{"id":29475,"date":"2024-11-12T13:00:24","date_gmt":"2024-11-12T13:00:24","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=29475"},"modified":"2024-11-13T07:41:37","modified_gmt":"2024-11-13T07:41:37","slug":"%d8%a7%d9%84%d9%86%d9%87%d8%a7%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d9%84%d8%a7%d9%86%d9%87%d8%a7%d8%a6%d9%8a%d8%a9-%d9%88%d8%a7%d9%84%d8%aa%d8%a8%d8%a7%d8%b9%d8%af","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/ar\/%d8%a7%d9%84%d9%86%d9%87%d8%a7%d9%8a%d8%a7%d8%aa-%d8%a7%d9%84%d9%84%d8%a7%d9%86%d9%87%d8%a7%d8%a6%d9%8a%d8%a9-%d9%88%d8%a7%d9%84%d8%aa%d8%a8%d8%a7%d8%b9%d8%af\/","title":{"rendered":"\u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629 \u0648\u0627\u0644\u062a\u0628\u0627\u0639\u062f"},"content":{"rendered":"<style>\n\tp {\n\ttext-align: justify;}\n<\/style>\n<p><center><\/p>\n<h1>\u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629 \u0648\u0627\u0644\u062a\u0628\u0627\u0639\u062f<\/h1>\n<p style=\"text-align:center;\"><em><strong>\u0645\u0644\u062e\u0635:<\/strong><br \/>\n\u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629\u060c \u0633\u0646\u062a\u0646\u0627\u0648\u0644 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629 \u0648\u0623\u0646\u0648\u0627\u0639 \u0627\u0644\u062a\u0628\u0627\u0639\u062f \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629 \u0641\u064a \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a\u060c \u0645\u0633\u062a\u0639\u0631\u0636\u064a\u0646 \u0627\u0644\u0645\u0641\u0627\u0647\u064a\u0645 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0644\u0641\u0647\u0645 \u0643\u064a\u0641\u064a\u0629 \u0639\u062f\u0645 \u062a\u0642\u0627\u0631\u0628 \u0628\u0639\u0636 \u0627\u0644\u062f\u0648\u0627\u0644 \u0625\u0644\u0649 \u0642\u064a\u0645\u0629 \u062d\u0642\u064a\u0642\u064a\u0629 \u0645\u062d\u062f\u062f\u0629. \u0633\u0646\u0631\u0627\u062c\u0639 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629\u060c \u0627\u0644\u062f\u0648\u0627\u0644 \u0630\u0627\u062a \u0627\u0644\u062a\u0630\u0628\u0630\u0628\u0627\u062a \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629\u060c \u0648\u0627\u0644\u062d\u0627\u0644\u0627\u062a \u0627\u0644\u062a\u064a \u0644\u0627 \u062a\u0648\u062c\u062f \u0641\u064a\u0647\u0627 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0628\u0633\u0628\u0628 \u0645\u0634\u0627\u0643\u0644 \u0641\u064a \u0627\u0644\u0645\u062c\u0627\u0644 \u0623\u0648 \u0627\u0644\u0646\u0645\u0648 \u063a\u064a\u0631 \u0627\u0644\u0645\u062d\u062f\u0648\u062f.<br \/>\n<\/em><\/p>\n<p style=\"text-align:center;\"><strong>\u0623\u0647\u062f\u0627\u0641 \u0627\u0644\u062a\u0639\u0644\u0645:<\/strong><br \/>\n\u0639\u0646\u062f \u0646\u0647\u0627\u064a\u0629 \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629\u060c \u0633\u064a\u0643\u0648\u0646 \u0627\u0644\u0637\u0627\u0644\u0628 \u0642\u0627\u062f\u0631\u0627\u064b \u0639\u0644\u0649\n<\/p>\n<ol style=\"text-align:left;\">\n<li><strong>\u062a\u0639\u0631\u064a\u0641<\/strong> \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u0645\u062a\u0628\u0627\u0639\u062f\u0629 \u0648\u0627\u0644\u062a\u0639\u0631\u0641 \u0639\u0644\u0649 \u0627\u0644\u062d\u0627\u0644\u0627\u062a \u0627\u0644\u062a\u064a \u062a\u0643\u0648\u0646 \u0641\u064a\u0647\u0627 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0645\u062a\u0628\u0627\u0639\u062f\u0629.<\/li>\n<li><strong>\u062a\u062d\u062f\u064a\u062f<\/strong> \u0627\u0644\u0623\u0646\u0648\u0627\u0639 \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629 \u0645\u0646 \u0627\u0644\u062a\u0628\u0627\u0639\u062f \u0641\u064a \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a\u060c \u0645\u062b\u0644 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629 \u0648\u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629.<\/li>\n<li><strong>\u062a\u062d\u0644\u064a\u0644<\/strong> \u0627\u0644\u062d\u0627\u0644\u0627\u062a \u0627\u0644\u062a\u064a \u062a\u0639\u0627\u0646\u064a \u0641\u064a\u0647\u0627 \u0627\u0644\u062f\u0627\u0644\u0629 \u0645\u0646 \u0645\u0634\u0627\u0643\u0644 \u0641\u064a \u0627\u0644\u0645\u062c\u0627\u0644 \u0648\u0643\u064a\u0641 \u064a\u0624\u062b\u0631 \u0630\u0644\u0643 \u0639\u0644\u0649 \u0648\u062c\u0648\u062f \u0627\u0644\u0646\u0647\u0627\u064a\u0629.<\/li>\n<li><strong>\u062a\u0642\u064a\u064a\u0645<\/strong> \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0644\u062a\u062d\u062f\u064a\u062f \u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0645\u062e\u062a\u0644\u0641\u0629 \u0648\u062a\u0623\u062b\u064a\u0631 \u0630\u0644\u0643 \u0639\u0644\u0649 \u062a\u0642\u0627\u0631\u0628 \u0627\u0644\u0646\u0647\u0627\u064a\u0629.<\/li>\n<li><strong>\u062d\u0633\u0627\u0628<\/strong> \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629 \u0648\u0627\u0644\u062a\u0645\u064a\u064a\u0632 \u0628\u064a\u0646 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u062a\u064a \u062a\u062a\u0628\u0627\u0639\u062f \u0646\u062d\u0648 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u0645\u0648\u062c\u0628\u0629 \u0648\u0627\u0644\u0633\u0627\u0644\u0628\u0629.<\/li>\n<\/ol>\n<p style=\"text-align:center;\">\n<u><strong>\u0641\u0647\u0631\u0633 \u0627\u0644\u0645\u062d\u062a\u0648\u064a\u0627\u062a<\/strong><\/u>:<br \/>\n<a href=\"#1\"><strong>\u0645\u062a\u0649 \u0646\u0642\u0648\u0644 \u0623\u0646 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0645\u062a\u0628\u0627\u0639\u062f\u0629\u061f<\/strong><\/a><br \/>\n<a href=\"#2\"><strong>\u0623\u0646\u0648\u0627\u0639 \u0627\u0644\u062a\u0628\u0627\u0639\u062f \u0641\u064a \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a<\/strong><\/a><br \/>\n<a href=\"#3\">\u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u062a\u064a \u062a\u0639\u0627\u0646\u064a \u0645\u0646 \u0645\u0634\u0627\u0643\u0644 \u0641\u064a \u0627\u0644\u0645\u062c\u0627\u0644<\/a><br \/>\n<a href=\"#4\">\u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629<\/a><br \/>\n<a href=\"#5\">\u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062f\u0648\u0627\u0644 \u0630\u0627\u062a \u0627\u0644\u062a\u0630\u0628\u0630\u0628\u0627\u062a \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629<\/a><br \/>\n<a href=\"#6\">\u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629<\/a><br \/>\n<a href=\"#7\">\u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629 \u0639\u0646\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629<\/a>\n<\/p>\n<p><\/center><\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/SFBMSd0Q7Io\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<p>\u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0645\u0631\u0629\u060c \u0644\u0646 \u0646\u0631\u0627\u062c\u0639 \u0641\u0642\u0637 <strong>\u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629\u060c<\/strong> \u0628\u0644 \u0633\u0646\u062a\u0646\u0627\u0648\u0644 <strong>\u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u0645\u062a\u0628\u0627\u0639\u062f\u0629<\/strong> \u0628\u0634\u0643\u0644 \u0639\u0627\u0645. \u062a\u0648\u0636\u062d \u0644\u0646\u0627 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u0645\u062a\u0628\u0627\u0639\u062f\u0629 \u0643\u064a\u0641 \u0623\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 \u0644\u0627 \u062a\u0628\u062f\u0648 \u0648\u0643\u0623\u0646\u0647\u0627 \u062a\u062a\u0642\u0627\u0631\u0628\u060c \u0648\u064a\u0645\u0643\u0646 \u0623\u0646 \u064a\u062d\u062f\u062b \u0647\u0630\u0627 \u0628\u0637\u0631\u0642 \u0645\u062a\u0639\u062f\u062f\u0629.<\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u0645\u062a\u0649 \u0646\u0642\u0648\u0644 \u0623\u0646 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0645\u062a\u0628\u0627\u0639\u062f\u0629\u061f<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=SFBMSd0Q7Io&amp;t=106s\" target=\"_blank\" rel=\"noopener\"><strong>\u0646\u0642\u0648\u0644 \u0623\u0646 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0645\u062a\u0628\u0627\u0639\u062f\u0629 \u0639\u0646\u062f\u0645\u0627 \u0644\u0627 \u062a\u062a\u0642\u0627\u0631\u0628 \u0625\u0644\u0649 \u0623\u064a \u0642\u064a\u0645\u0629 \u062d\u0642\u064a\u0642\u064a\u0629.<\/strong><\/a> \u0648\u0647\u0630\u0627 \u0642\u062f \u064a\u0628\u062f\u0648 \u0648\u0627\u0636\u062d\u0627\u064b\u060c \u0644\u0643\u0646\u0647 \u064a\u0645\u0643\u0646 \u0623\u0646 \u064a\u062d\u062f\u062b \u0628\u0637\u0631\u0642 \u0645\u062e\u062a\u0644\u0641\u0629:<\/p>\n<ul>\n<li>\u0639\u0646\u062f\u0645\u0627 \u062a\u0643\u0648\u0646 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0645\u062e\u062a\u0644\u0641\u0629 \u0623\u0648 \u063a\u064a\u0631 \u0645\u0648\u062c\u0648\u062f\u0629\u060c \u0641\u0625\u0646 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u062b\u0646\u0627\u0626\u064a\u0629 \u0644\u0627 \u062a\u0643\u0648\u0646 \u0645\u0648\u062c\u0648\u062f\u0629.<\/li>\n<li>\u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0627\u0644\u062f\u0627\u0644\u0629 \u063a\u064a\u0631 \u0645\u0639\u0631\u0641\u0629 \u0628\u0634\u0643\u0644 \u062c\u064a\u062f\u060c \u0623\u0648 \u062a\u0646\u0645\u0648 \u0628\u0644\u0627 \u062d\u062f\u0648\u062f\u060c \u0623\u0648 \u062a\u062a\u0630\u0628\u0630\u0628 \u0628\u0634\u0643\u0644 \u0644\u0627 \u0646\u0647\u0627\u0626\u064a \u0639\u0646\u062f \u0627\u0642\u062a\u0631\u0627\u0628\u0647\u0627 \u0645\u0646 \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u062a\u064a \u062a\u064f\u062d\u0633\u0628 \u0639\u0646\u062f\u0647\u0627 \u0627\u0644\u0646\u0647\u0627\u064a\u0629\u060c \u0641\u0644\u0627 \u064a\u0645\u0643\u0646 \u0623\u0646 \u062a\u0648\u062c\u062f \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629.<\/li>\n<\/ul>\n<p>\u064a\u0645\u0643\u0646 \u0623\u0646 \u064a\u0646\u0637\u0628\u0642 \u0630\u0644\u0643\u060c \u0645\u0639 \u062e\u0635\u0648\u0635\u064a\u0627\u062a\u0647\u060c \u0639\u0644\u0649 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u0645\u062d\u062f\u0648\u062f\u0629 \u0648\u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0639\u0646\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629\u060c \u0648\u0633\u0646\u062d\u0635\u0644 \u062d\u0633\u0628 \u0627\u0644\u062d\u0627\u0644\u0629 \u0639\u0644\u0649 \u0646\u0648\u0639 \u0645\u0639\u064a\u0646 \u0645\u0646 \u0627\u0644\u062a\u0628\u0627\u0639\u062f.<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u0623\u0646\u0648\u0627\u0639 \u0627\u0644\u062a\u0628\u0627\u0639\u062f \u0641\u064a \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a<\/h2>\n<p><a name=\"3\"><\/a><\/p>\n<h3>\u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u062a\u064a \u062a\u0639\u0627\u0646\u064a \u0645\u0646 \u0645\u0634\u0627\u0643\u0644 \u0641\u064a \u0627\u0644\u0645\u062c\u0627\u0644<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=SFBMSd0Q7Io&amp;t=210s\" target=\"_blank\" rel=\"noopener\"><strong>\u0639\u0646\u062f \u0645\u062d\u0627\u0648\u0644\u0629 \u062d\u0633\u0627\u0628 \u0646\u0647\u0627\u064a\u0629 \u0645\u0646 \u0646\u0648\u0639 <\/strong><\/a><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{x\\to x_0}f(x)<\/span><\/span> \u0623\u0648 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{x\\to +\\infty}f(x),<\/span><\/span> \u0646\u062a\u0648\u0642\u0639 \u0639\u0644\u0649 \u0627\u0644\u0623\u0642\u0644 \u0623\u0646 \u062a\u0643\u0648\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u0645\u0639\u0631\u0641\u0629 \u0628\u0634\u0643\u0644 \u062c\u064a\u062f \u0644\u0642\u064a\u0645 \u0642\u0631\u064a\u0628\u0629 \u0645\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span><\/span> \u0623\u0648 \u0639\u0644\u0649 \u0628\u0639\u0636 \u0627\u0644\u0641\u062a\u0631\u0627\u062a \u0645\u0646 \u0627\u0644\u0646\u0648\u0639 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">[a,+\\infty[, <\/span><\/span> \u0639\u0644\u0649 \u0627\u0644\u062a\u0648\u0627\u0644\u064a. \u0625\u0646 \u0644\u0645 \u064a\u0643\u0646 \u0647\u0630\u0627 \u0645\u062a\u062d\u0642\u0642\u0627\u064b\u060c \u0641\u0644\u0646 \u064a\u0643\u0648\u0646 \u0644\u0623\u064a \u0645\u0646 \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u064a\u0646 \u0623\u064a \u0645\u0639\u0646\u0649\u061b \u0641\u0644\u0627 \u064a\u0645\u0643\u0646 \u0644\u0644\u062f\u0627\u0644\u0629 \u00ab\u0623\u0646 \u062a\u0645\u064a\u0644\u00bb \u0625\u0644\u0649 \u0642\u064a\u0645\u0629 \u0645\u0639\u064a\u0646\u0629 \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u063a\u064a\u0631 \u0645\u0639\u0631\u0641\u0629 \u0639\u0646\u062f \u0627\u0644\u0627\u0642\u062a\u0631\u0627\u0628 \u0645\u0646 \u0647\u0630\u0647 \u0627\u0644\u0642\u064a\u0645\u0629. \u0641\u064a \u0645\u062b\u0644 \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0627\u062a\u060c \u0646\u0643\u062a\u0628 \u0628\u0628\u0633\u0627\u0637\u0629 \u0623\u0646 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u063a\u064a\u0631 \u0645\u0648\u062c\u0648\u062f\u0629: <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{x\\to x_0}f(x)=\\cancel{\\exists}<\/span><\/span> \u0648 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{x\\to +\\infty}f(x)=\\cancel{\\exists},<\/span><\/span> \u062d\u0633\u0628\u0645\u0627 \u064a\u0642\u062a\u0636\u064a \u0627\u0644\u0623\u0645\u0631. \u064a\u0646\u0637\u0628\u0642 \u0630\u0644\u0643 \u0623\u064a\u0636\u0627\u064b \u0639\u0644\u0649 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629\u060c \u0648\u0644\u064a\u0633 \u0647\u0646\u0627\u0643 \u0645\u0627 \u064a\u064f\u0642\u0627\u0644 \u0623\u0643\u062b\u0631 \u0639\u0646 \u0647\u0630\u0627 \u0627\u0644\u0646\u0648\u0639 \u0645\u0646 \u0627\u0644\u062d\u0627\u0644\u0627\u062a.<\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h3>\u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=SFBMSd0Q7Io&amp;t=180s\" target=\"_blank\" rel=\"noopener\"><strong>\u0644\u0646\u0623\u062e\u0630 \u062f\u0627\u0644\u0629 \u0645\u0646 \u0627\u0644\u0646\u0648\u0639<\/strong><\/a> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x) = x\/|x|<\/span><\/span> \u0648\u0646\u062d\u0633\u0628 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0639\u0646\u062f\u0645\u0627 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\to 0<\/span><\/span>. \u0623\u0648\u0644 \u0645\u0627 \u0633\u0646\u0644\u0627\u062d\u0638\u0647 \u0647\u0648<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to 0^+} f(x) = 1<\/span><\/span><\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to 0^-} f(x) = -1<\/span><\/span><\/p>\n<p>\u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629\u060c \u0633\u0646\u0644\u0627\u062d\u0638 \u0623\u0646\u0647 \u0639\u0644\u0649 \u0627\u0644\u0631\u063a\u0645 \u0645\u0646 \u0623\u0646 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0645\u0648\u062c\u0648\u062f\u0629\u060c \u0625\u0644\u0627 \u0623\u0646\u0647\u0627 \u0645\u062e\u062a\u0644\u0641\u0629. \u0639\u0646\u062f\u0645\u0627 \u064a\u062d\u062f\u062b \u0647\u0630\u0627\u060c \u0646\u0642\u0648\u0644 \u0628\u0628\u0633\u0627\u0637\u0629 \u0623\u0646 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 (\u0627\u0644\u062b\u0646\u0627\u0626\u064a\u0629) \u063a\u064a\u0631 \u0645\u062a\u0642\u0627\u0631\u0628\u0629\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to 0} f(x) = \\cancel{\\exists}<\/span><\/span><\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h3>\u0646\u0647\u0627\u064a\u0629 \u0627\u0644\u062f\u0648\u0627\u0644 \u0630\u0627\u062a \u0627\u0644\u062a\u0630\u0628\u0630\u0628\u0627\u062a \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=SFBMSd0Q7Io&amp;t=415s\" target=\"_blank\" rel=\"noopener\"><strong>\u062a\u0648\u062c\u062f \u0623\u064a\u0636\u0627\u064b \u062d\u0627\u0644\u0627\u062a \u062d\u064a\u062b \u062a\u0645\u064a\u0644 \u0627\u0644\u062f\u0648\u0627\u0644\u060c \u0628\u062f\u0644\u0627\u064b \u0645\u0646 \u0627\u0644\u0627\u0642\u062a\u0631\u0627\u0628 \u0645\u0646 \u0642\u064a\u0645\u0629 \u0645\u0639\u064a\u0646\u0629\u060c<\/strong><\/a> \u0625\u0644\u0649 \u0627\u0644\u062a\u0630\u0628\u0630\u0628 \u062f\u0627\u062e\u0644 \u0646\u0637\u0627\u0642 \u0645\u0639\u064a\u0646. \u0645\u062b\u0627\u0644 \u0639\u0644\u0649 \u0630\u0644\u0643 \u0647\u0648 \u062f\u0627\u0644\u0629 \u0645\u0646 \u0627\u0644\u0646\u0648\u0639 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)= \\sin(1\/x)<\/span><\/span>. \u0625\u0630\u0627 \u062a\u0627\u0628\u0639\u0646\u0627 \u0647\u0630\u0647 \u0627\u0644\u062f\u0627\u0644\u0629 \u0639\u0646\u062f\u0645\u0627 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\to 0<\/span><\/span> \u0633\u0646\u0631\u0649 \u0623\u0646\u0647\u0627 \u062a\u062a\u0630\u0628\u0630\u0628 \u0628\u0644\u0627 \u0646\u0647\u0627\u064a\u0629.<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-vrdcIAmLV50\/YGoC903Q62I\/AAAAAAAAE1M\/6AM7D-RM9lAy9ZrG105MbfCN8ltu6J09ACLcBGAsYHQ\/s0\/sin1sobrex.PNG\" alt=\"f(x) = sin(1\/x)\" class=\"alignnone size-full lazyload\" width=\"856\" height=\"442\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-vrdcIAmLV50\/YGoC903Q62I\/AAAAAAAAE1M\/6AM7D-RM9lAy9ZrG105MbfCN8ltu6J09ACLcBGAsYHQ\/s0\/sin1sobrex.PNG\" alt=\"f(x) = sin(1\/x)\" class=\"alignnone size-full lazyload\" width=\"856\" height=\"442\" \/><\/noscript><\/p>\n<p>\u0639\u0646\u062f\u0645\u0627 \u062a\u062d\u062f\u062b \u0645\u062b\u0644 \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0627\u062a\u060c \u0646\u0642\u0648\u0644 \u0628\u0628\u0633\u0627\u0637\u0629 \u0623\u0646 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u063a\u064a\u0631 \u0645\u0648\u062c\u0648\u062f\u0629.<\/p>\n<p><a name=\"6\"><\/a><\/p>\n<h3>\u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=SFBMSd0Q7Io&amp;t=658s\" target=\"_blank\" rel=\"noopener\"><strong>\u0644\u0646\u0646\u0638\u0631 \u0641\u064a \u0645\u0627 \u064a\u062d\u062f\u062b \u0645\u0639 \u0627\u0644\u062f\u0627\u0644\u0629<\/strong><\/a> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x) = 1\/x.<\/span><\/span> \u0623\u0648\u0644 \u0645\u0627 \u0633\u0646\u0631\u0627\u0647 \u0647\u0648 \u0623\u0646\u0647 \u0639\u0646\u062f\u0645\u0627 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\to 0<\/span><\/span>\u060c \u0641\u0625\u0646 \u0642\u064a\u0645\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u062a\u0632\u062f\u0627\u062f \u0628\u0644\u0627 \u062d\u062f\u0648\u062f\u060c \u0648\u0644\u0643\u0646 \u0637\u0631\u064a\u0642\u0629 \u062d\u062f\u0648\u062b \u0630\u0644\u0643 \u062a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u0645\u0643\u0627\u0646 \u062d\u0633\u0627\u0628 \u0627\u0644\u0646\u0647\u0627\u064a\u0629. \u0633\u0646\u0643\u062a\u0628 \u0630\u0644\u0643 \u0628\u0634\u0643\u0644 \u062d\u062f\u0633\u064a \u0639\u0644\u0649 \u0627\u0644\u0646\u062d\u0648 \u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to 0^+} \\dfrac{1}{x} = +\\infty<\/span><\/span><\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to 0^-} \\dfrac{1}{x} = -\\infty<\/span><\/span><\/p>\n<p>\u0628\u0647\u0630\u0627 \u0627\u0644\u0634\u0643\u0644\u060c \u0646\u062d\u0646 \u0644\u0627 \u0646\u0642\u0648\u0644 \u0623\u0646 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0645\u0648\u062c\u0648\u062f\u0629 \u0628\u0623\u064a \u0634\u0643\u0644 \u0645\u0646 \u0627\u0644\u0623\u0634\u0643\u0627\u0644\u061b \u0628\u0644 \u0646\u062d\u0646 \u0646\u0628\u064a\u0646 \u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0627\u0644\u062a\u064a \u0644\u0627 \u062a\u0648\u062c\u062f \u0628\u0647\u0627 \u0627\u0644\u0646\u0647\u0627\u064a\u0629. \u0639\u0644\u0649 \u0639\u0643\u0633 \u0627\u0644\u062d\u0627\u0644\u0627\u062a \u0627\u0644\u0633\u0627\u0628\u0642\u0629\u060c \u062d\u064a\u062b \u0644\u0627 \u062a\u0648\u062c\u062f \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0648\u0644\u0627 \u062a\u062a\u0642\u0627\u0631\u0628 \u0625\u0644\u0649 \u0642\u064a\u0645\u0629 \u0645\u062d\u062f\u062f\u0629\u061b \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629 \u062a\u062a\u0628\u0627\u0639\u062f \u0644\u0623\u0646 \u0642\u064a\u0645\u062a\u0647\u0627 \u062a\u062a\u062c\u0627\u0648\u0632 \u0623\u064a \u0631\u0642\u0645 \u062d\u0642\u064a\u0642\u064a.<\/p>\n<p>\u064a\u0645\u0643\u0646\u0646\u0627 \u062a\u0644\u062e\u064a\u0635 \u0645\u0627 \u0631\u0627\u062c\u0639\u0646\u0627\u0647 \u0627\u0644\u0622\u0646 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u0627\u062a \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to x_0^+}f(x) = +\\infty := \\left(\\forall M \\in \\mathbb{R}\\right)\\left( \\exists \\delta \\gt 0 \\right) ( x_0 \\lt x \\lt x_0 + \\delta \\rightarrow M \\lt f(x) )<\/span><\/span><\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to x_0^-}f(x) = +\\infty := \\left(\\forall M \\in \\mathbb{R}\\right)\\left( \\exists \\delta \\gt 0 \\right) ( x_0 - \\delta \\lt x \\lt x_0 \\rightarrow M \\lt f(x) )<\/span><\/span><\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to x_0}f(x) = +\\infty := \\left(\\lim_{x\\to x_0^+}f(x) = +\\infty \\right) \\wedge \\left(\\lim_{x\\to x_0^-}f(x) = +\\infty \\right)<\/span><\/span><\/p>\n<p>\u0648\u0628\u0634\u0643\u0644 \u0645\u0634\u0627\u0628\u0647:<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to x_0^+}f(x) = -\\infty := \\left(\\forall m \\in \\mathbb{R}\\right)\\left( \\exists \\delta \\gt 0 \\right) ( x_0 \\lt x \\lt x_0 + \\delta \\rightarrow f(x) \\lt m )<\/span><\/span><\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to x_0^-}f(x) = -\\infty := \\left(\\forall m \\in \\mathbb{R}\\right)\\left( \\exists \\delta \\gt 0 \\right) ( x_0 - \\delta \\lt x \\lt x_0 \\rightarrow f(x) \\lt m )<\/span><\/span><\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to x_0}f(x) = -\\infty := \\left(\\lim_{x\\to x_0^+}f(x) = -\\infty \\right) \\wedge \\left(\\lim_{x\\to x_0^-}f(x) = -\\infty \\right)<\/span><\/span><\/p>\n<p>\u0648\u0641\u064a \u0628\u0639\u0636 \u0627\u0644\u0623\u062d\u064a\u0627\u0646 \u064a\u064f\u0642\u0627\u0644 \u0623\u0646 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u062a\u0645\u064a\u0644 \u0625\u0644\u0649 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 (\u0628\u062f\u0648\u0646 \u0625\u0634\u0627\u0631\u0629):<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to x_0}f(x) = \\infty := \\lim_{x\\to x_0}|f(x)| = +\\infty <\/span><\/span><\/p>\n<p><a name=\"7\"><\/a><\/p>\n<h3>\u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629 \u0639\u0646\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=SFBMSd0Q7Io&amp;t=1147s\" target=\"_blank\" rel=\"noopener\"><strong>\u0639\u0644\u0649 \u063a\u0631\u0627\u0631 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u062a\u064a \u0627\u0633\u062a\u0639\u0631\u0636\u0646\u0627\u0647\u0627 \u0633\u0627\u0628\u0642\u0627\u064b\u060c<\/strong><\/a> \u064a\u0645\u0643\u0646 \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629 \u0639\u0646\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629. \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644:<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{x\\to +\\infty}f(x) = +\\infty := \\left(\\forall M \\in \\mathbb{R}\\right)\\left( \\exists N \\in\\mathbb{R} \\right) ( N\\lt x \\rightarrow M \\lt f(x) )<\/span><\/span><\/p>\n<p>\u0648\u0628\u0647\u0630\u0627\u060c \u0642\u062f \u0627\u0633\u062a\u0639\u0631\u0636\u0646\u0627 \u062c\u0645\u064a\u0639 \u0627\u0644\u0623\u0634\u0643\u0627\u0644 \u0627\u0644\u062a\u064a \u064a\u0645\u0643\u0646 \u0623\u0646 \u062a\u062a\u0628\u0627\u0639\u062f \u0641\u064a\u0647\u0627 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0641\u064a \u0627\u0644\u062f\u0648\u0627\u0644.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629 \u0648\u0627\u0644\u062a\u0628\u0627\u0639\u062f \u0645\u0644\u062e\u0635: \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629\u060c \u0633\u0646\u062a\u0646\u0627\u0648\u0644 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629 \u0648\u0623\u0646\u0648\u0627\u0639 \u0627\u0644\u062a\u0628\u0627\u0639\u062f \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629 \u0641\u064a \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a\u060c \u0645\u0633\u062a\u0639\u0631\u0636\u064a\u0646 \u0627\u0644\u0645\u0641\u0627\u0647\u064a\u0645 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0644\u0641\u0647\u0645 \u0643\u064a\u0641\u064a\u0629 \u0639\u062f\u0645 \u062a\u0642\u0627\u0631\u0628 \u0628\u0639\u0636 \u0627\u0644\u062f\u0648\u0627\u0644 \u0625\u0644\u0649 \u0642\u064a\u0645\u0629 \u062d\u0642\u064a\u0642\u064a\u0629 \u0645\u062d\u062f\u062f\u0629. \u0633\u0646\u0631\u0627\u062c\u0639 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u062c\u0627\u0646\u0628\u064a\u0629 \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629\u060c \u0627\u0644\u062f\u0648\u0627\u0644 \u0630\u0627\u062a \u0627\u0644\u062a\u0630\u0628\u0630\u0628\u0627\u062a \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629\u060c \u0648\u0627\u0644\u062d\u0627\u0644\u0627\u062a \u0627\u0644\u062a\u064a \u0644\u0627 \u062a\u0648\u062c\u062f \u0641\u064a\u0647\u0627 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0628\u0633\u0628\u0628 \u0645\u0634\u0627\u0643\u0644 \u0641\u064a \u0627\u0644\u0645\u062c\u0627\u0644 \u0623\u0648 \u0627\u0644\u0646\u0645\u0648 \u063a\u064a\u0631 \u0627\u0644\u0645\u062d\u062f\u0648\u062f. \u0623\u0647\u062f\u0627\u0641 \u0627\u0644\u062a\u0639\u0644\u0645: \u0639\u0646\u062f \u0646\u0647\u0627\u064a\u0629 \u0647\u0630\u0647 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":29458,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":15,"footnotes":""},"categories":[860,565],"tags":[],"class_list":["post-29475","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-860","category-565"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629 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