{"id":29351,"date":"2024-10-22T13:00:51","date_gmt":"2024-10-22T13:00:51","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=29351"},"modified":"2024-10-23T14:37:05","modified_gmt":"2024-10-23T14:37:05","slug":"%d8%ad%d8%af-%d8%a7%d9%84%d9%84%d8%a7%d9%86%d9%87%d8%a7%d9%8a%d8%a9-%d8%a7%d9%84%d8%aa%d8%b9%d8%b1%d9%8a%d9%81%d8%a7%d8%aa-%d9%88%d8%a7%d9%84%d8%a3%d9%85%d8%ab%d9%84%d8%a9","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/ar\/%d8%ad%d8%af-%d8%a7%d9%84%d9%84%d8%a7%d9%86%d9%87%d8%a7%d9%8a%d8%a9-%d8%a7%d9%84%d8%aa%d8%b9%d8%b1%d9%8a%d9%81%d8%a7%d8%aa-%d9%88%d8%a7%d9%84%d8%a3%d9%85%d8%ab%d9%84%d8%a9\/","title":{"rendered":"\u062d\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629: \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u0627\u062a \u0648\u0627\u0644\u0623\u0645\u062b\u0644\u0629"},"content":{"rendered":"<p><center><\/p>\n<h1>\u062d\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629: \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u0627\u062a \u0648\u0627\u0644\u0623\u0645\u062b\u0644\u0629<\/h1>\n<p>  <em><\/p>\n<p><strong>\u0645\u0644\u062e\u0635:<\/strong><br \/>\n  \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629\u060c \u0633\u064a\u062a\u0645 \u062a\u0646\u0627\u0648\u0644 \u062d\u062f\u0648\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629\u060c \u0648\u0634\u0631\u062d \u0633\u0644\u0648\u0643 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u0639\u0646\u062f\u0645\u0627 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x<\/span><\/span> \u064a\u062a\u062c\u0647 \u0646\u062d\u0648 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629. \u064a\u062a\u0645 \u0634\u0631\u062d \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0645\u062b\u0644 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{x\\to \\infty} \\frac{1}{x} = 0<\/span><\/span> \u0648 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{x\\to \\infty} k = k<\/span><\/span>\u060c \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u062e\u0635\u0627\u0626\u0635 \u062c\u0628\u0631\u064a\u0629 \u0645\u0634\u0627\u0628\u0647\u0629 \u0644\u062a\u0644\u0643 \u0627\u0644\u062e\u0627\u0635\u0629 \u0628\u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0646\u0647\u0627\u0626\u064a\u0629.\n  <\/p>\n<p><\/em><\/p>\n<p><strong>\u0623\u0647\u062f\u0627\u0641 \u0627\u0644\u062a\u0639\u0644\u0645:<\/strong><br \/>\n  \u0641\u064a \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\u064b\u0627 \u0639\u0644\u0649:<\/p>\n<ol style=\"text-align:left;\">\n<li><strong>\u0648\u0635\u0641<\/strong> \u0633\u0644\u0648\u0643 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u0639\u0646\u062f\u0645\u0627 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x<\/span><\/span> \u064a\u062a\u062c\u0647 \u0646\u062d\u0648 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629.<\/li>\n<li><strong>\u062a\u0639\u0631\u064a\u0641<\/strong> \u062d\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062a\u062f\u0648\u064a\u0646 \u0627\u0644\u0631\u064a\u0627\u0636\u064a \u0627\u0644\u0631\u0633\u0645\u064a.<\/li>\n<li><strong>\u062a\u0637\u0628\u064a\u0642<\/strong> \u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u062c\u0628\u0631\u064a\u0629 \u0641\u064a \u062d\u0633\u0627\u0628 \u062d\u062f\u0648\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629.<\/li>\n<li><strong>\u062a\u0645\u064a\u064a\u0632<\/strong> \u0628\u064a\u0646 \u062d\u0627\u0644\u0627\u062a \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629 \u0641\u064a \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0646\u0633\u0628\u064a\u0629 \u0639\u0646\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629.<\/li>\n<li><strong>\u0625\u062b\u0628\u0627\u062a<\/strong> \u0635\u062d\u0629 \u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u062c\u0645\u0639\u060c \u0627\u0644\u0637\u0631\u062d\u060c \u0627\u0644\u0636\u0631\u0628\u060c \u0627\u0644\u0642\u0633\u0645\u0629 \u0648\u0631\u0641\u0639 \u0627\u0644\u062d\u062f\u0648\u062f \u0625\u0644\u0649 \u0627\u0644\u0642\u0648\u0649 \u0639\u0646\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629.<\/li>\n<li><strong>\u062d\u0644<\/strong> \u062a\u0645\u0627\u0631\u064a\u0646 \u0639\u0645\u0644\u064a\u0629 \u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 \u0641\u064a \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629.<\/li>\n<\/ol>\n<p>  <u>\u0641\u0647\u0631\u0633 \u0627\u0644\u0645\u062d\u062a\u0648\u064a\u0627\u062a<\/u>:<br \/>\n  <a href=\"#1\">\u0645\u0642\u062f\u0645\u0629<\/a><br \/>\n  <a href=\"#2\">\u062a\u0639\u0631\u064a\u0641 \u062d\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629<\/a><br \/>\n  <a href=\"#3\">\u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0639\u0646\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629<\/a><br \/>\n  <a href=\"#4\">\u0627\u0644\u062c\u0628\u0631 \u0639\u0646\u062f \u062d\u062f\u0648\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629<\/a><br \/>\n  <a href=\"#5\">\u062d\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 \u0641\u064a \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0646\u0633\u0628\u064a\u0629<\/a><br \/>\n  <a href=\"#6\">\u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u062d\u062f\u0648\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629<\/a><br \/>\n  <\/center><\/p>\n<p>  <center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/MjjSAQLeNBE\" title=\"\u0645\u0634\u063a\u0644 \u0641\u064a\u062f\u064a\u0648 YouTube\" 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>\u0645\u0642\u062f\u0645\u0629<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=41s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0623\u062d\u062f \u0627\u0644\u0639\u0646\u0627\u0635\u0631 \u0627\u0644\u0623\u0643\u062b\u0631 \u062a\u0645\u064a\u0632\u064b\u0627 \u0641\u064a \u0627\u0644\u062d\u0633\u0627\u0628 \u0647\u0648 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 \u0648\u062d\u062f\u0648\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629.<\/span><\/strong><\/a> \u0645\u0641\u0647\u0648\u0645 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 \u0644\u0627 \u064a\u0634\u064a\u0631 \u0625\u0644\u0649 \u0639\u062f\u062f \u062d\u0642\u064a\u0642\u064a\u060c \u0628\u0644 \u064a\u062d\u0627\u0648\u0644 \u0648\u0635\u0641 \u0645\u0642\u062f\u0627\u0631 \u064a\u062a\u062c\u0627\u0648\u0632 \u0623\u064a \u062d\u062f \u062d\u0642\u064a\u0642\u064a. \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0639\u0646\u062f\u0645\u0627 \u064a\u0643\u0648\u0646 \u0644\u062f\u064a\u0646\u0627 \u0627\u0644\u062f\u0627\u0644\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x) = 1\/x<\/span><\/span> \u0648\u0646\u062a\u0633\u0627\u0621\u0644 \u0639\u0646 \u0633\u0644\u0648\u0643\u0647\u0627 \u0639\u0646\u062f\u0645\u0627 \u064a\u0635\u0628\u062d <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x<\/span><\/span> \u0643\u0628\u064a\u0631\u064b\u0627 \u0628\u0642\u062f\u0631 \u0645\u0627 \u0646\u0631\u064a\u062f\u060c \u0639\u0646\u062f\u0645\u0627 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x<\/span><\/span> \u064a\u062a\u062c\u0647 \u0646\u062d\u0648 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 (<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\to \\infty<\/span><\/span>)\u060c \u0645\u0627 \u0646\u0644\u0627\u062d\u0638\u0647 \u0647\u0648 \u0623\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u064a\u0645\u0643\u0646 \u0623\u0646 \u064a\u0642\u062a\u0631\u0628 \u0645\u0646 \u0627\u0644\u0635\u0641\u0631 \u0628\u0642\u062f\u0631 \u0645\u0627 \u0646\u0631\u064a\u062f. \u0628\u0646\u0627\u0621\u064b \u0639\u0644\u0649 \u0630\u0644\u0643 \u0646\u0643\u062a\u0628:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to + \\infty}\\dfrac{1}{x} = 0<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u0628\u064a\u0627\u0646\u064a\u064b\u0627\u060c \u064a\u0628\u062f\u0648 \u0647\u0630\u0627 \u0627\u0644\u0645\u0648\u0636\u0648\u0639 \u0643\u0645\u0627 \u064a\u0644\u064a:<\/p>\n<p>  <center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-fX0lg2ICTTU\/YGD0hNJWI6I\/AAAAAAAAEwQ\/0v8hW6ARkQYDIzT_eG5WVgZ0-pPwwPBwgCLcBGAsYHQ\/s0\/limiteAlinfinito.PNG\" alt=\"\u062d\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629\" class=\"alignnone size-full lazyload\" width=\"400\" height=\"300\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-fX0lg2ICTTU\/YGD0hNJWI6I\/AAAAAAAAEwQ\/0v8hW6ARkQYDIzT_eG5WVgZ0-pPwwPBwgCLcBGAsYHQ\/s0\/limiteAlinfinito.PNG\" alt=\"\u062d\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629\" class=\"alignnone size-full lazyload\" width=\"400\" height=\"300\" \/><\/noscript><\/center><\/p>\n<p>  <a name=\"2\"><\/a><\/p>\n<h2>\u062a\u0639\u0631\u064a\u0641 \u062d\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=144s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0645\u0646 \u0647\u0630\u0647 \u0627\u0644\u0641\u0643\u0631\u0629 \u0627\u0644\u062a\u064a \u0642\u062f\u0645\u0646\u0627\u0647\u0627<\/span><\/strong><\/a> \u064a\u0645\u0643\u0646\u0646\u0627 \u0635\u064a\u0627\u063a\u0629 \u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0631\u064a\u0627\u0636\u064a \u0644\u062d\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629:<\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to +\\infty}f(x) = L := (\\forall\\epsilon\\gt 0) (\\exists M\\in\\mathbb{R})(M\\lt x \\rightarrow |f(x) - L|\\lt \\epsilon )<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to -\\infty}f(x) = L := (\\forall\\epsilon\\gt 0) (\\exists N\\in\\mathbb{R})(x\\lt N \\rightarrow |f(x) - L|\\lt \\epsilon )<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u064a\u0634\u064a\u0631 \u0627\u0644\u0645\u0641\u0647\u0648\u0645 \u0627\u0644\u0628\u062f\u064a\u0647\u064a \u0644\u0647\u0630\u0627 \u0627\u0644\u062d\u062f \u0625\u0644\u0649 \u0645\u0627 \u064a\u062d\u062f\u062b \u0645\u0639 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u0639\u0646\u062f\u0645\u0627 \u064a\u0628\u062a\u0639\u062f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x<\/span><\/span> \u0639\u0646 \u0627\u0644\u0623\u0635\u0644 \u0628\u0642\u062f\u0631 \u0645\u0627 \u0646\u0631\u064a\u062f\u060c \u0633\u0648\u0627\u0621\u064b \u0625\u0644\u0649 \u0627\u0644\u064a\u0645\u064a\u0646 \u0623\u0648 \u0625\u0644\u0649 \u0627\u0644\u064a\u0633\u0627\u0631. \u0625\u0646 \u0627\u0644\u0627\u0633\u062a\u0631\u0627\u062a\u064a\u062c\u064a\u0629 \u0644\u062d\u0633\u0627\u0628 \u062d\u062f\u0648\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 \u0644\u0627 \u062a\u062e\u062a\u0644\u0641 \u0643\u062b\u064a\u0631\u064b\u0627 \u0639\u0646 \u062a\u0644\u0643 \u0627\u0644\u062a\u064a \u0646\u0633\u062a\u062e\u062f\u0645\u0647\u0627 \u0641\u064a \u062d\u0633\u0627\u0628 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0646\u0647\u0627\u0626\u064a\u0629 \u0644\u0623\u0646 \u0627\u0644\u062c\u0628\u0631 \u0627\u0644\u062e\u0627\u0635 \u0628\u0647\u0627 \u0647\u0648 \u0646\u0641\u0633\u0647 \u062a\u0642\u0631\u064a\u0628\u064b\u0627\u060c \u0641\u0642\u0637 \u064a\u062c\u0628 \u0623\u0646 \u0646\u0623\u062e\u0630 \u0641\u064a \u0627\u0644\u0627\u0639\u062a\u0628\u0627\u0631 \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0627\u0644\u062a\u0627\u0644\u064a\u0629.<\/p>\n<p>  <a name=\"3\"><\/a><\/p>\n<h2>\u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0639\u0646\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629<\/h2>\n<p>  <a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=450s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0627\u0633\u062a\u0646\u0627\u062f\u064b\u0627 \u0625\u0644\u0649 \u0647\u0630\u0647 \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u0627\u062a\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0625\u062b\u0628\u0627\u062a<\/span><\/strong><\/a> \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629.<\/p>\n<ol style=\"text-align: justify;\">\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to \\pm\\infty}k = k <\/span><\/span><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to \\pm\\infty}\\dfrac{1}{x} = 0 <\/span><\/span><\/li>\n<\/ol>\n<p style=\"text-align: justify;\"><span style=\"color: #000080;\">\u0627\u0644\u0625\u062b\u0628\u0627\u062a:<\/span><\/p>\n<ol style=\"text-align: justify;\">\n<li>\u062d\u0633\u0628 \u062a\u0639\u0631\u064a\u0641 \u062d\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629\u060c \u0644\u062f\u064a\u0646\u0627 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to +\\infty}k = k <\/span><\/span> \u0648\u0647\u0648 \u0645\u0643\u0627\u0641\u0626 \u0644\u0644\u0642\u0648\u0644:<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\forall\\epsilon\\gt 0) (\\exists M\\in\\mathbb{R})\\left(M\\lt x \\rightarrow \\left|k-k\\right|\\lt \\epsilon \\right)<\/span><\/span>\u0648\u0644\u0643\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left|k-k\\right|=0\\lt \\epsilon <\/span><\/span> \u064a\u062a\u062d\u0642\u0642 \u062f\u0627\u0626\u0645\u064b\u0627 \u0644\u0623\u064a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\epsilon \\gt 0,<\/span><\/span> \u0628\u063a\u0636 \u0627\u0644\u0646\u0638\u0631 \u0639\u0646 \u0642\u064a\u0645\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">M<\/span><\/span>\u060c \u0644\u0630\u0644\u0643 \u064a\u062a\u0645 \u062a\u0623\u0643\u064a\u062f \u0627\u0644\u062d\u062f.\n<p>  &nbsp;<\/li>\n<li>\u0646\u0639\u0644\u0645 \u0623\u0646\u0647\u060c \u062d\u0633\u0628 \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u060c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to +\\infty}k = k <\/span><\/span> \u0648\u0647\u0648 \u0645\u0643\u0627\u0641\u0626 \u0644\u0644\u0642\u0648\u0644:<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\forall\\epsilon\\gt 0) (\\exists M\\in\\mathbb{R})\\left(M\\lt x \\rightarrow \\left|\\dfrac{1}{x}\\right|\\lt \\epsilon \\right)<\/span><\/span>\u0648\u0644\u0643\u0646 \u0647\u0630\u0627 \u0627\u0644\u0634\u0631\u0637 \u064a\u062a\u062d\u0642\u0642 \u0639\u0644\u0649 \u0627\u0644\u0641\u0648\u0631 \u0625\u0630\u0627 \u0627\u0639\u062a\u0628\u0631\u0646\u0627 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">M=1\/\\epsilon,<\/span><\/span> \u0645\u0645\u0627 \u064a\u0636\u0645\u0646 \u0627\u0644\u062d\u062f.\n<p>  &nbsp;<\/li>\n<\/ol>\n<p style=\"text-align: justify;\">\u064a\u062a\u0645 \u0625\u062c\u0631\u0627\u0621 \u0647\u0630\u0647 \u0627\u0644\u0625\u062b\u0628\u0627\u062a\u0627\u062a \u0628\u0634\u0643\u0644 \u0645\u0634\u0627\u0628\u0647 \u0639\u0646\u062f\u0645\u0627 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\to+\\infty.<\/span><\/span><\/p>\n<p>  <a name=\"4\"><\/a><\/p>\n<h2>\u0627\u0644\u062c\u0628\u0631 \u0639\u0646\u062f \u062d\u062f\u0648\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=620s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0627\u0644\u062c\u0628\u0631 \u0639\u0646\u062f \u062d\u062f\u0648\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 \u0645\u0634\u0627\u0628\u0647 \u0644\u0644\u062c\u0628\u0631 \u0639\u0646\u062f \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0646\u0647\u0627\u0626\u064a\u0629.<\/span> <\/strong><\/a>\u0625\u0630\u0627 \u0643\u0627\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to \\pm \\infty}f(x) = L<\/span><\/span> \u0648 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to \\pm \\infty}g(x) = M,<\/span><\/span> \u0641\u0625\u0646 \u0627\u0644\u0642\u0648\u0627\u0639\u062f \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u062a\u062a\u062d\u0642\u0642:<\/p>\n<ol style=\"text-align: justify;\">\n<li><strong>\u062c\u0645\u0639 \u0648\u0637\u0631\u062d \u0627\u0644\u062d\u062f\u0648\u062f:<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to \\pm\\infty}(f(x)\\pm g(x)) = L \\pm M<\/span><\/span><\/li>\n<li><strong>\u0627\u0644\u0636\u0631\u0628 \u0641\u064a \u062b\u0627\u0628\u062a:<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to \\pm\\infty}cf(x) = cL<\/span><\/span><\/li>\n<li><strong>\u0636\u0631\u0628 \u0627\u0644\u062d\u062f\u0648\u062f:<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to \\pm\\infty}f(x)g(x) = LM<\/span><\/span><\/li>\n<li><strong>\u0642\u0633\u0645\u0629 \u0627\u0644\u062d\u062f\u0648\u062f:<\/strong> \u0637\u0627\u0644\u0645\u0627 \u0623\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">M\\neq 0,<\/span><\/span> \u0641\u0625\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to \\pm\\infty}f(x)\/g(x)=L\/M<\/span><\/span><\/li>\n<li><strong>\u0631\u0641\u0639 \u0627\u0644\u062d\u062f\u0648\u062f \u0625\u0644\u0649 \u0642\u0648\u0649:<\/strong> \u0625\u0630\u0627 \u0643\u0627\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">p,q \\in\\mathbb{Z}<\/span><\/span> \u0648 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q\\neq 0<\/span><\/span>\u060c \u0641\u0625\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to \\pm\\infty}[f(x)]^{p\/q} = L^{p\/q}<\/span><\/span><br \/>\n  \u0625\u0630\u0627 \u0643\u0627\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q<\/span><\/span> \u0632\u0648\u062c\u064a\u064b\u0627\u060c \u0641\u0645\u0646 \u0627\u0644\u0645\u0641\u062a\u0631\u0636 \u0623\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">L\\geq 0<\/span><\/span><\/li>\n<\/ol>\n<p style=\"text-align: justify;\">\u0641\u064a \u0627\u0644\u0648\u0627\u0642\u0639\u060c \u0641\u0625\u0646 \u0625\u062b\u0628\u0627\u062a \u062c\u0645\u064a\u0639 \u0647\u0630\u0647 \u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u064a\u0634\u0628\u0647 \u0625\u062b\u0628\u0627\u062a <a href=\"https:\/\/toposuranos.com\/la-definicion-de-limite-demostraciones-y-teoremas\/\" target=\"_blank\" rel=\"noopener\">\u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0646\u0647\u0627\u0626\u064a\u0629<\/a><\/p>\n<p>  <a name=\"5\"><\/a><\/p>\n<h2>\u062d\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 \u0641\u064a \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0646\u0633\u0628\u064a\u0629<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=792s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0646\u0633\u0628\u064a\u0629 \u0647\u064a \u0627\u0644\u062a\u064a \u064a\u0645\u0643\u0646 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0639\u0646\u0647\u0627 \u0643\u0646\u0633\u0628\u0629 \u0628\u064a\u0646 \u0643\u062b\u064a\u0631\u062a\u064a \u062d\u062f\u0648\u062f.<\/span><\/strong><\/a> \u0639\u0646\u062f \u062d\u0633\u0627\u0628 \u062d\u062f\u0648\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 \u0639\u0644\u0649 \u0647\u0630\u0627 \u0627\u0644\u0646\u0648\u0639 \u0645\u0646 \u0627\u0644\u062f\u0648\u0627\u0644\u060c \u064a\u0645\u0643\u0646 \u0645\u0644\u0627\u062d\u0638\u0629 \u062e\u0627\u0635\u064a\u0629 \u062a\u0643\u0648\u0646 \u0630\u0627\u062a \u0641\u0627\u0626\u062f\u0629 \u0643\u0628\u064a\u0631\u0629:<\/p>\n<p style=\"text-align: justify;\">\u0644\u0646\u0641\u062a\u0631\u0636 \u0623\u0646\u0646\u0627 \u0646\u0631\u064a\u062f \u062d\u0633\u0627\u0628 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to \\infty}P(x)\/Q(x)<\/span><\/span><\/p>\n<ul style=\"text-align: justify;\">\n<li>\u0625\u0630\u0627 \u0643\u0627\u0646 \u062f\u0631\u062c\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(x)<\/span><\/span> \u0623\u0643\u0628\u0631 \u0645\u0646 \u062f\u0631\u062c\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Q(x)<\/span><\/span>\u060c \u0641\u0625\u0646 \u062d\u062c\u0645 \u0627\u0644\u062f\u0627\u0644\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u0633\u0648\u0641 \u064a\u0646\u0645\u0648 \u0628\u062f\u0648\u0646 \u062d\u062f \u0639\u0646\u062f\u0645\u0627 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x\\to\\infty<\/span><\/span> (\u0627\u0644\u062d\u062f \u0644\u0646 \u064a\u0648\u062c\u062f)<\/li>\n<li>\u0639\u0646\u062f\u0645\u0627 \u064a\u0643\u0648\u0646 \u062f\u0631\u062c\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(x)<\/span><\/span> \u0623\u0642\u0644 \u0645\u0646 \u062f\u0631\u062c\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Q(x)<\/span><\/span>\u060c \u0641\u0625\u0646 \u0627\u0644\u062d\u062f \u0633\u064a\u0643\u0648\u0646 \u0635\u0641\u0631\u064b\u0627.<\/li>\n<li>\u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u062f\u0631\u062c\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(x)<\/span><\/span> \u0645\u0633\u0627\u0648\u064a\u0629 \u0644\u062f\u0631\u062c\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Q(x)<\/span><\/span>\u060c \u0641\u0625\u0646 \u0627\u0644\u062d\u062f \u0633\u064a\u0643\u0648\u0646 \u0645\u0633\u0627\u0648\u064a\u064b\u0627 \u0644\u0646\u0633\u0628\u0629 \u0627\u0644\u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0627\u0644\u0645\u0635\u0627\u062d\u0628\u0629 \u0644\u0623\u0639\u0644\u0649 \u062f\u0631\u062c\u0629.<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">\u0623\u0641\u0636\u0644 \u0645\u0627 \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0647\u0648 \u0623\u0646\u0647\u060c \u0643\u0645\u0627 \u0633\u0646\u0631\u0649 \u0641\u064a \u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629\u060c \u064a\u0639\u0645\u0644 \u0628\u0634\u0643\u0644 \u0645\u0634\u0627\u0628\u0647 \u062d\u062a\u0649 \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0627\u0644\u0642\u0648\u0649 \u0627\u0644\u0645\u0639\u0646\u064a\u0629 \u0644\u064a\u0633\u062a \u0623\u0639\u062f\u0627\u062f\u064b\u0627 \u0635\u062d\u064a\u062d\u0629.<\/p>\n<p>  <a name=\"6\"><\/a><\/p>\n<h2>\u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u062d\u062f\u0648\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629<\/h2>\n<ol style=\"text-align: justify;\">\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to +\\infty}\\dfrac{x+1}{x^2+3}<\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=907s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u0627\u0644\u062d\u0644]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to -\\infty}\\dfrac{2x^3 + 7}{x^3 - x^2 + x + 7}<\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=986s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u0627\u0644\u062d\u0644]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to +\\infty}\\dfrac{9x^4 + x}{2x^4 + 5x^2 - x + 6}<\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=1049s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u0627\u0644\u062d\u0644]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to +\\infty}\\dfrac{10x^5 + x4 + 31}{x^4 - 7x^3 + 7x^2 + 9}<\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=1111s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u0627\u0644\u062d\u0644]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to +\\infty}\\dfrac{2\\sqrt{x}+x^{-1}}{3x - 7}<\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=1220s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u0627\u0644\u062d\u0644]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to -\\infty}\\dfrac{2x^{5\/3} - x^{1\/3} + 7}{x^{8\/5}+3x + \\sqrt{x}}<\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=1284s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u0627\u0644\u062d\u0644]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to +\\infty}\\dfrac{\\sqrt[3]{x}-5x+3}{2x + x^{2\/3} - 4}<\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=1406s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u0627\u0644\u062d\u0644]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to +\\infty}\\dfrac{x^{8\/3}+2x + \\sqrt{x}}{x^2+x-3}<\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=MjjSAQLeNBE&amp;t=1521s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[\u0627\u0644\u062d\u0644]<\/span><\/strong><\/a><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u062d\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629: \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u0627\u062a \u0648\u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u0645\u0644\u062e\u0635: \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629\u060c \u0633\u064a\u062a\u0645 \u062a\u0646\u0627\u0648\u0644 \u062d\u062f\u0648\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629\u060c \u0648\u0634\u0631\u062d \u0633\u0644\u0648\u0643 \u0639\u0646\u062f\u0645\u0627 \u064a\u062a\u062c\u0647 \u0646\u062d\u0648 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629. \u064a\u062a\u0645 \u0634\u0631\u062d \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0645\u062b\u0644 \u0648 \u060c \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u062e\u0635\u0627\u0626\u0635 \u062c\u0628\u0631\u064a\u0629 \u0645\u0634\u0627\u0628\u0647\u0629 \u0644\u062a\u0644\u0643 \u0627\u0644\u062e\u0627\u0635\u0629 \u0628\u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0646\u0647\u0627\u0626\u064a\u0629. \u0623\u0647\u062f\u0627\u0641 \u0627\u0644\u062a\u0639\u0644\u0645: \u0641\u064a \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\u064b\u0627 \u0639\u0644\u0649: \u0648\u0635\u0641 \u0633\u0644\u0648\u0643 \u0639\u0646\u062f\u0645\u0627 \u064a\u062a\u062c\u0647 \u0646\u062d\u0648 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629. \u062a\u0639\u0631\u064a\u0641 \u062d\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062a\u062f\u0648\u064a\u0646 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":29336,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":21,"footnotes":""},"categories":[860,565],"tags":[],"class_list":["post-29351","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 v28.0 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u062d\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629: \u0627\u0644\u062a\u0639\u0631\u064a\u0641\u0627\u062a \u0648\u0627\u0644\u0623\u0645\u062b\u0644\u0629 - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u0639\u062f\u0645 \u0641\u0647\u0645 \u062d\u062f\u0648\u062f \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u064a\u0629 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