{"id":2306,"date":"2026-04-25T02:41:00","date_gmt":"2026-04-25T02:41:00","guid":{"rendered":"https:\/\/77.buffdemo.com\/index.php\/2026\/04\/25\/toan-thuc-te-chuyen-de-tiem-can-cua-do-thi-ham-so\/"},"modified":"2026-04-25T02:41:00","modified_gmt":"2026-04-25T02:41:00","slug":"toan-thuc-te-chuyen-de-tiem-can-cua-do-thi-ham-so","status":"publish","type":"post","link":"https:\/\/77.buffdemo.com\/index.php\/2026\/04\/25\/toan-thuc-te-chuyen-de-tiem-can-cua-do-thi-ham-so\/","title":{"rendered":"To\u00e1n th\u1ef1c t\u1ebf chuy\u00ean \u0111\u1ec1 ti\u1ec7m c\u1eadn c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1"},"content":{"rendered":"<div class=\"entry-content single-page\">\n<p>Chia s\u1ebb chuy\u00ean \u0111\u1ec1 ti\u1ec7m c\u1eadn c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 nh\u1ea5t qua c\u00e1c b\u00e0i to\u00e1n th\u1ef1c t\u1ebf nh\u01b0 t\u1ed1i \u01b0u h\u00f3a l\u1ee3i nhu\u1eadn, chi ph\u00ed; t\u1ed1i \u01b0u h\u00f3a di\u1ec7n t\u00edch th\u1ec3 t\u00edch, \u1ee9ng d\u1ee5ng trong v\u1eadt l\u00fd, sinh h\u1ecdc, h\u00f3a h\u1ecdc.<\/p>\n<div class=\"code-block code-block-2\" style=\"margin: 8px auto; text-align: center; display: block; clear: both;\">\n<div> <\/div>\n<\/div>\n<h2 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-f0969a2c5189e698ed12d83c9903c08a\" id=\"h-n\u1ed9i-dung-tai-li\u1ec7u-toan-th\u1ef1c-t\u1ebf-chuyen-d\u1ec1-ti\u1ec7m-c\u1eadn-c\u1ee7a-d\u1ed3-th\u1ecb-ham-s\u1ed1\"><span class=\"ez-toc-section\" id=\"Noi_dung_tai_lieu_Toan_thuc_te_chuyen_de_tiem_can_cua_do_thi_ham_so\"><\/span>N\u1ed9i dung t\u00e0i li\u1ec7u To\u00e1n th\u1ef1c t\u1ebf chuy\u00ean \u0111\u1ec1 ti\u1ec7m c\u1eadn c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>C\u00e1c n\u1ed9i dung ch\u00ednh bao g\u1ed3m:<\/p>\n<h3 class=\"wp-block-heading\" id=\"h-a-ki\u1ebfn-th\u1ee9c-c\u01a1-b\u1ea3n-c\u1ea7n-n\u1eafm-v\u1ec1-ti\u1ec7m-c\u1eadn\"><span class=\"ez-toc-section\" id=\"A_Kien_thuc_co_ban_can_nam_ve_tiem_can\"><\/span><strong>A. Ki\u1ebfn th\u1ee9c c\u01a1 b\u1ea3n c\u1ea7n n\u1eafm v\u1ec1 ti\u1ec7m c\u1eadn<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ol class=\"wp-block-list\">\n<li><strong>\u0110\u01b0\u1eddng ti\u1ec7m c\u1eadn \u0111\u1ee9ng:<\/strong>\u00a0\u0110\u01b0\u1eddng th\u1eb3ng $x=a$ l\u00e0 ti\u1ec7m c\u1eadn \u0111\u1ee9ng n\u1ebfu $\\lim_{x\\rightarrow a^{-}}f(x)=\\pm\\infty$ ho\u1eb7c $\\lim_{x\\rightarrow a^{+}}f(x)=\\pm\\infty$.<\/li>\n<li><strong>\u0110\u01b0\u1eddng ti\u1ec7m c\u1eadn ngang:<\/strong>\u00a0\u0110\u01b0\u1eddng th\u1eb3ng $y=m$ l\u00e0 ti\u1ec7m c\u1eadn ngang n\u1ebfu $\\lim_{x\\rightarrow-\\infty}f(x)=m$ ho\u1eb7c $\\lim_{x\\rightarrow+\\infty}f(x)=m$.<\/li>\n<li><strong>\u0110\u01b0\u1eddng ti\u1ec7m c\u1eadn xi\u00ean:<\/strong>\u00a0\u0110\u01b0\u1eddng th\u1eb3ng $y=ax+b$, $a\\ne0$, l\u00e0 ti\u1ec7m c\u1eadn xi\u00ean n\u1ebfu $\\lim_{x\\rightarrow-\\infty}[f(x)-(ax+b)]=0$ ho\u1eb7c $\\lim_{x\\rightarrow+\\infty}[f(x)-(ax+b)]=0$.\n<ul class=\"wp-block-list\">\n<li>C\u00f4ng th\u1ee9c t\u00ecm $a$ v\u00e0 $b$:\n<ul class=\"wp-block-list\">\n<li>$a=\\lim_{x\\rightarrow\\pm\\infty}\\frac{f(x)}{x}$<\/li>\n<li>$b=\\lim_{x\\rightarrow\\pm\\infty}[f(x)-ax]$<\/li>\n<\/ul>\n<\/li>\n<li>Nh\u1eadn x\u00e9t: Khi $a=0$, ti\u1ec7m c\u1eadn xi\u00ean tr\u1edf th\u00e0nh ti\u1ec7m c\u1eadn ngang $y=b$.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<h3 class=\"wp-block-heading\" id=\"h-b-bai-t\u1eadp-v\u1eadn-d\u1ee5ng-cac-bai-toan-th\u1ef1c-t\u1ebf\"><span class=\"ez-toc-section\" id=\"B_Bai_tap_van_dung_Cac_bai_toan_thuc_te\"><\/span><strong>B. B\u00e0i t\u1eadp v\u1eadn d\u1ee5ng (C\u00e1c b\u00e0i to\u00e1n th\u1ef1c t\u1ebf):<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>T\u00e0i li\u1ec7u \u0111\u01b0a ra 11 c\u00e2u h\u1ecfi b\u00e0i t\u1eadp th\u1ef1c t\u1ebf \u1ee9ng d\u1ee5ng kh\u00e1i ni\u1ec7m ti\u1ec7m c\u1eadn v\u00e0o c\u00e1c l\u0129nh v\u1ef1c nh\u01b0:<\/p>\n<ul class=\"wp-block-list\">\n<li><strong>Kinh doanh\/S\u1ea3n xu\u1ea5t:<\/strong>\n<ul class=\"wp-block-list\">\n<li>S\u1ed1 l\u01b0\u1ee3ng s\u1ea3n ph\u1ea9m b\u00e1n \u0111\u01b0\u1ee3c theo th\u1eddi gian (C\u00e2u 1, C\u00e2u 9).<\/li>\n<li>Chi ph\u00ed s\u1ea3n xu\u1ea5t trung b\u00ecnh (C\u00e2u 2, C\u00e2u 8, C\u00e2u 11).<\/li>\n<li>T\u1ed1c \u0111\u1ed9 \u0111\u00e1nh m\u00e1y trung b\u00ecnh theo th\u1eddi gian h\u1ecdc (C\u00e2u 10).<\/li>\n<\/ul>\n<\/li>\n<li><strong>M\u00f4i tr\u01b0\u1eddng\/Y t\u1ebf:<\/strong>\n<ul class=\"wp-block-list\">\n<li>N\u1ed3ng \u0111\u1ed9 oxygen trong h\u1ed3 theo th\u1eddi gian (C\u00e2u 5).<\/li>\n<li>N\u1ed3ng \u0111\u1ed9 dung d\u1ecbch mu\u1ed1i sau khi pha th\u00eam (C\u00e2u 6).<\/li>\n<li>Chi ph\u00ed l\u00e0m s\u1ea1ch d\u1ea7u loang tr\u00ean bi\u1ec3n theo ph\u1ea7n tr\u0103m l\u01b0\u1ee3ng d\u1ea7u (C\u00e2u 7).<\/li>\n<\/ul>\n<\/li>\n<li><strong>H\u00ecnh h\u1ecdc\/Thi\u1ebft k\u1ebf:<\/strong>\n<ul class=\"wp-block-list\">\n<li>\u0110\u01b0\u1eddng vi\u1ec1n b\u00f3ng \u0111\u00e8n ng\u1ee7 (t\u00ecm ti\u1ec7m c\u1eadn xi\u00ean) (C\u00e2u 3).<\/li>\n<li>Chu vi m\u1ea3nh v\u01b0\u1eddn h\u00ecnh ch\u1eef nh\u1eadt theo \u0111\u1ed9 d\u00e0i m\u1ed9t c\u1ea1nh (t\u00ecm ti\u1ec7m c\u1eadn) (C\u00e2u 4).<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>M\u1ee5c \u0111\u00edch ch\u00ednh c\u1ee7a ph\u1ea7n b\u00e0i t\u1eadp l\u00e0 y\u00eau c\u1ea7u h\u1ecdc sinh:<\/p>\n<ul class=\"wp-block-list\">\n<li>X\u00e1c \u0111\u1ecbnh c\u00f4ng th\u1ee9c h\u00e0m s\u1ed1 t\u1eeb m\u00f4 t\u1ea3 th\u1ef1c t\u1ebf.<\/li>\n<li>T\u00ecm ti\u1ec7m c\u1eadn ngang, ti\u1ec7m c\u1eadn \u0111\u1ee9ng, ti\u1ec7m c\u1eadn xi\u00ean c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 \u0111\u00f3.<\/li>\n<li>N\u00eau nh\u1eadn x\u00e9t v\u00e0 \u00fd ngh\u0129a th\u1ef1c t\u1ebf c\u1ee7a c\u00e1c ti\u1ec7m c\u1eadn t\u00ecm \u0111\u01b0\u1ee3c (v\u00ed d\u1ee5: s\u1ed1 l\u01b0\u1ee3ng s\u1ea3n ph\u1ea9m t\u1ed1i \u0111a c\u00f3 th\u1ec3 b\u00e1n \u0111\u01b0\u1ee3c, chi ph\u00ed trung b\u00ecnh t\u1ed1i thi\u1ec3u, n\u1ed3ng \u0111\u1ed9 \u1ed5n \u0111\u1ecbnh khi th\u1eddi gian r\u1ea5t l\u1edbn).<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><strong>Xem tr\u01b0\u1edbc t\u00e0i li\u1ec7u:<\/strong><\/p>\n<p class=\"has-text-align-center\"><iframe loading=\"lazy\" allow=\"autoplay\" height=\"480\" src=\"https:\/\/drive.google.com\/file\/d\/1wsUwTginJbLv0cQX7qT4azKkIMXVGHPw\/preview\" width=\"640\"><\/iframe><\/p>\n<h2 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-f9bdef11194652b7a001b22fd4a9fbf8\" id=\"h-t\u1ea3i-tai-li\u1ec7u-toan-th\u1ef1c-t\u1ebf-chuyen-d\u1ec1-ti\u1ec7m-c\u1eadn-c\u1ee7a-d\u1ed3-th\u1ecb-ham-s\u1ed1\"><span class=\"ez-toc-section\" id=\"Tai_tai_lieu_Toan_thuc_te_chuyen_de_tiem_can_cua_do_thi_ham_so\"><\/span>T\u1ea3i t\u00e0i li\u1ec7u To\u00e1n th\u1ef1c t\u1ebf chuy\u00ean \u0111\u1ec1 ti\u1ec7m c\u1eadn c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>C\u00e1c b\u1ea1n c\u00f3 th\u1ec3 t\u1ea3i t\u00e0i li\u1ec7u \u00f4n t\u1eadp mi\u1ec5n ph\u00ed \u1edf \u0111\u00e2y nh\u00e9<\/p>\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-container-core-buttons-is-layout-16018d1d wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-white-color has-luminous-vivid-orange-background-color has-text-color has-background has-link-color has-text-align-center wp-element-button\" href=\"https:\/\/drive.google.com\/drive\/folders\/18dW_8QratLyu1BTedfP9rZzfjtIhSq5M?usp=sharing\" rel=\"noreferrer noopener nofollow\" target=\"_blank\"><strong>T\u1ea2I T\u00c0I LI\u1ec6U (\u0110\u1ec0 + \u0110\u00c1P \u00c1N)<\/strong><\/a><\/div>\n<\/div>\n<p>\u2026<\/p>\n<p>Tham kh\u1ea3o:<strong> <a href=\"https:\/\/tailieuonthi.org\/toan-thuc-te-chuyen-de-gia-tri-lon-nhat-nho-nhat-ham-so\/\" rel=\"noreferrer noopener\" target=\"_blank\">To\u00e1n th\u1ef1c t\u1ebf chuy\u00ean \u0111\u1ec1 gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t, gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t h\u00e0m s\u1ed1<\/a><\/strong><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Chia s\u1ebb chuy\u00ean \u0111\u1ec1 ti\u1ec7m c\u1eadn c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 nh\u1ea5t qua c\u00e1c b\u00e0i to\u00e1n th\u1ef1c t\u1ebf nh\u01b0 t\u1ed1i \u01b0u h\u00f3a l\u1ee3i nhu\u1eadn, chi ph\u00ed; t\u1ed1i \u01b0u h\u00f3a di\u1ec7n t\u00edch th\u1ec3 t\u00edch, \u1ee9ng d\u1ee5ng trong v\u1eadt l\u00fd, sinh h\u1ecdc, h\u00f3a h\u1ecdc. N\u1ed9i dung t\u00e0i li\u1ec7u To\u00e1n th\u1ef1c t\u1ebf chuy\u00ean \u0111\u1ec1 ti\u1ec7m c\u1eadn c\u1ee7a \u0111\u1ed3 [&#8230;]\n","protected":false},"author":1,"featured_media":2305,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[23,26],"tags":[],"class_list":["post-2306","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-tai-lieu-toan","category-toan-12"],"_links":{"self":[{"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/2306","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/comments?post=2306"}],"version-history":[{"count":0,"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/2306\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/2305"}],"wp:attachment":[{"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=2306"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=2306"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=2306"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}