{"id":21550,"date":"2025-07-08T14:45:57","date_gmt":"2025-07-08T07:45:57","guid":{"rendered":"https:\/\/www.ckconitsha.com\/vn\/?p=21550"},"modified":"2025-07-10T21:35:58","modified_gmt":"2025-07-10T14:35:58","slug":"tong-hop-cac-dang-bai-tap-ham-so-lien-tuc-tu-co-ban-den-nang-cao","status":"publish","type":"post","link":"https:\/\/www.ckconitsha.com\/vn\/tong-hop-cac-dang-bai-tap-ham-so-lien-tuc-tu-co-ban-den-nang-cao\/","title":{"rendered":"T\u1ed5ng h\u1ee3p c\u00e1c d\u1ea1ng b\u00e0i t\u1eadp h\u00e0m s\u1ed1 li\u00ean t\u1ee5c t\u1eeb c\u01a1 b\u1ea3n \u0111\u1ebfn n\u00e2ng cao"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_79_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.ckconitsha.com\/vn\/tong-hop-cac-dang-bai-tap-ham-so-lien-tuc-tu-co-ban-den-nang-cao\/#Xem_lai_ly_thuyet_nen_tang_cua_chuc_nang\" >Xem l\u1ea1i l\u00fd thuy\u1ebft n\u1ec1n t\u1ea3ng c\u1ee7a ch\u1ee9c n\u0103ng<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.ckconitsha.com\/vn\/tong-hop-cac-dang-bai-tap-ham-so-lien-tuc-tu-co-ban-den-nang-cao\/#Chuc_nang_la_gi\" >Ch\u1ee9c n\u0103ng l\u00e0 g\u00ec?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.ckconitsha.com\/vn\/tong-hop-cac-dang-bai-tap-ham-so-lien-tuc-tu-co-ban-den-nang-cao\/#Cac_thuoc_tinh_chuc_nang_co_ban_can_nho\" >C\u00e1c thu\u1ed9c t\u00ednh ch\u1ee9c n\u0103ng c\u01a1 b\u1ea3n c\u1ea7n nh\u1edb<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.ckconitsha.com\/vn\/tong-hop-cac-dang-bai-tap-ham-so-lien-tuc-tu-co-ban-den-nang-cao\/#Ham_lien_tuc_la_gi_Lien_tuc_o_1_diem1_doan1_khoang\" >H\u00e0m li\u00ean t\u1ee5c l\u00e0 g\u00ec? (Li\u00ean t\u1ee5c \u1edf 1 \u0111i\u1ec3m\/1 \u0111o\u1ea1n\/1 kho\u1ea3ng)<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.ckconitsha.com\/vn\/tong-hop-cac-dang-bai-tap-ham-so-lien-tuc-tu-co-ban-den-nang-cao\/#Chuc_nang_lien_tuc_tai_mot_diem\" >Ch\u1ee9c n\u0103ng li\u00ean t\u1ee5c t\u1ea1i m\u1ed9t \u0111i\u1ec3m<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.ckconitsha.com\/vn\/tong-hop-cac-dang-bai-tap-ham-so-lien-tuc-tu-co-ban-den-nang-cao\/#Chuc_nang_lien_tuc_o_khoang_cach_xa\" >Ch\u1ee9c n\u0103ng li\u00ean t\u1ee5c \u1edf kho\u1ea3ng c\u00e1ch xa<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.ckconitsha.com\/vn\/tong-hop-cac-dang-bai-tap-ham-so-lien-tuc-tu-co-ban-den-nang-cao\/#Cac_chuc_nang_lien_tuc_tai_mot_doan_van\" >C\u00e1c ch\u1ee9c n\u0103ng li\u00ean t\u1ee5c t\u1ea1i m\u1ed9t \u0111o\u1ea1n v\u0103n<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.ckconitsha.com\/vn\/tong-hop-cac-dang-bai-tap-ham-so-lien-tuc-tu-co-ban-den-nang-cao\/#Cac_dinh_ly_co_ban_cua_ham_lien_tuc\" >C\u00e1c \u0111\u1ecbnh l\u00fd c\u01a1 b\u1ea3n c\u1ee7a h\u00e0m li\u00ean t\u1ee5c<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/www.ckconitsha.com\/vn\/tong-hop-cac-dang-bai-tap-ham-so-lien-tuc-tu-co-ban-den-nang-cao\/#Toan_hoc_cac_chuc_nang_lien_tuc_la_pho_bien\" >To\u00e1n h\u1ecdc c\u00e1c ch\u1ee9c n\u0103ng li\u00ean t\u1ee5c l\u00e0 ph\u1ed5 bi\u1ebfn<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/www.ckconitsha.com\/vn\/tong-hop-cac-dang-bai-tap-ham-so-lien-tuc-tu-co-ban-den-nang-cao\/#Mau_1_Xem_xet_tinh_lien_tuc_cua_ham_tai_mot_diem_cu_the\" >M\u1eabu 1: Xem x\u00e9t t\u00ednh li\u00ean t\u1ee5c c\u1ee7a h\u00e0m t\u1ea1i m\u1ed9t \u0111i\u1ec3m c\u1ee5 th\u1ec3.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/www.ckconitsha.com\/vn\/tong-hop-cac-dang-bai-tap-ham-so-lien-tuc-tu-co-ban-den-nang-cao\/#Mau_2_Xem_xet_tinh_toan_lien_tuc_chung_minh_chuc_nang_lien_tuc_tren_mot_doan_van_hoac_tap_hop\" >M\u1eabu 2: Xem x\u00e9t t\u00ednh to\u00e1n li\u00ean t\u1ee5c, ch\u1ee9ng minh ch\u1ee9c n\u0103ng li\u00ean t\u1ee5c tr\u00ean m\u1ed9t \u0111o\u1ea1n v\u0103n ho\u1eb7c t\u1eadp h\u1ee3p<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/www.ckconitsha.com\/vn\/tong-hop-cac-dang-bai-tap-ham-so-lien-tuc-tu-co-ban-den-nang-cao\/#Mau_3_Tim_dieu_kien_cho_ham_lien_tuc_tai_mot_diem\" >M\u1eabu 3: T\u00ecm \u0111i\u1ec1u ki\u1ec7n cho h\u00e0m li\u00ean t\u1ee5c t\u1ea1i m\u1ed9t \u0111i\u1ec3m<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/www.ckconitsha.com\/vn\/tong-hop-cac-dang-bai-tap-ham-so-lien-tuc-tu-co-ban-den-nang-cao\/#Mau_4_Tim_dieu_kien_cho_ham_lien_tuc_tren_khoang_cach_hoac_dat\" >M\u1eabu 4: T\u00ecm \u0111i\u1ec1u ki\u1ec7n cho h\u00e0m li\u00ean t\u1ee5c tr\u00ean kho\u1ea3ng c\u00e1ch ho\u1eb7c \u0111\u1eb7t<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/www.ckconitsha.com\/vn\/tong-hop-cac-dang-bai-tap-ham-so-lien-tuc-tu-co-ban-den-nang-cao\/#Mau_5_Ap_dung_ham_lien_tuc_chung_minh_phuong_trinh_voi_cac_giai_phap\" >M\u1eabu 5: \u00c1p d\u1ee5ng h\u00e0m li\u00ean t\u1ee5c ch\u1ee9ng minh ph\u01b0\u01a1ng tr\u00ecnh v\u1edbi c\u00e1c gi\u1ea3i ph\u00e1p<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/www.ckconitsha.com\/vn\/tong-hop-cac-dang-bai-tap-ham-so-lien-tuc-tu-co-ban-den-nang-cao\/#Tap_the_duc_ve_cac_thuoc_tinh_chuc_nang_lien_tuc_cho_hoc_sinh_thuc_hanh\" >T\u1eadp th\u1ec3 d\u1ee5c v\u1ec1 c\u00e1c thu\u1ed9c t\u00ednh ch\u1ee9c n\u0103ng li\u00ean t\u1ee5c cho h\u1ecdc sinh th\u1ef1c h\u00e0nh<\/a><\/li><\/ul><\/nav><\/div>\n<\/p>\n<p>C\u00e1c ch\u1ee9c n\u0103ng li\u00ean t\u1ee5c l\u00e0 m\u1ed9t ph\u1ea7n quan tr\u1ecdng c\u1ee7a ki\u1ebfn \u200b\u200bth\u1ee9c to\u00e1n h\u1ecdc. \u0110\u1ec3 th\u1ef1c hi\u1ec7n c\u00e1c b\u00e0i t\u1eadp v\u1ec1 lo\u1ea1i n\u00e0y, b\u1ea1n c\u1ea7n n\u1eafm b\u1eaft l\u00fd thuy\u1ebft v\u00e0 c\u00e1c thu\u1ed9c t\u00ednh c\u01a1 b\u1ea3n. D\u01b0\u1edbi \u0111\u00e2y Shining Home &#8211; Gia \u0111\u00ecnh Anh Ng\u1eef mu\u1ed1n t\u00f3m t\u1eaft t\u1ea5t c\u1ea3 c\u00e1c ki\u1ebfn \u200b\u200bth\u1ee9c v\u00e0 lo\u1ea1i b\u00e0i t\u1eadp \u0111\u1ec3 gi\u00fap b\u1ea1n h\u1ecdc t\u1ed1t h\u01a1n. H\u00e3y theo d\u00f5i b\u00e0i vi\u1ebft n\u00e0y!<\/p>\n<p>                                    <img decoding=\"async\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/image\/600x480.png\"><\/p>\n<h2 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Xem_lai_ly_thuyet_nen_tang_cua_chuc_nang\"><\/span>Xem l\u1ea1i l\u00fd thuy\u1ebft n\u1ec1n t\u1ea3ng c\u1ee7a ch\u1ee9c n\u0103ng<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p dir=\"ltr\">\u0110\u1ea7u ti\u00ean, \u0111\u1ec3 l\u00e0m quen v\u1edbi ki\u1ebfn \u200b\u200bth\u1ee9c ch\u1ee9c n\u0103ng li\u00ean t\u1ee5c. H\u00e3y xem x\u00e9t ki\u1ebfn \u200b\u200bth\u1ee9c v\u1ec1 ch\u1ee9c n\u0103ng c\u00f9ng nhau. V\u1eady ch\u1ee9c n\u0103ng l\u00e0 g\u00ec? C\u00e1c thu\u1ed9c t\u00ednh c\u1ee7a ch\u1ee9c n\u0103ng c\u01a1 b\u1ea3n c\u1ea7n nh\u1edb?<\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Chuc_nang_la_gi\"><\/span>Ch\u1ee9c n\u0103ng l\u00e0 g\u00ec?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">Ch\u1ec9 c\u1ea7n hi\u1ec3u ch\u1ee9c n\u0103ng ch\u00ednh l\u00e0 m\u1ed9t quy t\u1eafc \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng tr\u00ean c\u00e1c s\u1ed1. N\u1ebfu ch\u00fang ta c\u00f3 m\u1ed9t l\u01b0\u1ee3ng y nh\u1ea5t \u0111\u1ecbnh t\u00f9y thu\u1ed9c v\u00e0o s\u1ed1 l\u01b0\u1ee3ng gi\u00e1 tr\u1ecb c\u1ee7a thay \u0111\u1ed5i gi\u00e1 tr\u1ecb. Sau \u0111\u00f3, ch\u00fang t\u00f4i lu\u00f4n x\u00e1c \u0111\u1ecbnh m\u1ed9t s\u1ed1 ti\u1ec1n t\u01b0\u01a1ng \u1ee9ng c\u1ee7a y t\u1ebf. Sau \u0111\u00f3 s\u1ed1 l\u01b0\u1ee3ng y \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 h\u00e0m c\u1ee7a X.<\/p>\n<p dir=\"ltr\">Ho\u1eb7c hi\u1ec3u th\u00eam chi ti\u1ebft, ch\u00fang ta c\u00f3 th\u1ec3 x\u00e1c \u0111\u1ecbnh kh\u00e1i ni\u1ec7m v\u1ec1 ch\u1ee9c n\u0103ng sau:<\/p>\n<ul>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">\u0110\u1ed1i v\u1edbi t\u1eadp d, n\u00f3 \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 m\u1ed9t t\u1eadp h\u1ee3p c\u00e1c t\u1eadp tr\u1ed1ng kh\u00e1c nhau R. Khi h\u00e0m F \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh tr\u00ean t\u1eadp h\u1ee3p D l\u00e0 m\u1ed9t quy t\u1eafc cho m\u1ed7i x n\u1eb1m trong D. th\u00ec v\u1edbi m\u1ed9t s\u1ed1 th\u1ef1c y g\u1ecdi l\u00e0 gi\u00e1 tr\u1ecb c\u1ee7a h\u00e0m f t\u1ea1i \u0111i\u1ec3m x, ch\u00fang t\u00f4i k\u00fd nh\u01b0 sau y = f (x).<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">T\u1eadp D \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 m\u1ed9t t\u1eadp h\u1ee3p quy\u1ebft \u0111\u1ecbnh ho\u1eb7c m\u1ed9t mi\u1ec1n \u0111\u01b0\u1ee3c ch\u1ec9 \u0111\u1ecbnh. V\u00e0 x l\u00e0 \u0111\u1ed1i s\u1ed1 ho\u1eb7c bi\u1ebfn c\u1ee7a h\u00e0m f, ch\u00fang t\u00f4i vi\u1ebft nh\u01b0 sau: f: dx\u27f6 r \u27fc y = f (x); T = {y = f (x) | x\u2208D} \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 mi\u1ec1n gi\u00e1 tr\u1ecb ho\u1eb7c t\u1eadp gi\u00e1 tr\u1ecb c\u1ee7a h\u00e0m \u0111\u00f3.<\/p>\n<\/li>\n<\/ul>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Cac_thuoc_tinh_chuc_nang_co_ban_can_nho\"><\/span>C\u00e1c thu\u1ed9c t\u00ednh ch\u1ee9c n\u0103ng c\u01a1 b\u1ea3n c\u1ea7n nh\u1edb<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">\u0110\u1ec3 n\u00eau c\u00e1c thu\u1ed9c t\u00ednh c\u1ee7a h\u00e0m, c\u00f3 hai thu\u1ed9c t\u00ednh c\u01a1 b\u1ea3n m\u00e0 b\u1ea1n c\u1ea7n nh\u1edb khi h\u1ecdc c\u00e1ch \u00e1p d\u1ee5ng \u0111\u1ec3 l\u00e0m b\u00e0i t\u1eadp v\u1ec1 nh\u00e0. H\u00e0m y = ax + b (a \u2260 0) \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh cho t\u1ea5t c\u1ea3 x c\u1ee7a R.<\/p>\n<ul>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">N\u1ebfu h\u1ec7 s\u1ed1 A l\u1edbn h\u01a1n 0, h\u00e0m \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 bi\u1ebfn.<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">N\u1ebfu h\u1ec7 s\u1ed1 A nh\u1ecf h\u01a1n 0, h\u00e0m \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 ngh\u1ecbch \u0111\u1ea3o.<\/p>\n<\/li>\n<\/ul>\n<p dir=\"ltr\">C\u1ea7n l\u01b0u \u00fd r\u1eb1ng ch\u1ee9c n\u0103ng c\u1ee7a h\u00e0m li\u00ean t\u1ee5c t\u01b0\u01a1ng t\u1ef1 nh\u01b0 c\u00e1c thu\u1ed9c t\u00ednh c\u1ee7a h\u00e0m v\u00e0 c\u00f3 c\u00e1c y\u1ebfu t\u1ed1 &#8220;li\u00ean t\u1ee5c&#8221; h\u01a1n.<\/p>\n<p dir=\"ltr\">Duy tr\u00ec hai thu\u1ed9c t\u00ednh n\u00e0y \u0111\u1ec3 \u00e1p d\u1ee5ng khi gi\u1ea3i c\u00e1c b\u00e0i t\u1eadp. H\u1ecdc to\u00e1n s\u1ebd tr\u1edf n\u00ean d\u1ec5 d\u00e0ng h\u01a1n nhi\u1ec1u n\u1ebfu ch\u00fang ta n\u1eafm b\u1eaft ch\u1eafc l\u00fd thuy\u1ebft.<\/p>\n<h2 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Ham_lien_tuc_la_gi_Lien_tuc_o_1_diem1_doan1_khoang\"><\/span>H\u00e0m li\u00ean t\u1ee5c l\u00e0 g\u00ec? (Li\u00ean t\u1ee5c \u1edf 1 \u0111i\u1ec3m\/1 \u0111o\u1ea1n\/1 kho\u1ea3ng)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p dir=\"ltr\">M\u1ed9t khi b\u1ea1n hi\u1ec3u ch\u1ee9c n\u0103ng, h\u00e3y t\u00ecm hi\u1ec3u th\u00eam v\u1ec1 ki\u1ebfn \u200b\u200bth\u1ee9c s\u00e2u s\u1eafc h\u01a1n l\u00e0 ch\u1ee9c n\u0103ng li\u00ean t\u1ee5c. V\u1eady khi n\u00e0o ch\u1ee9c n\u0103ng li\u00ean t\u1ee5c? V\u00e0 n\u00f3 li\u00ean t\u1ee5c \u0111i\u1ec3m n\u00e0o?<\/p>\n<p dir=\"ltr\">Trong to\u00e1n h\u1ecdc, khi m\u1ed9t h\u00e0m \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 li\u00ean t\u1ee5c, n\u00f3 kh\u00f4ng c\u00f3 s\u1ef1 thay \u0111\u1ed5i \u0111\u1ed9t ng\u1ed9t v\u1ec1 gi\u00e1 tr\u1ecb. Ch\u00fang \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 c\u00e1c \u0111i\u1ec3m gi\u00e1n \u0111o\u1ea1n c\u1ee7a ch\u1ee9c n\u0103ng. C\u1ee5 th\u1ec3, khi \u0111\u1ea7u v\u00e0o c\u1ee7a h\u00e0m nh\u1ecf, h\u00e0m s\u1ebd c\u00f3 ch\u00eanh l\u1ec7ch \u0111\u1ea7u ra nh\u1ecf. Khi m\u1ed9t ch\u1ee9c n\u0103ng kh\u00f4ng li\u00ean t\u1ee5c \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 gi\u00e1n \u0111o\u1ea1n.<\/p>\n<p dir=\"ltr\"><img decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/1-ham-so-lien-tuc.png\" alt=\"\u0110\u1ed3 th\u1ecb ch\u1ee9c n\u0103ng li\u00ean t\u1ee5c. (\u1ea2nh: B\u1ed9 s\u01b0u t\u1eadp Internet)\" width=\"100%\"><\/p>\n<p dir=\"ltr\">Khi b\u1ea1n h\u1ecdc tr\u00ean m\u1ed9t ch\u01b0\u01a1ng tr\u00ecnh cao h\u01a1n, b\u1ea1n s\u1ebd t\u00ecm hi\u1ec3u v\u1ec1 c\u00e1c ch\u1ee9c n\u0103ng to\u00e1n h\u1ecdc cao, c\u00e1c ch\u1ee9c n\u0103ng li\u00ean t\u1ee5c c\u1ee7a CASIO. T\u1ea1i th\u1eddi \u0111i\u1ec3m n\u00e0y, kh\u00e1i ni\u1ec7m v\u1ec1 ch\u1ee9c n\u0103ng li\u00ean t\u1ee5c \u0111\u01b0\u1ee3c hi\u1ec3u theo m\u1ed9t c\u00e1ch tr\u1eebu t\u01b0\u1ee3ng.<\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Chuc_nang_lien_tuc_tai_mot_diem\"><\/span>Ch\u1ee9c n\u0103ng li\u00ean t\u1ee5c t\u1ea1i m\u1ed9t \u0111i\u1ec3m<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">Khi n\u00e0o ch\u1ee9c n\u0103ng li\u00ean t\u1ee5c \u1edf 1 \u0111i\u1ec3m? \u0110\u1eb7t h\u00e0m y = f (x) \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh tr\u00ean m\u1ed9t kho\u1ea3ng (a; b) v\u00e0 x0 (a; b). Sau \u0111\u00f3, h\u00e0m f (x) s\u1ebd li\u00ean t\u1ee5c t\u1ea1i x0 khi: lim[x\u2192x0] f (x) = f (x0). Khi h\u00e0m kh\u00f4ng li\u00ean t\u1ee5c t\u1ea1i \u0111i\u1ec3m x0, n\u00f3 c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 h\u00e0m b\u1ecb gi\u00e1n \u0111o\u1ea1n t\u1ea1i x0.<\/p>\n<p dir=\"ltr\">Gi\u1ea3 s\u1eed c\u00e1c h\u00e0m y = f (x), y = g (x) \u0111\u01b0\u1ee3c coi l\u00e0 li\u00ean t\u1ee5c t\u1ea1i \u0111i\u1ec3m x0. Sau \u0111\u00f3:<\/p>\n<ul>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">C\u00e1c h\u00e0m y = f (x) + g (x) v\u00e0 y = f (x) &#8211; g (x), y = f (x) .g (x) s\u1ebd li\u00ean t\u1ee5c t\u1ea1i x0.<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">H\u00e0m y = f (x)\/g (x) s\u1ebd li\u00ean t\u1ee5c t\u1ea1i x0 n\u1ebfu g (x0) kh\u00e1c v\u1edbi 0.<\/p>\n<\/li>\n<\/ul>\n<p dir=\"ltr\"><img decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/2-ham-so-lien-tuc.png\" alt=\"Bi\u1ec3u \u0111\u1ed3 c\u1ee7a h\u00e0m li\u00ean t\u1ee5c t\u1ea1i m\u1ed9t \u0111i\u1ec3m. (\u1ea2nh: B\u1ed9 s\u01b0u t\u1eadp Internet)\" width=\"100%\"><\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Chuc_nang_lien_tuc_o_khoang_cach_xa\"><\/span>Ch\u1ee9c n\u0103ng li\u00ean t\u1ee5c \u1edf kho\u1ea3ng c\u00e1ch xa<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Ch\u00fang ta c\u00f3 h\u00e0m y = f (x) \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 h\u00e0m li\u00ean t\u1ee5c tr\u00ean kho\u1ea3ng (a; b) khi n\u00f3 li\u00ean t\u1ee5c t\u1ea1i c\u00e1c \u0111i\u1ec3m n\u1eb1m trong kho\u1ea3ng.<\/p>\n<p>Khi h\u00e0m li\u00ean t\u1ee5c \u0111\u01b0\u1ee3c li\u00ean t\u1ee5c trong kho\u1ea3ng (a; b), t\u01b0\u01a1ng \u1ee9ng v\u1edbi ph\u1ea1m vi \u0111\u00f3, bi\u1ec3u \u0111\u1ed3 c\u1ee7a h\u00e0m s\u1ebd l\u00e0 m\u1ed9t d\u00f2ng li\u00ean t\u1ee5c v\u00e0 kh\u00f4ng b\u1ecb h\u1ecfng.<\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Cac_chuc_nang_lien_tuc_tai_mot_doan_van\"><\/span>C\u00e1c ch\u1ee9c n\u0103ng li\u00ean t\u1ee5c t\u1ea1i m\u1ed9t \u0111o\u1ea1n v\u0103n<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">H\u00e0m y = f (x) \u0111\u01b0\u1ee3c coi l\u00e0 li\u00ean t\u1ee5c tr\u00ean ph\u00e2n \u0111o\u1ea1n [a;b] Khi n\u00f3 li\u00ean t\u1ee5c tr\u00ean t\u1ea5t c\u1ea3 c\u00e1c \u0111i\u1ec3m \u1edf ph\u1ea1m vi (a; b) v\u00e0 sau \u0111\u00f3: limx \u2192 a + f (x) = f (a), limx \u2192 b &#8211; f (x) = f (b).<\/p>\n<h2 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Cac_dinh_ly_co_ban_cua_ham_lien_tuc\"><\/span>C\u00e1c \u0111\u1ecbnh l\u00fd c\u01a1 b\u1ea3n c\u1ee7a h\u00e0m li\u00ean t\u1ee5c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p dir=\"ltr\">\u0110\u1ec3 gi\u00fap ng\u01b0\u1eddi \u0111\u1ecdc hi\u1ec3u th\u00eam v\u1ec1 ch\u1ee9c n\u0103ng li\u00ean t\u1ee5c. D\u01b0\u1edbi \u0111\u00e2y kh\u1ec9 \u0111\u00e3 t\u00f3m t\u1eaft ng\u1eafn g\u1ecdn ki\u1ebfn \u200b\u200bth\u1ee9c v\u1ec1 \u0111\u1ecbnh l\u00fd c\u1ee7a h\u00e0m li\u00ean t\u1ee5c. H\u00e3y l\u00e0m theo \u0111\u1ec3 l\u00e0m b\u00e0i t\u1eadp v\u1ec1 nh\u00e0 t\u1ed1t h\u01a1n!<\/p>\n<p dir=\"ltr\">\u0110\u1ecbnh l\u00fd 1: Khi t\u00ednh to\u00e1n t\u1ed5ng, s\u1ea3n ph\u1ea9m, th\u01b0\u01a1ng t\u00edch, s\u1ef1 kh\u00e1c bi\u1ec7t c\u1ee7a hai h\u00e0m li\u00ean t\u1ee5c v\u1edbi nhau t\u1ea1i m\u1ed9t \u0111i\u1ec3m. Sau \u0111\u00f3, c\u00e1c ch\u1ee9c n\u0103ng \u0111\u00f3 s\u1ebd li\u00ean t\u1ee5c t\u1ea1i th\u1eddi \u0111i\u1ec3m \u0111\u00f3 (Thuong v\u00e0 m\u1eabu t\u1ea1i th\u1eddi \u0111i\u1ec3m \u0111\u00f3 ph\u1ea3i kh\u00e1c v\u1edbi 0).<\/p>\n<p dir=\"ltr\">\u0110\u1ecbnh l\u00fd 2:<\/p>\n<ol>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">H\u00e0m \u0111a th\u1ee9c li\u00ean t\u1ee5c tr\u00ean R.<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">Ph\u00e2n b\u00f3n l\u01b0\u1ee3ng gi\u00e1c v\u00e0 h\u1ee3p l\u00fd li\u00ean t\u1ee5c tr\u00ean c\u00e1c kho\u1ea3ng th\u1eddi gian \u0111\u01b0\u1ee3c ch\u1ec9 \u0111\u1ecbnh c\u1ee7a t\u1eadp h\u1ee3p.<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">C\u00e1c ch\u1ee9c n\u0103ng ch\u00ednh s\u1ebd lu\u00f4n lu\u00f4n \u0111\u01b0\u1ee3c li\u00ean t\u1ee5c tr\u00ean c\u00e1c kho\u1ea3ng th\u1eddi gian \u0111\u01b0\u1ee3c ch\u1ec9 \u0111\u1ecbnh.<\/p>\n<\/li>\n<\/ol>\n<p dir=\"ltr\">\u0110\u1ecbnh l\u00fd 3: N\u1ebfu h\u00e0m y = f (x) \u0111\u01b0\u1ee3c coi l\u00e0 li\u00ean t\u1ee5c tr\u00ean \u0111o\u1ea1n v\u0103n [a;b] v\u00e0 f (a) .f (b) \u00cdt h\u01a1n 0 s\u1ebd lu\u00f4n t\u1ed3n t\u1ea1i \u00edt nh\u1ea5t m\u1ed9t \u0111i\u1ec3m c thu\u1ed9c v\u1ec1 (a; b) sao cho f (c) = 0.<\/p>\n<p dir=\"ltr\">\n<h2 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Toan_hoc_cac_chuc_nang_lien_tuc_la_pho_bien\"><\/span>To\u00e1n h\u1ecdc c\u00e1c ch\u1ee9c n\u0103ng li\u00ean t\u1ee5c l\u00e0 ph\u1ed5 bi\u1ebfn<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p dir=\"ltr\">\u0110\u1ec3 t\u0103ng c\u01b0\u1eddng ki\u1ebfn \u200b\u200bth\u1ee9c v\u1ec1 ch\u1ee9c n\u0103ng li\u00ean t\u1ee5c, b\u00ean d\u01b0\u1edbi kh\u1ec9 mu\u1ed1n gi\u1edbi thi\u1ec7u v\u1edbi b\u1ea1n m\u1ed9t s\u1ed1 lo\u1ea1i to\u00e1n h\u1ecdc ph\u1ed5 bi\u1ebfn trong ch\u1ee9c n\u0103ng li\u00ean t\u1ee5c.<\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Mau_1_Xem_xet_tinh_lien_tuc_cua_ham_tai_mot_diem_cu_the\"><\/span>M\u1eabu 1: Xem x\u00e9t t\u00ednh li\u00ean t\u1ee5c c\u1ee7a h\u00e0m t\u1ea1i m\u1ed9t \u0111i\u1ec3m c\u1ee5 th\u1ec3.<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">\u0110\u1ec3 xem x\u00e9t t\u00ednh li\u00ean t\u1ee5c c\u1ee7a m\u1ed9t h\u00e0m \u0111\u00e3 cho t\u1ea1i \u0111i\u1ec3m X0, ch\u00fang t\u00f4i th\u1ef1c hi\u1ec7n c\u00e1c b\u01b0\u1edbc sau:<\/p>\n<ul>\n<li dir=\"ltr\">B\u01b0\u1edbc 1: Ki\u1ec3m tra xem h\u00e0m \u0111\u00e3 cho c\u00f3 \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh tr\u00ean kho\u1ea3ng c\u00e1ch X0 hay kh\u00f4ng, sau \u0111\u00f3 t\u00ednh to\u00e1n gi\u00e1 tr\u1ecb t\u1ea1i F (x0).<\/li>\n<li dir=\"ltr\">B\u01b0\u1edbc 2: T\u00ednh to\u00e1n Limx \u2192 X0F (x). Trong nhi\u1ec1u tr\u01b0\u1eddng h\u1ee3p, ch\u00fang ta c\u1ea7n t\u00ednh to\u00e1n Limx \u2192 X0 + F (x), Limx \u2192 X0 &#8211; F (x).<\/li>\n<li dir=\"ltr\">B\u01b0\u1edbc 3: So s\u00e1nh Limx \u2192 X0F (x) v\u1edbi F (x0) v\u00e0 k\u1ebft lu\u1eadn.<\/li>\n<\/ul>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Mau_2_Xem_xet_tinh_toan_lien_tuc_chung_minh_chuc_nang_lien_tuc_tren_mot_doan_van_hoac_tap_hop\"><\/span>M\u1eabu 2: Xem x\u00e9t t\u00ednh to\u00e1n li\u00ean t\u1ee5c, ch\u1ee9ng minh ch\u1ee9c n\u0103ng li\u00ean t\u1ee5c tr\u00ean m\u1ed9t \u0111o\u1ea1n v\u0103n ho\u1eb7c t\u1eadp h\u1ee3p<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">\u0110\u1ec3 gi\u1ea3i quy\u1ebft h\u00ecnh th\u1ee9c to\u00e1n h\u1ecdc n\u00e0y, h\u00e3y xem x\u00e9t v\u00ed d\u1ee5 sau:<\/p>\n<p dir=\"ltr\">V\u00ed d\u1ee5 1: Xem x\u00e9t t\u00ednh li\u00ean t\u1ee5c c\u1ee7a h\u00e0m: f (x) = (x2+5x)\/x khi x kh\u00e1c v\u1edbi 0 v\u00e0 khi x = 0, tr\u00ean R.<\/p>\n<p dir=\"ltr\">H\u01b0\u1edbng d\u1eabn:<\/p>\n<p dir=\"ltr\">R\u00f5 r\u00e0ng ch\u00fang ta c\u00f3 th\u1ec3 th\u1ea5y khi X kh\u00e1c v\u1edbi 0, h\u00e0m \u0111\u01b0\u1ee3c cho l\u00e0 lu\u00f4n lu\u00f4n l\u00e0 ch\u1ee9c n\u0103ng. V\u00e0 n\u00f3 ho\u00e0n to\u00e0n \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh n\u00ean n\u00f3 li\u00ean t\u1ee5c tr\u00ean m\u1ed7i kh\u00f4ng gian.<\/p>\n<p dir=\"ltr\">Do \u0111\u00f3, t\u1ea1i th\u1eddi \u0111i\u1ec3m n\u00e0y, ch\u00fang t\u00f4i ch\u1ec9 c\u1ea7n xem x\u00e9t li\u00ean t\u1ee5c t\u1ea1i x = 0. Ch\u00fang t\u00f4i c\u00f3:<\/p>\n<p dir=\"ltr\">Gi\u00e1 tr\u1ecb c\u1ee7a h\u00e0m t\u1ea1i x = 0 l\u00e0 f (0) = 5<\/p>\n<p dir=\"ltr\">Gi\u1edbi h\u1ea1n c\u1ee7a h\u00e0m t\u1ea1i x = 0 l\u00e0 Limx \u2192 0f (x) = Limx \u2192 0.2 + 5.x = Limx \u2192 0 (x + 5) = 5<\/p>\n<p dir=\"ltr\">Ch\u00fang ta th\u1ea5y Limx \u2192 0f (x) = f (0) sao cho h\u00e0m \u0111\u00e3 cho s\u1ebd li\u00ean t\u1ee5c t\u1ea1i x = 0<\/p>\n<p dir=\"ltr\">M\u1eb9o b\u1ea1n c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng ch\u1ee9c n\u0103ng c\u1ee7a m\u00e1y t\u00ednh \u0111\u1ec3 t\u00ednh to\u00e1n ch\u1ee9c n\u0103ng li\u00ean t\u1ee5c. S\u1eed d\u1ee5ng ph\u00edm gi\u1ea3i quy\u1ebft tr\u00ean m\u00e1y t\u00ednh c\u1ee7a b\u1ea1n \u0111\u1ec3 nhanh ch\u00f3ng ki\u1ec3m tra c\u00e2u tr\u1ea3 l\u1eddi c\u1ee7a v\u1ea5n \u0111\u1ec1.<\/p>\n<p dir=\"ltr\">Xem th\u00eam: L\u00fd thuy\u1ebft v\u1ec1 c\u00f9ng m\u1ed9t h\u00e0m bi\u1ebfn v\u00e0 c\u00e1c lo\u1ea1i b\u00e0i t\u1eadp ph\u1ed5 bi\u1ebfn<\/p>\n<p dir=\"ltr\"><img decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/3-ham-so-lien-tuc.png\" alt=\"S\u1eed d\u1ee5ng m\u00e1y t\u00ednh \u0111\u1ec3 ki\u1ec3m tra t\u00ednh li\u00ean t\u1ee5c c\u1ee7a ch\u1ee9c n\u0103ng. (\u1ea2nh: B\u1ed9 s\u01b0u t\u1eadp Internet)\" width=\"100%\"><\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Mau_3_Tim_dieu_kien_cho_ham_lien_tuc_tai_mot_diem\"><\/span>M\u1eabu 3: T\u00ecm \u0111i\u1ec1u ki\u1ec7n cho h\u00e0m li\u00ean t\u1ee5c t\u1ea1i m\u1ed9t \u0111i\u1ec3m<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">\u0110\u1ec3 gi\u1ea3i quy\u1ebft h\u00ecnh th\u1ee9c to\u00e1n h\u1ecdc n\u00e0y, ch\u00fang t\u00f4i s\u1eed d\u1ee5ng ph\u01b0\u01a1ng ph\u00e1p sau. \u0110\u1ea7u ti\u00ean, c\u1ea7n ph\u1ea3i \u00e1p d\u1ee5ng c\u00e1c \u0111i\u1ec1u ki\u1ec7n c\u1ee7a c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh v\u1edbi c\u00e1c gi\u1ea3i ph\u00e1p v\u00e0 ch\u1ee9c n\u0103ng li\u00ean t\u1ee5c:<\/p>\n<ul>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">\u0110i\u1ec1u ki\u1ec7n cho c\u00e1c ch\u1ee9c n\u0103ng li\u00ean t\u1ee5c t\u1ea1i X0:<\/p>\n<\/li>\n<\/ul>\n<p dir=\"ltr\"><img loading=\"lazy\" decoding=\"async\" style=\"margin-left: auto;margin-right: auto\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/4-ham-so-lien-tuc.png\" alt=\"\" width=\"150\" height=\"42\"><\/p>\n<ul>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">\u0110i\u1ec1u ki\u1ec7n cho h\u00e0m \u0111\u00e3 cho tr\u00ean m\u1ed9t b\u1ed9 d l\u00e0 f (x) li\u00ean t\u1ee5c \u1edf m\u1ecdi \u0111i\u1ec3m c\u1ee7a D.<\/p>\n<\/li>\n<\/ul>\n<p dir=\"ltr\">Ph\u01b0\u01a1ng tr\u00ecnh f (x) = 0 ph\u1ea3i c\u00f3 \u00edt nh\u1ea5t m\u1ed9t gi\u1ea3i ph\u00e1p n\u1ebfu h\u00e0m y = f (x) li\u00ean t\u1ee5c tr\u00ean d, 2 s\u1ed1 a v\u00e0 b \u0111\u1ec1u l\u00e0 D.<\/p>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Mau_4_Tim_dieu_kien_cho_ham_lien_tuc_tren_khoang_cach_hoac_dat\"><\/span>M\u1eabu 4: T\u00ecm \u0111i\u1ec1u ki\u1ec7n cho h\u00e0m li\u00ean t\u1ee5c tr\u00ean kho\u1ea3ng c\u00e1ch ho\u1eb7c \u0111\u1eb7t<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">\u0110\u1ec3 gi\u1ea3i quy\u1ebft lo\u1ea1i n\u00e0y, b\u1ea1n c\u1ea7n \u00e1p d\u1ee5ng \u0110\u1ecbnh l\u00fd 1 v\u00e0 2 \u0111\u1ec3 c\u00f3 th\u1ec3 t\u00ecm th\u1ea5y t\u00ednh li\u00ean t\u1ee5c c\u1ee7a n\u00f3 tr\u00ean m\u1ed7i kho\u1ea3ng th\u1eddi gian \u0111\u01b0\u1ee3c ch\u1ec9 \u0111\u1ecbnh. N\u1ebfu h\u00e0m \u0111\u00e3 cho \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1edfi 2 ho\u1eb7c 3 c\u00f4ng th\u1ee9c, ch\u00fang t\u00f4i s\u1ebd xem x\u00e9t li\u00ean t\u1ee5c t\u1ea1i c\u00e1c t\u00ednh n\u0103ng \u0111\u1eb7c bi\u1ec7t \u0111\u00f3.<\/p>\n<p dir=\"ltr\">V\u00ed d\u1ee5: T\u00ecm m\u1ed9t \u0111\u1ec3 h\u00e0m li\u00ean t\u1ee5c tr\u00ean t\u1eadp h\u1ee3p: f (x) = (2 &#8211; 7x + 5&#215;2)\/(x &#8211; 1) v\u1edbi c\u00e1c \u0111i\u1ec1u ki\u1ec7n kh\u00e1c x kh\u00e1c 1 ho\u1eb7c x = 1<\/p>\n<p dir=\"ltr\">H\u01b0\u1edbng d\u1eabn gi\u1ea3i quy\u1ebft:<\/p>\n<ul>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">Tr\u01b0\u1edbc ti\u00ean h\u00e3y xem x\u00e9t tr\u01b0\u1eddng h\u1ee3p c\u1ee7a m\u1ed9t X kh\u00e1c, h\u00e0m \u0111\u01b0\u1ee3c coi l\u00e0 m\u1ed9t c\u00f4ng th\u1ee9c h\u1ee3p l\u00fd.<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">Khi x = 1 thay v\u00ec h\u00e0m \u0111\u00e3 cho. Sau \u0111\u00f3, h\u00e0m f (x) li\u00ean t\u1ee5c t\u1ea1i \u0111i\u1ec3m x = 1 khi v\u00e0 ch\u1ec9 khi m = -4\/3.<\/p>\n<\/li>\n<\/ul>\n<h3 dir=\"ltr\"><span class=\"ez-toc-section\" id=\"Mau_5_Ap_dung_ham_lien_tuc_chung_minh_phuong_trinh_voi_cac_giai_phap\"><\/span>M\u1eabu 5: \u00c1p d\u1ee5ng h\u00e0m li\u00ean t\u1ee5c ch\u1ee9ng minh ph\u01b0\u01a1ng tr\u00ecnh v\u1edbi c\u00e1c gi\u1ea3i ph\u00e1p<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p dir=\"ltr\">\u0110\u1ea7u ti\u00ean ch\u00fang ta c\u1ea7n \u00e1p d\u1ee5ng \u0111\u1ecbnh l\u00fd: n\u1ebfu h\u00e0m y = f (x) li\u00ean t\u1ee5c tr\u00ean ph\u00e2n \u0111o\u1ea1n [a; b] Cho v\u00e0 f (a) .f (b) nh\u1ecf h\u01a1n 0, sau \u0111\u00f3 ph\u01b0\u01a1ng tr\u00ecnh f (x) = 0 s\u1ebd lu\u00f4n c\u00f3 \u00edt nh\u1ea5t 1 gi\u1ea3i ph\u00e1p trong ph\u1ea1m vi (a; b).<\/p>\n<p dir=\"ltr\">C\u00e1c b\u01b0\u1edbc c\u1ee5 th\u1ec3 \u0111\u1ec3 th\u1ef1c hi\u1ec7n ki\u1ec3m tra ch\u1ee9ng minh ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 gi\u1ea3i ph\u00e1p sau:<\/p>\n<ul>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">B\u01b0\u1edbc 1: Thay \u0111\u1ed5i ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho n\u00ean \u0111\u01b0\u1ee3c ch\u1ee9ng minh th\u00e0nh Form F (x) = 0.<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">B\u01b0\u1edbc 2: Ti\u1ebfp theo, b\u1ea1n c\u1ea7n t\u00ecm 2 s\u1ed1 A v\u00e0 B (A nh\u1ecf h\u01a1n b) sao cho f (a) .f (b) nh\u1ecf h\u01a1n 0 0<\/p>\n<\/li>\n<li dir=\"ltr\">\n<p dir=\"ltr\" role=\"presentation\">B\u01b0\u1edbc 3: Cu\u1ed1i c\u00f9ng, ch\u1ee9ng minh h\u00e0m y = f (x) lu\u00f4n lu\u00f4n li\u00ean t\u1ee5c tr\u00ean \u0111o\u1ea1n v\u0103n [a; b] \u0111\u01b0\u1ee3c cho.<\/p>\n<\/li>\n<\/ul>\n<table style=\"border-collapse: collapse;width: 100%;background-color: #fbeeb8\" border=\"1\">\n<tr>\n<td style=\"width: 98.5189%\">\n<p style=\"text-align: center\">Gi\u00fap con b\u1ea1n h\u1ecdc to\u00e1n k\u1ebft h\u1ee3p v\u1edbi ti\u1ebfng Anh si\u00eau ti\u1ebft ki\u1ec7m ch\u1ec9 tr\u00ean \u1ee9ng d\u1ee5ng to\u00e1n h\u1ecdc kh\u1ec9. V\u1edbi n\u1ed9i dung gi\u1ea3ng d\u1ea1y v\u1ea1n n\u0103ng \u0111\u1ec3 gi\u00fap tr\u1ebb ph\u00e1t tri\u1ec3n t\u01b0 duy n\u00e3o b\u1ed9 v\u00e0 ng\u00f4n ng\u1eef to\u00e0n di\u1ec7n ch\u1ec9 v\u1edbi 2K\/ng\u00e0y.<\/p>\n<p style=\"text-align: center\">\n<p><img loading=\"lazy\" decoding=\"async\" style=\"margin-left: auto;margin-right: auto\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia.monkeyuni.net\/upload\/web\/img\/button_dang-ky-ngay-1.png\" alt=\"\" width=\"185\" height=\"25\"><\/p>\n<\/td>\n<\/tr>\n<\/table>\n<h2><span class=\"ez-toc-section\" id=\"Tap_the_duc_ve_cac_thuoc_tinh_chuc_nang_lien_tuc_cho_hoc_sinh_thuc_hanh\"><\/span>T\u1eadp th\u1ec3 d\u1ee5c v\u1ec1 c\u00e1c thu\u1ed9c t\u00ednh ch\u1ee9c n\u0103ng li\u00ean t\u1ee5c cho h\u1ecdc sinh th\u1ef1c h\u00e0nh<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Ngo\u00e0i c\u00e1c b\u00e0i t\u1eadp trong s\u00e1ch gi\u00e1o khoa to\u00e1n l\u1edbp 11, \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 b\u00e0i t\u1eadp tham kh\u1ea3o li\u00ean quan \u0111\u1ebfn ch\u1ee9c n\u0103ng li\u00ean t\u1ee5c cho h\u1ecdc sinh th\u1ef1c h\u00e0nh:<\/p>\n<p><img decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/ham-so-lien-tuc-a.jpg\" alt=\"(Ngu\u1ed3n: T\u00f3m t\u1eaft)\" width=\"100%\"><\/p>\n<p>Tr\u00ean \u0111\u00e2y l\u00e0 ki\u1ebfn \u200b\u200bth\u1ee9c chung v\u1ec1 ch\u1ee9c n\u0103ng li\u00ean t\u1ee5c. Hy v\u1ecdng b\u00e0i vi\u1ebft n\u00e0y s\u1ebd gi\u00fap b\u1ea1n trong qu\u00e1 tr\u00ecnh h\u1ecdc t\u1eadp. Th\u1ef1c h\u00e0nh c\u00e1c lo\u1ea1i to\u00e1n h\u1ecdc m\u00e0 kh\u1ec9 \u0111\u00e3 gi\u1edbi thi\u1ec7u trong b\u00e0i vi\u1ebft \u0111\u1ec3 h\u1ecdc t\u1ed1t h\u01a1n!<\/p>\n<p>Ngu\u1ed3n: <a href=\"http:\/\/www.ckconitsha.com\/vn\/\">http:\/\/www.ckconitsha.com\/vn\/<\/a> T\u00e1c gi\u1ea3: <a href=\"https:\/\/www.ckconitsha.com\/vn\/author\/nguyenlandung\">Nguy\u1ec5n L\u00e2n d\u0169ng<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>C\u00e1c ch\u1ee9c n\u0103ng li\u00ean t\u1ee5c l\u00e0 m\u1ed9t ph\u1ea7n quan tr\u1ecdng c\u1ee7a ki\u1ebfn \u200b\u200bth\u1ee9c to\u00e1n h\u1ecdc. \u0110\u1ec3 th\u1ef1c hi\u1ec7n c\u00e1c b\u00e0i t\u1eadp v\u1ec1 lo\u1ea1i n\u00e0y, b\u1ea1n c\u1ea7n n\u1eafm b\u1eaft l\u00fd thuy\u1ebft v\u00e0 c\u00e1c thu\u1ed9c t\u00ednh c\u01a1 b\u1ea3n. D\u01b0\u1edbi \u0111\u00e2y Shining Home &#8211; Gia \u0111\u00ecnh Anh Ng\u1eef mu\u1ed1n t\u00f3m t\u1eaft t\u1ea5t c\u1ea3 c\u00e1c ki\u1ebfn \u200b\u200bth\u1ee9c v\u00e0 lo\u1ea1i&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[100],"tags":[],"class_list":["post-21550","post","type-post","status-publish","format-standard","hentry","category-kien-thuc"],"_links":{"self":[{"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/posts\/21550","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/comments?post=21550"}],"version-history":[{"count":2,"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/posts\/21550\/revisions"}],"predecessor-version":[{"id":26453,"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/posts\/21550\/revisions\/26453"}],"wp:attachment":[{"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/media?parent=21550"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/categories?post=21550"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/tags?post=21550"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}