com\/la-definicion-de-limite-demostraciones-y-teoremas\/\" rel=\"noopener\" target=\"_blank\">\u092a\u0939\u0932\u0947 \u0939\u0940 \u092a\u094d\u0930\u092e\u093e\u0923\u093f\u0924 \u0915\u0930 \u091a\u0941\u0915\u0947 \u0939\u0948\u0902<\/a>, \u0907\u0938\u0932\u093f\u090f \u0939\u092e\u0947\u0902 \u0907\u0938\u0947 \u0926\u094b\u092c\u093e\u0930\u093e \u0915\u0930\u0928\u0947 \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0928\u0939\u0940\u0902 \u0939\u0948\u0964<\/p>\n<h5>\u0928\u093f\u0930\u0902\u0924\u0930 \u0915\u093e\u0930\u094d\u092f\u094b\u0902 \u0915\u093e \u0938\u0902\u092f\u094b\u091c\u0928<\/h5>\n<p >\u092f\u0926\u093f <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">I\\subseteq Dom(f)<\/span> \u092a\u0930 \u0928\u093f\u0930\u0902\u0924\u0930 \u0939\u0948 \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">g<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">f(I)<\/span> \u092a\u0930 \u0928\u093f\u0930\u0902\u0924\u0930 \u0939\u0948, \u0924\u094b \u0938\u0902\u092f\u094b\u091c\u0928 <span class=\"katex-eq\" data-katex-display=\"false\">(g\\circ f)(x) = g(f(x))<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">I<\/span> \u092a\u0930 \u0928\u093f\u0930\u0902\u0924\u0930 \u0939\u0948\u0964 \u091c\u0948\u0938\u093e \u0915\u093f \u092a\u0939\u0932\u0947 \u0938\u0947 \u0905\u0928\u0941\u092e\u093e\u0928\u093f\u0924 \u0925\u093e, \u092f\u0939 \u0915\u093e\u0930\u094d\u092f\u094b\u0902 \u0915\u0940 \u0938\u0940\u092e\u093e\u0913\u0902 \u0915\u0947 \u0938\u0902\u092f\u094b\u091c\u0928 \u0915\u0947 \u0928\u093f\u092f\u092e\u094b\u0902 \u0915\u093e \u0938\u0940\u0927\u093e \u092a\u0930\u093f\u0923\u093e\u092e \u0939\u0948\u0964<\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>\u0905\u092d\u094d\u092f\u093e\u0938<\/h2>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/R91vswfQT_Q\" title=\"YouTube \u0935\u0940\u0921\u093f\u092f\u094b \u092a\u094d\u0932\u0947\u092f\u0930\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<ol >\n<li>\u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0915\u093e\u0930\u094d\u092f\u094b\u0902 \u0915\u0940 \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e \u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0947\u0902<br \/>\n<table>\n<tbody>\n<tr>\n<td width=\"30\">a.<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">y=\\dfrac{1}{x-2} - 3x<\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=33s\" target=\"_blank\" rel=\"noopener\"><strong>\u0938\u092e\u093e\u0927\u093e\u0928<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>b.<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">y=\\dfrac{x+1}{x^2-4x+3}<\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=97s\" target=\"_blank\" rel=\"noopener\"><strong>\u0938\u092e\u093e\u0927\u093e\u0928<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>c.<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">y=|x-1| + \\sin(x)<\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=215s\" target=\"_blank\" rel=\"noopener\"><strong>\u0938\u092e\u093e\u0927\u093e\u0928<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>d.<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">y=\\dfrac{\\cos(x)}{x}<\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=450s\" target=\"_blank\" rel=\"noopener\"><strong>\u0938\u092e\u093e\u0927\u093e\u0928<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>e.<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">y=csc(2x)<\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=564s\" target=\"_blank\" rel=\"noopener\"><strong>\u0938\u092e\u093e\u0927\u093e\u0928<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>f.<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">y=\\dfrac{x\\tan(x)}{x^2 + 1}<\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=666s\" target=\"_blank\" rel=\"noopener\"><strong>\u0938\u092e\u093e\u0927\u093e\u0928<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>g.<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">y=\\sqrt{2x + 3}<\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=784s\" target=\"_blank\" rel=\"noopener\"><strong>\u0938\u092e\u093e\u0927\u093e\u0928<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>h.<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">y=\\dfrac{x+2}{\\cos(x)}<\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=917s\" target=\"_blank\" rel=\"noopener\"><strong>\u0938\u092e\u093e\u0927\u093e\u0928<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>i.<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">y=\\dfrac{\\sqrt{x^4 + 1}}{1+\\sin^2(x)}<\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=952s\" target=\"_blank\" rel=\"noopener\"><strong>\u0938\u092e\u093e\u0927\u093e\u0928<\/strong><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>\u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u0940\u092e\u093e\u0913\u0902 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0947\u0902\u0964 \u0915\u094d\u092f\u093e \u092f\u0947 \u0915\u093e\u0930\u094d\u092f \u0909\u0928 \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u092a\u0930 \u0928\u093f\u0930\u0902\u0924\u0930 \u0939\u0948\u0902 \u091c\u093f\u0928\u0915\u0947 \u092a\u093e\u0938 \u0935\u0947 \u092a\u0939\u0941\u0901\u091a\u0924\u0947 \u0939\u0948\u0902?<br \/>\n<table>\n<tbody>\n<tr>\n<td width=\"30\">a.<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to\\pi} \\sin(x -\\sin(x))<\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=1033s\" target=\"_blank\" rel=\"noopener\"><strong>\u0938\u092e\u093e\u0927\u093e\u0928<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>b.<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to 0} \\sin\\left(\\dfrac{\\pi}{2}\\cos(\\tan(x)) \\right)<\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=1092s\" target=\"_blank\" rel=\"noopener\"><strong>\u0938\u092e\u093e\u0927\u093e\u0928<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>c.<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to 1} \\sec\\left(x\\sec^2(x) - \\tan^2(x) -1 \\right)<\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=1162s\" target=\"_blank\" rel=\"noopener\"><strong>\u0938\u092e\u093e\u0927\u093e\u0928<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>d.<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to 0} \\tan\\left(\\dfrac{\\pi}{4}\\cos\\left(\\sin\\left(x^{1\/3}\\right)\\right) \\right)<\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=1274s\" target=\"_blank\" rel=\"noopener\"><strong>\u0938\u092e\u093e\u0927\u093e\u0928<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>e.<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to 0} \\cos\\left(\\dfrac{\\pi}{\\sqrt{19 - 3\\sec{2x}}} \\right)<\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=1424s\" target=\"_blank\" rel=\"noopener\"><strong>\u0938\u092e\u093e\u0927\u093e\u0928<\/strong><\/a><\/td>\n<\/tr>\n<tr>\n<td>f.<\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to \\pi\/6} \\sqrt{\\csc^2(x) + 5\\sqrt{3}\\tan(x)}<\/span><\/td>\n<td><a href=\"https:\/\/www.youtube.com\/watch?v=R91vswfQT_Q&amp;t=1505s\" target=\"_blank\" rel=\"noopener\"><strong>\u0938\u092e\u093e\u0927\u093e\u0928<\/strong><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u0938\u0940\u092e\u093e \u0914\u0930 \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e \u0938\u093e\u0930\u093e\u0902\u0936: \u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0939\u092e \u090f\u0915 \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0915\u0940 \u0938\u0940\u092e\u093e \u0914\u0930 \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e \u0915\u0947 \u092c\u0940\u091a \u0915\u0947 \u0938\u0902\u092c\u0902\u0927 \u092a\u0930 \u091a\u0930\u094d\u091a\u093e \u0915\u0930\u0947\u0902\u0917\u0947, \u091c\u093f\u0938\u0947 \u090f\u0915 \u0938\u0939\u091c \u0914\u0930 \u0914\u092a\u091a\u093e\u0930\u093f\u0915 \u0938\u094d\u092a\u0937\u094d\u091f\u0940\u0915\u0930\u0923 \u0915\u0947 \u0938\u093e\u0925 \u0936\u0941\u0930\u0942 \u0915\u093f\u092f\u093e \u091c\u093e\u090f\u0917\u093e\u0964 \u0915\u093f\u0938\u0940 \u092c\u093f\u0902\u0926\u0941 \u0914\u0930 \u0915\u093f\u0938\u0940 \u0938\u0947\u091f \u092a\u0930 \u0928\u093f\u0930\u0902\u0924\u0930\u0924\u093e \u0915\u093e \u092a\u0924\u093e \u0932\u0917\u093e\u092f\u093e \u091c\u093e\u090f\u0917\u093e, \u092f\u0939 \u0938\u092e\u091d\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f \u090f\u0915 \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0915\u0947 \u0928\u093f\u0930\u0902\u0924\u0930 \u0939\u094b\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":29557,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":3,"footnotes":""},"categories":[862,577],"tags":[],"class_list":["post-29568","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 - 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