{"id":27906,"date":"2024-08-15T19:51:14","date_gmt":"2024-08-15T19:51:14","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=27906"},"modified":"2024-08-15T19:51:14","modified_gmt":"2024-08-15T19:51:14","slug":"%d1%80%d0%b5%d1%88%d0%b5%d0%bd%d0%bd%d1%8b%d0%b5-%d0%b7%d0%b0%d0%b4%d0%b0%d1%87%d0%b8-%d0%ba%d0%be%d0%bd%d0%b5%d1%87%d0%bd%d1%8b%d0%b5-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/ru\/%d1%80%d0%b5%d1%88%d0%b5%d0%bd%d0%bd%d1%8b%d0%b5-%d0%b7%d0%b0%d0%b4%d0%b0%d1%87%d0%b8-%d0%ba%d0%be%d0%bd%d0%b5%d1%87%d0%bd%d1%8b%d0%b5-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b\/","title":{"rendered":"\u0420\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438: \u041a\u043e\u043d\u0435\u0447\u043d\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b"},"content":{"rendered":"<p><center><\/p>\n<h1>\u0420\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438: \u041a\u043e\u043d\u0435\u0447\u043d\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b<\/h1>\n<p><em><strong>\u0420\u0435\u0437\u044e\u043c\u0435:<\/strong><br \/>\n\u042d\u0442\u043e\u0442 \u043a\u0443\u0440\u0441 \u043f\u0440\u0435\u0434\u043b\u0430\u0433\u0430\u0435\u0442 \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u043f\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044e \u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0445 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432, \u0441\u043e\u043f\u0440\u043e\u0432\u043e\u0436\u0434\u0430\u0435\u043c\u044b\u0435 \u0432\u0438\u0434\u0435\u043e\u0443\u0440\u043e\u043a\u043e\u043c. \u0421\u0442\u0443\u0434\u0435\u043d\u0442\u044b \u043f\u043e\u043b\u0443\u0447\u0430\u044e\u0442 \u0440\u0443\u043a\u043e\u0432\u043e\u0434\u0441\u0442\u0432\u043e \u043f\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u044e \u0437\u0430\u0434\u0430\u0447 \u0438 \u0441\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044e \u0441\u0432\u043e\u0438\u0445 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u043e\u0432 \u0441 \u043f\u0440\u0435\u0434\u043e\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u043d\u044b\u043c\u0438 \u0440\u0435\u0448\u0435\u043d\u0438\u044f\u043c\u0438. \u0410\u043a\u0446\u0435\u043d\u0442 \u0434\u0435\u043b\u0430\u0435\u0442\u0441\u044f \u043d\u0430 \u043a\u043b\u044e\u0447\u0435\u0432\u044b\u0435 \u043c\u0435\u0442\u043e\u0434\u044b, \u0442\u0430\u043a\u0438\u0435 \u043a\u0430\u043a \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u044f \u0438 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u0435 \u0433\u0440\u0430\u0444\u0438\u043a\u043e\u0432, \u0447\u0442\u043e \u043f\u043e\u043e\u0449\u0440\u044f\u0435\u0442 \u0440\u0430\u0437\u043d\u044b\u0435 \u043f\u043e\u0434\u0445\u043e\u0434\u044b \u043a \u0434\u043e\u0441\u0442\u0438\u0436\u0435\u043d\u0438\u044e \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u043e\u0433\u043e \u043e\u0442\u0432\u0435\u0442\u0430.<\/em><\/p>\n<p><strong>\u0423\u0447\u0435\u0431\u043d\u044b\u0435 \u0446\u0435\u043b\u0438<\/strong><br \/>\n\u041f\u043e \u0437\u0430\u0432\u0435\u0440\u0448\u0435\u043d\u0438\u0438 \u044d\u0442\u043e\u0433\u043e \u043a\u0443\u0440\u0441\u0430 \u0441\u0442\u0443\u0434\u0435\u043d\u0442 \u0431\u0443\u0434\u0435\u0442 \u0441\u043f\u043e\u0441\u043e\u0431\u0435\u043d:<\/p>\n<ul style=\"text-align:left;\">\n<li><strong>\u0412\u044b\u0447\u0438\u0441\u043b\u044f\u0442\u044c<\/strong> \u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0434\u043b\u044f \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u044b\u0445 \u0438 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439.<\/li>\n<li><strong>\u0418\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c<\/strong> \u043c\u0435\u0442\u043e\u0434\u044b \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u0438 \u0434\u043b\u044f \u0443\u043f\u0440\u043e\u0449\u0435\u043d\u0438\u044f \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432.<\/li>\n<li><strong>\u0421\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u0442\u044c<\/strong> \u0440\u0430\u0437\u043d\u044b\u0435 \u043c\u0435\u0442\u043e\u0434\u044b \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0438 \u043f\u043e\u043d\u0438\u043c\u0430\u0442\u044c, \u0447\u0442\u043e \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043f\u0443\u0442\u0435\u0439 \u043a \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u043e\u043c\u0443 \u043e\u0442\u0432\u0435\u0442\u0443.<\/li>\n<\/ul>\n<p><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/VY1gr1EUq3o\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\n<\/center><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u042d\u0442\u0438 \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f \u043f\u043e\u043c\u043e\u0433\u0443\u0442 \u0432\u0430\u043c \u043e\u0432\u043b\u0430\u0434\u0435\u0442\u044c \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435\u043c \u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0445 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432. \u0420\u0435\u0448\u0435\u043d\u0438\u044f \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u044b \u0432 \u0432\u0438\u0434\u0435\u043e.<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0414\u043b\u044f \u0443\u043b\u0443\u0447\u0448\u0435\u043d\u0438\u044f \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u0430 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f \u044f \u0441\u043e\u0437\u0434\u0430\u043b \u044d\u0442\u043e \u0432\u0438\u0434\u0435\u043e \u0441 \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u043c\u0438 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f\u043c\u0438 \u043f\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044e \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432, \u043f\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u044f \u0432\u0441\u0435 \u043e\u0441\u043e\u0431\u0435\u043d\u043d\u043e\u0441\u0442\u0438, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043c\u043e\u0436\u043d\u043e \u0438\u0437 \u043d\u0438\u0445 \u0438\u0437\u0432\u043b\u0435\u0447\u044c.<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u041f\u043e\u043f\u0440\u043e\u0431\u0443\u0439\u0442\u0435 \u0440\u0435\u0448\u0438\u0442\u044c \u044d\u0442\u0438 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f \u0441\u0430\u043c\u043e\u0441\u0442\u043e\u044f\u0442\u0435\u043b\u044c\u043d\u043e, \u0430 \u0437\u0430\u0442\u0435\u043c \u0441\u0440\u0430\u0432\u043d\u0438\u0442\u0435 \u0441\u0432\u043e\u0438 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u044b.<br \/>\n\u0420\u044f\u0434\u043e\u043c \u0441 \u043a\u0430\u0436\u0434\u044b\u043c \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435\u043c \u0432\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u0441\u0441\u044b\u043b\u043a\u0443, \u0432\u0435\u0434\u0443\u0449\u0443\u044e \u043a \u0447\u0430\u0441\u0442\u0438 \u0432\u0438\u0434\u0435\u043e \u043d\u0430 YouTube, \u0433\u0434\u0435 \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u044e\u0442\u0441\u044f \u0432\u0441\u0435 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f \u0434\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u044f.<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0418\u043d\u043e\u0433\u0434\u0430 \u0432\u0430\u043c \u043f\u0440\u0438\u0434\u0435\u0442\u0441\u044f \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u0442\u044c, \u0430 \u0438\u043d\u043e\u0433\u0434\u0430 \u043f\u043e\u043b\u0430\u0433\u0430\u0442\u044c\u0441\u044f \u043d\u0430 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u0430 \u0434\u043b\u044f \u043e\u0431\u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u044f \u043e\u0442\u0432\u0435\u0442\u0430. \u0418\u043d\u043e\u0433\u0434\u0430 \u0433\u0440\u0430\u0444\u0438\u043a \u043c\u043e\u0436\u0435\u0442 \u0437\u043d\u0430\u0447\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043e\u0431\u043b\u0435\u0433\u0447\u0438\u0442\u044c \u0432\u0430\u043c \u0437\u0430\u0434\u0430\u0447\u0443 \u043f\u0440\u0438 \u0432\u044b\u0431\u043e\u0440\u0435 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044f \u0440\u0430\u0441\u0441\u0443\u0436\u0434\u0435\u043d\u0438\u0439.<\/p>\n<h3>I. \u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b:<\/h3>\n<ol style=\"text-align: justify; color: #000000;\">\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to -1} (x^3+2x^2 - 3x - 4) <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=VY1gr1EUq3o&amp;t=35s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">[\u0420\u0415\u0428\u0415\u041d\u0418\u0415]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to 0} \\dfrac{3^x - 3^{-x}}{3^x + 3^{-x}} <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=VY1gr1EUq3o&amp;t=64s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">[\u0420\u0415\u0428\u0415\u041d\u0418\u0415]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to 2} \\dfrac{x-1}{x^2-1} <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=VY1gr1EUq3o&amp;t=91s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">[\u0420\u0415\u0428\u0415\u041d\u0418\u0415]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to 2} \\dfrac{x^2-4}{x^2-5x+6} <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=VY1gr1EUq3o&amp;t=161s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">[\u0420\u0415\u0428\u0415\u041d\u0418\u0415]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to -1} \\dfrac{x^2+3x+2}{x^2+4x+3} <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=VY1gr1EUq3o&amp;t=351s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">[\u0420\u0415\u0428\u0415\u041d\u0418\u0415]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to 2} \\dfrac{x-2}{\\sqrt{x^2-4}} <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=VY1gr1EUq3o&amp;t=594s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">[\u0420\u0415\u0428\u0415\u041d\u0418\u0415]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to 2} \\dfrac{\\sqrt{x-2}}{x^2-4} <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=VY1gr1EUq3o&amp;t=887s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">[\u0420\u0415\u0428\u0415\u041d\u0418\u0415]<\/span><\/strong><\/a><\/li>\n<\/ol>\n<h3>II. \u041d\u0430\u0439\u0434\u0438\u0442\u0435 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\lim_{h\\to 0} \\frac{f(x+h)-f(x)}{h}<\/span><\/span> \u0434\u043b\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439:<\/h3>\n<ol style=\"text-align: justify; color: #000000;\">\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle f(x) = \\dfrac{1}{x-2} <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=VY1gr1EUq3o&amp;t=1088s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">[\u0420\u0415\u0428\u0415\u041d\u0418\u0415]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle f(x) = \\sqrt{x-4} <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=VY1gr1EUq3o&amp;t=1263s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">[\u0420\u0415\u0428\u0415\u041d\u0418\u0415]<\/span><\/strong><\/a><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle f(x) = \\dfrac{x}{x+1} <\/span><\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=VY1gr1EUq3o&amp;t=1366s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #d00000;\">[\u0420\u0415\u0428\u0415\u041d\u0418\u0415]<\/span><\/strong><\/a><\/li>\n<\/ol>\n<p style=\"text-align: justify; color: #000000;\">\u0423\u0434\u0430\u043b\u043e\u0441\u044c \u043b\u0438 \u0432\u0430\u043c \u0440\u0435\u0448\u0438\u0442\u044c \u0438\u0445 \u0432\u0441\u0435 \u0441\u0430\u043c\u043e\u0441\u0442\u043e\u044f\u0442\u0435\u043b\u044c\u043d\u043e?<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u041d\u0430\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0432\u0430\u0448\u0438 \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u043e\u0442\u043b\u0438\u0447\u0430\u044e\u0442\u0441\u044f \u043e\u0442 \u043c\u043e\u0438\u0445?<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u041f\u043e\u043c\u043d\u0438\u0442\u0435, \u0447\u0442\u043e \u043f\u0443\u0442\u044c \u043a \u0440\u0435\u0448\u0435\u043d\u0438\u044e \u0437\u0430\u0434\u0430\u0447\u0438 \u043d\u0435 \u043e\u0431\u044f\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u0435\u0434\u0438\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u044b\u0439.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0420\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438: \u041a\u043e\u043d\u0435\u0447\u043d\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b \u0420\u0435\u0437\u044e\u043c\u0435: \u042d\u0442\u043e\u0442 \u043a\u0443\u0440\u0441 \u043f\u0440\u0435\u0434\u043b\u0430\u0433\u0430\u0435\u0442 \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u043f\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044e \u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0445 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432, \u0441\u043e\u043f\u0440\u043e\u0432\u043e\u0436\u0434\u0430\u0435\u043c\u044b\u0435 \u0432\u0438\u0434\u0435\u043e\u0443\u0440\u043e\u043a\u043e\u043c. \u0421\u0442\u0443\u0434\u0435\u043d\u0442\u044b \u043f\u043e\u043b\u0443\u0447\u0430\u044e\u0442 \u0440\u0443\u043a\u043e\u0432\u043e\u0434\u0441\u0442\u0432\u043e \u043f\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u044e \u0437\u0430\u0434\u0430\u0447 \u0438 \u0441\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044e \u0441\u0432\u043e\u0438\u0445 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u043e\u0432 \u0441 \u043f\u0440\u0435\u0434\u043e\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u043d\u044b\u043c\u0438 \u0440\u0435\u0448\u0435\u043d\u0438\u044f\u043c\u0438. \u0410\u043a\u0446\u0435\u043d\u0442 \u0434\u0435\u043b\u0430\u0435\u0442\u0441\u044f \u043d\u0430 \u043a\u043b\u044e\u0447\u0435\u0432\u044b\u0435 \u043c\u0435\u0442\u043e\u0434\u044b, \u0442\u0430\u043a\u0438\u0435 \u043a\u0430\u043a \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u044f \u0438 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u0435 \u0433\u0440\u0430\u0444\u0438\u043a\u043e\u0432, \u0447\u0442\u043e \u043f\u043e\u043e\u0449\u0440\u044f\u0435\u0442 \u0440\u0430\u0437\u043d\u044b\u0435 \u043f\u043e\u0434\u0445\u043e\u0434\u044b \u043a \u0434\u043e\u0441\u0442\u0438\u0436\u0435\u043d\u0438\u044e \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u043e\u0433\u043e \u043e\u0442\u0432\u0435\u0442\u0430. \u0423\u0447\u0435\u0431\u043d\u044b\u0435 \u0446\u0435\u043b\u0438 \u041f\u043e \u0437\u0430\u0432\u0435\u0440\u0448\u0435\u043d\u0438\u0438 \u044d\u0442\u043e\u0433\u043e \u043a\u0443\u0440\u0441\u0430 \u0441\u0442\u0443\u0434\u0435\u043d\u0442 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":27893,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":3,"footnotes":""},"categories":[864,573],"tags":[],"class_list":["post-27906","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-864","category-573"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u0420\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438: \u041a\u043e\u043d\u0435\u0447\u043d\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u041e\u0441\u0432\u043e\u0439\u0442\u0435 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 \u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0445 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432 \u0441 \u044d\u0442\u0438\u043c \u043a\u0443\u0440\u0441\u043e\u043c, \u0432\u043a\u043b\u044e\u0447\u0430\u044e\u0449\u0438\u043c \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438. \u0423\u0437\u043d\u0430\u0439\u0442\u0435 \u043a\u043b\u044e\u0447\u0435\u0432\u044b\u0435 \u043c\u0435\u0442\u043e\u0434\u044b, \u0442\u0430\u043a\u0438\u0435 \u043a\u0430\u043a \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u044f\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"http:\/\/toposuranos.com\/material\/ru\/\u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0435-\u0437\u0430\u0434\u0430\u0447\u0438-\u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0435-\u043f\u0440\u0435\u0434\u0435\u043b\u044b\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0420\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438: \u041a\u043e\u043d\u0435\u0447\u043d\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b\" \/>\n<meta property=\"og:description\" content=\"\u041e\u0441\u0432\u043e\u0439\u0442\u0435 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 \u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0445 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432 \u0441 \u044d\u0442\u0438\u043c \u043a\u0443\u0440\u0441\u043e\u043c, \u0432\u043a\u043b\u044e\u0447\u0430\u044e\u0449\u0438\u043c \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438. \u0423\u0437\u043d\u0430\u0439\u0442\u0435 \u043a\u043b\u044e\u0447\u0435\u0432\u044b\u0435 \u043c\u0435\u0442\u043e\u0434\u044b, \u0442\u0430\u043a\u0438\u0435 \u043a\u0430\u043a \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u044f\" \/>\n<meta property=\"og:url\" content=\"http:\/\/toposuranos.com\/material\/ru\/\u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0435-\u0437\u0430\u0434\u0430\u0447\u0438-\u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0435-\u043f\u0440\u0435\u0434\u0435\u043b\u044b\/\" \/>\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=\"2024-08-15T19:51:14+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/ejerciciolimites.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"\u0420\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438: \u041a\u043e\u043d\u0435\u0447\u043d\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b\" \/>\n<meta name=\"twitter:description\" content=\"\u041e\u0441\u0432\u043e\u0439\u0442\u0435 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 \u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0445 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432 \u0441 \u044d\u0442\u0438\u043c \u043a\u0443\u0440\u0441\u043e\u043c, \u0432\u043a\u043b\u044e\u0447\u0430\u044e\u0449\u0438\u043c \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438. \u0423\u0437\u043d\u0430\u0439\u0442\u0435 \u043a\u043b\u044e\u0447\u0435\u0432\u044b\u0435 \u043c\u0435\u0442\u043e\u0434\u044b, \u0442\u0430\u043a\u0438\u0435 \u043a\u0430\u043a \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u044f\" \/>\n<meta name=\"twitter:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/ejerciciolimites.jpg\" \/>\n<meta name=\"twitter:creator\" content=\"@topuranos\" \/>\n<meta name=\"twitter:site\" content=\"@topuranos\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"giorgio.reveco\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tiempo de lectura\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minuto\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/ru\\\/%d1%80%d0%b5%d1%88%d0%b5%d0%bd%d0%bd%d1%8b%d0%b5-%d0%b7%d0%b0%d0%b4%d0%b0%d1%87%d0%b8-%d0%ba%d0%be%d0%bd%d0%b5%d1%87%d0%bd%d1%8b%d0%b5-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b\\\/#article\",\"isPartOf\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/ru\\\/%d1%80%d0%b5%d1%88%d0%b5%d0%bd%d0%bd%d1%8b%d0%b5-%d0%b7%d0%b0%d0%b4%d0%b0%d1%87%d0%b8-%d0%ba%d0%be%d0%bd%d0%b5%d1%87%d0%bd%d1%8b%d0%b5-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b\\\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/person\\\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"\u0420\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438: \u041a\u043e\u043d\u0435\u0447\u043d\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b\",\"datePublished\":\"2024-08-15T19:51:14+00:00\",\"mainEntityOfPage\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/ru\\\/%d1%80%d0%b5%d1%88%d0%b5%d0%bd%d0%bd%d1%8b%d0%b5-%d0%b7%d0%b0%d0%b4%d0%b0%d1%87%d0%b8-%d0%ba%d0%be%d0%bd%d0%b5%d1%87%d0%bd%d1%8b%d0%b5-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b\\\/\"},\"wordCount\":334,\"commentCount\":0,\"publisher\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#organization\"},\"image\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/ru\\\/%d1%80%d0%b5%d1%88%d0%b5%d0%bd%d0%bd%d1%8b%d0%b5-%d0%b7%d0%b0%d0%b4%d0%b0%d1%87%d0%b8-%d0%ba%d0%be%d0%bd%d0%b5%d1%87%d0%bd%d1%8b%d0%b5-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b\\\/#primaryimage\"},\"thumbnailUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2024\\\/08\\\/ejerciciolimites.jpg\",\"articleSection\":[\"\u0414\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0438\u0441\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435\",\"\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"http:\\\/\\\/toposuranos.com\\\/material\\\/ru\\\/%d1%80%d0%b5%d1%88%d0%b5%d0%bd%d0%bd%d1%8b%d0%b5-%d0%b7%d0%b0%d0%b4%d0%b0%d1%87%d0%b8-%d0%ba%d0%be%d0%bd%d0%b5%d1%87%d0%bd%d1%8b%d0%b5-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/ru\\\/%d1%80%d0%b5%d1%88%d0%b5%d0%bd%d0%bd%d1%8b%d0%b5-%d0%b7%d0%b0%d0%b4%d0%b0%d1%87%d0%b8-%d0%ba%d0%be%d0%bd%d0%b5%d1%87%d0%bd%d1%8b%d0%b5-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b\\\/\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/ru\\\/%d1%80%d0%b5%d1%88%d0%b5%d0%bd%d0%bd%d1%8b%d0%b5-%d0%b7%d0%b0%d0%b4%d0%b0%d1%87%d0%b8-%d0%ba%d0%be%d0%bd%d0%b5%d1%87%d0%bd%d1%8b%d0%b5-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b\\\/\",\"name\":\"\u0420\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438: \u041a\u043e\u043d\u0435\u0447\u043d\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b - toposuranos.com\\\/material\",\"isPartOf\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/ru\\\/%d1%80%d0%b5%d1%88%d0%b5%d0%bd%d0%bd%d1%8b%d0%b5-%d0%b7%d0%b0%d0%b4%d0%b0%d1%87%d0%b8-%d0%ba%d0%be%d0%bd%d0%b5%d1%87%d0%bd%d1%8b%d0%b5-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b\\\/#primaryimage\"},\"image\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/ru\\\/%d1%80%d0%b5%d1%88%d0%b5%d0%bd%d0%bd%d1%8b%d0%b5-%d0%b7%d0%b0%d0%b4%d0%b0%d1%87%d0%b8-%d0%ba%d0%be%d0%bd%d0%b5%d1%87%d0%bd%d1%8b%d0%b5-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b\\\/#primaryimage\"},\"thumbnailUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2024\\\/08\\\/ejerciciolimites.jpg\",\"datePublished\":\"2024-08-15T19:51:14+00:00\",\"description\":\"\u041e\u0441\u0432\u043e\u0439\u0442\u0435 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 \u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0445 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432 \u0441 \u044d\u0442\u0438\u043c \u043a\u0443\u0440\u0441\u043e\u043c, \u0432\u043a\u043b\u044e\u0447\u0430\u044e\u0449\u0438\u043c \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438. \u0423\u0437\u043d\u0430\u0439\u0442\u0435 \u043a\u043b\u044e\u0447\u0435\u0432\u044b\u0435 \u043c\u0435\u0442\u043e\u0434\u044b, \u0442\u0430\u043a\u0438\u0435 \u043a\u0430\u043a \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u044f\",\"breadcrumb\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/ru\\\/%d1%80%d0%b5%d1%88%d0%b5%d0%bd%d0%bd%d1%8b%d0%b5-%d0%b7%d0%b0%d0%b4%d0%b0%d1%87%d0%b8-%d0%ba%d0%be%d0%bd%d0%b5%d1%87%d0%bd%d1%8b%d0%b5-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b\\\/#breadcrumb\"},\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"http:\\\/\\\/toposuranos.com\\\/material\\\/ru\\\/%d1%80%d0%b5%d1%88%d0%b5%d0%bd%d0%bd%d1%8b%d0%b5-%d0%b7%d0%b0%d0%b4%d0%b0%d1%87%d0%b8-%d0%ba%d0%be%d0%bd%d0%b5%d1%87%d0%bd%d1%8b%d0%b5-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/ru\\\/%d1%80%d0%b5%d1%88%d0%b5%d0%bd%d0%bd%d1%8b%d0%b5-%d0%b7%d0%b0%d0%b4%d0%b0%d1%87%d0%b8-%d0%ba%d0%be%d0%bd%d0%b5%d1%87%d0%bd%d1%8b%d0%b5-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b\\\/#primaryimage\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2024\\\/08\\\/ejerciciolimites.jpg\",\"contentUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2024\\\/08\\\/ejerciciolimites.jpg\",\"width\":1792,\"height\":431},{\"@type\":\"BreadcrumbList\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/ru\\\/%d1%80%d0%b5%d1%88%d0%b5%d0%bd%d0%bd%d1%8b%d0%b5-%d0%b7%d0%b0%d0%b4%d0%b0%d1%87%d0%b8-%d0%ba%d0%be%d0%bd%d0%b5%d1%87%d0%bd%d1%8b%d0%b5-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Portada\",\"item\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/es\\\/cursos-de-matematica-y-fisica\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u0420\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438: \u041a\u043e\u043d\u0435\u0447\u043d\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b\"}]},{\"@type\":\"WebSite\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#website\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/\",\"name\":\"toposuranos.com\\\/material\",\"description\":\"\",\"publisher\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"es\"},{\"@type\":\"Organization\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#organization\",\"name\":\"toposuranos.com\\\/material\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/logo.png\",\"contentUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/logo.png\",\"width\":2400,\"height\":2059,\"caption\":\"toposuranos.com\\\/material\"},\"image\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/logo\\\/image\\\/\"},\"sameAs\":[\"https:\\\/\\\/www.facebook.com\\\/groups\\\/toposuranos\",\"https:\\\/\\\/x.com\\\/topuranos\",\"https:\\\/\\\/www.youtube.com\\\/channel\\\/UC16yDm12cPcrwsE0fAM7X1g\",\"https:\\\/\\\/www.linkedin.com\\\/company\\\/69429190\"]},{\"@type\":\"Person\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/person\\\/e15164361c3f9a2a02cf6c234cf7fdc1\",\"name\":\"giorgio.reveco\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/1694478625378-96x96.jpeg\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/1694478625378-96x96.jpeg\",\"contentUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/1694478625378-96x96.jpeg\",\"caption\":\"giorgio.reveco\"},\"description\":\"Soy Licenciado en F\u00edsica, Magister en Ingenier\u00eda Industrial y Docente Universitario. Me dedico a desmitificar la f\u00edsica y las matem\u00e1ticas. Mi objetivo es hacer que estos campos sean f\u00e1cilmente comprensibles para todos, proporcionando las herramientas para explorar no solo el mundo que nos rodea, sino tambi\u00e9n las profundidades de nuestra propia existencia y el orden natural que nos conecta con el cosmos.\",\"sameAs\":[\"http:\\\/\\\/toposuranos.com\\\/material\"],\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/author\\\/giorgio-reveco\\\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u0420\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438: \u041a\u043e\u043d\u0435\u0447\u043d\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b - toposuranos.com\/material","description":"\u041e\u0441\u0432\u043e\u0439\u0442\u0435 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 \u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0445 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432 \u0441 \u044d\u0442\u0438\u043c \u043a\u0443\u0440\u0441\u043e\u043c, \u0432\u043a\u043b\u044e\u0447\u0430\u044e\u0449\u0438\u043c \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438. \u0423\u0437\u043d\u0430\u0439\u0442\u0435 \u043a\u043b\u044e\u0447\u0435\u0432\u044b\u0435 \u043c\u0435\u0442\u043e\u0434\u044b, \u0442\u0430\u043a\u0438\u0435 \u043a\u0430\u043a \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u044f","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"http:\/\/toposuranos.com\/material\/ru\/\u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0435-\u0437\u0430\u0434\u0430\u0447\u0438-\u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0435-\u043f\u0440\u0435\u0434\u0435\u043b\u044b\/","og_locale":"es_ES","og_type":"article","og_title":"\u0420\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438: \u041a\u043e\u043d\u0435\u0447\u043d\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b","og_description":"\u041e\u0441\u0432\u043e\u0439\u0442\u0435 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 \u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0445 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432 \u0441 \u044d\u0442\u0438\u043c \u043a\u0443\u0440\u0441\u043e\u043c, \u0432\u043a\u043b\u044e\u0447\u0430\u044e\u0449\u0438\u043c \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438. \u0423\u0437\u043d\u0430\u0439\u0442\u0435 \u043a\u043b\u044e\u0447\u0435\u0432\u044b\u0435 \u043c\u0435\u0442\u043e\u0434\u044b, \u0442\u0430\u043a\u0438\u0435 \u043a\u0430\u043a \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u044f","og_url":"http:\/\/toposuranos.com\/material\/ru\/\u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0435-\u0437\u0430\u0434\u0430\u0447\u0438-\u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0435-\u043f\u0440\u0435\u0434\u0435\u043b\u044b\/","og_site_name":"toposuranos.com\/material","article_publisher":"https:\/\/www.facebook.com\/groups\/toposuranos","article_published_time":"2024-08-15T19:51:14+00:00","og_image":[{"url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/ejerciciolimites.jpg","type":"","width":"","height":""}],"author":"giorgio.reveco","twitter_card":"summary_large_image","twitter_title":"\u0420\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438: \u041a\u043e\u043d\u0435\u0447\u043d\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b","twitter_description":"\u041e\u0441\u0432\u043e\u0439\u0442\u0435 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 \u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0445 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432 \u0441 \u044d\u0442\u0438\u043c \u043a\u0443\u0440\u0441\u043e\u043c, \u0432\u043a\u043b\u044e\u0447\u0430\u044e\u0449\u0438\u043c \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438. \u0423\u0437\u043d\u0430\u0439\u0442\u0435 \u043a\u043b\u044e\u0447\u0435\u0432\u044b\u0435 \u043c\u0435\u0442\u043e\u0434\u044b, \u0442\u0430\u043a\u0438\u0435 \u043a\u0430\u043a \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u044f","twitter_image":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/ejerciciolimites.jpg","twitter_creator":"@topuranos","twitter_site":"@topuranos","twitter_misc":{"Escrito por":"giorgio.reveco","Tiempo de lectura":"1 minuto"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"http:\/\/toposuranos.com\/material\/ru\/%d1%80%d0%b5%d1%88%d0%b5%d0%bd%d0%bd%d1%8b%d0%b5-%d0%b7%d0%b0%d0%b4%d0%b0%d1%87%d0%b8-%d0%ba%d0%be%d0%bd%d0%b5%d1%87%d0%bd%d1%8b%d0%b5-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b\/#article","isPartOf":{"@id":"http:\/\/toposuranos.com\/material\/ru\/%d1%80%d0%b5%d1%88%d0%b5%d0%bd%d0%bd%d1%8b%d0%b5-%d0%b7%d0%b0%d0%b4%d0%b0%d1%87%d0%b8-%d0%ba%d0%be%d0%bd%d0%b5%d1%87%d0%bd%d1%8b%d0%b5-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b\/"},"author":{"name":"giorgio.reveco","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1"},"headline":"\u0420\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438: \u041a\u043e\u043d\u0435\u0447\u043d\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b","datePublished":"2024-08-15T19:51:14+00:00","mainEntityOfPage":{"@id":"http:\/\/toposuranos.com\/material\/ru\/%d1%80%d0%b5%d1%88%d0%b5%d0%bd%d0%bd%d1%8b%d0%b5-%d0%b7%d0%b0%d0%b4%d0%b0%d1%87%d0%b8-%d0%ba%d0%be%d0%bd%d0%b5%d1%87%d0%bd%d1%8b%d0%b5-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b\/"},"wordCount":334,"commentCount":0,"publisher":{"@id":"http:\/\/toposuranos.com\/material\/#organization"},"image":{"@id":"http:\/\/toposuranos.com\/material\/ru\/%d1%80%d0%b5%d1%88%d0%b5%d0%bd%d0%bd%d1%8b%d0%b5-%d0%b7%d0%b0%d0%b4%d0%b0%d1%87%d0%b8-%d0%ba%d0%be%d0%bd%d0%b5%d1%87%d0%bd%d1%8b%d0%b5-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b\/#primaryimage"},"thumbnailUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/ejerciciolimites.jpg","articleSection":["\u0414\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0438\u0441\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435","\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430"],"inLanguage":"es","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["http:\/\/toposuranos.com\/material\/ru\/%d1%80%d0%b5%d1%88%d0%b5%d0%bd%d0%bd%d1%8b%d0%b5-%d0%b7%d0%b0%d0%b4%d0%b0%d1%87%d0%b8-%d0%ba%d0%be%d0%bd%d0%b5%d1%87%d0%bd%d1%8b%d0%b5-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b\/#respond"]}]},{"@type":"WebPage","@id":"http:\/\/toposuranos.com\/material\/ru\/%d1%80%d0%b5%d1%88%d0%b5%d0%bd%d0%bd%d1%8b%d0%b5-%d0%b7%d0%b0%d0%b4%d0%b0%d1%87%d0%b8-%d0%ba%d0%be%d0%bd%d0%b5%d1%87%d0%bd%d1%8b%d0%b5-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b\/","url":"http:\/\/toposuranos.com\/material\/ru\/%d1%80%d0%b5%d1%88%d0%b5%d0%bd%d0%bd%d1%8b%d0%b5-%d0%b7%d0%b0%d0%b4%d0%b0%d1%87%d0%b8-%d0%ba%d0%be%d0%bd%d0%b5%d1%87%d0%bd%d1%8b%d0%b5-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b\/","name":"\u0420\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438: \u041a\u043e\u043d\u0435\u0447\u043d\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b - toposuranos.com\/material","isPartOf":{"@id":"http:\/\/toposuranos.com\/material\/#website"},"primaryImageOfPage":{"@id":"http:\/\/toposuranos.com\/material\/ru\/%d1%80%d0%b5%d1%88%d0%b5%d0%bd%d0%bd%d1%8b%d0%b5-%d0%b7%d0%b0%d0%b4%d0%b0%d1%87%d0%b8-%d0%ba%d0%be%d0%bd%d0%b5%d1%87%d0%bd%d1%8b%d0%b5-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b\/#primaryimage"},"image":{"@id":"http:\/\/toposuranos.com\/material\/ru\/%d1%80%d0%b5%d1%88%d0%b5%d0%bd%d0%bd%d1%8b%d0%b5-%d0%b7%d0%b0%d0%b4%d0%b0%d1%87%d0%b8-%d0%ba%d0%be%d0%bd%d0%b5%d1%87%d0%bd%d1%8b%d0%b5-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b\/#primaryimage"},"thumbnailUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/ejerciciolimites.jpg","datePublished":"2024-08-15T19:51:14+00:00","description":"\u041e\u0441\u0432\u043e\u0439\u0442\u0435 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 \u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0445 \u043f\u0440\u0435\u0434\u0435\u043b\u043e\u0432 \u0441 \u044d\u0442\u0438\u043c \u043a\u0443\u0440\u0441\u043e\u043c, \u0432\u043a\u043b\u044e\u0447\u0430\u044e\u0449\u0438\u043c \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438. \u0423\u0437\u043d\u0430\u0439\u0442\u0435 \u043a\u043b\u044e\u0447\u0435\u0432\u044b\u0435 \u043c\u0435\u0442\u043e\u0434\u044b, \u0442\u0430\u043a\u0438\u0435 \u043a\u0430\u043a \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u044f","breadcrumb":{"@id":"http:\/\/toposuranos.com\/material\/ru\/%d1%80%d0%b5%d1%88%d0%b5%d0%bd%d0%bd%d1%8b%d0%b5-%d0%b7%d0%b0%d0%b4%d0%b0%d1%87%d0%b8-%d0%ba%d0%be%d0%bd%d0%b5%d1%87%d0%bd%d1%8b%d0%b5-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b\/#breadcrumb"},"inLanguage":"es","potentialAction":[{"@type":"ReadAction","target":["http:\/\/toposuranos.com\/material\/ru\/%d1%80%d0%b5%d1%88%d0%b5%d0%bd%d0%bd%d1%8b%d0%b5-%d0%b7%d0%b0%d0%b4%d0%b0%d1%87%d0%b8-%d0%ba%d0%be%d0%bd%d0%b5%d1%87%d0%bd%d1%8b%d0%b5-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b\/"]}]},{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/ru\/%d1%80%d0%b5%d1%88%d0%b5%d0%bd%d0%bd%d1%8b%d0%b5-%d0%b7%d0%b0%d0%b4%d0%b0%d1%87%d0%b8-%d0%ba%d0%be%d0%bd%d0%b5%d1%87%d0%bd%d1%8b%d0%b5-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b\/#primaryimage","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/ejerciciolimites.jpg","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/08\/ejerciciolimites.jpg","width":1792,"height":431},{"@type":"BreadcrumbList","@id":"http:\/\/toposuranos.com\/material\/ru\/%d1%80%d0%b5%d1%88%d0%b5%d0%bd%d0%bd%d1%8b%d0%b5-%d0%b7%d0%b0%d0%b4%d0%b0%d1%87%d0%b8-%d0%ba%d0%be%d0%bd%d0%b5%d1%87%d0%bd%d1%8b%d0%b5-%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%8b\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Portada","item":"http:\/\/toposuranos.com\/material\/es\/cursos-de-matematica-y-fisica\/"},{"@type":"ListItem","position":2,"name":"\u0420\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438: \u041a\u043e\u043d\u0435\u0447\u043d\u044b\u0435 \u043f\u0440\u0435\u0434\u0435\u043b\u044b"}]},{"@type":"WebSite","@id":"http:\/\/toposuranos.com\/material\/#website","url":"http:\/\/toposuranos.com\/material\/","name":"toposuranos.com\/material","description":"","publisher":{"@id":"http:\/\/toposuranos.com\/material\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"http:\/\/toposuranos.com\/material\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"es"},{"@type":"Organization","@id":"http:\/\/toposuranos.com\/material\/#organization","name":"toposuranos.com\/material","url":"http:\/\/toposuranos.com\/material\/","logo":{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png","width":2400,"height":2059,"caption":"toposuranos.com\/material"},"image":{"@id":"http:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/groups\/toposuranos","https:\/\/x.com\/topuranos","https:\/\/www.youtube.com\/channel\/UC16yDm12cPcrwsE0fAM7X1g","https:\/\/www.linkedin.com\/company\/69429190"]},{"@type":"Person","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1","name":"giorgio.reveco","image":{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","caption":"giorgio.reveco"},"description":"Soy Licenciado en F\u00edsica, Magister en Ingenier\u00eda Industrial y Docente Universitario. Me dedico a desmitificar la f\u00edsica y las matem\u00e1ticas. Mi objetivo es hacer que estos campos sean f\u00e1cilmente comprensibles para todos, proporcionando las herramientas para explorar no solo el mundo que nos rodea, sino tambi\u00e9n las profundidades de nuestra propia existencia y el orden natural que nos conecta con el cosmos.","sameAs":["http:\/\/toposuranos.com\/material"],"url":"http:\/\/toposuranos.com\/material\/author\/giorgio-reveco\/"}]}},"_links":{"self":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/27906","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/comments?post=27906"}],"version-history":[{"count":0,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/27906\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media\/27893"}],"wp:attachment":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media?parent=27906"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/categories?post=27906"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/tags?post=27906"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}