{"id":21049,"date":"2025-07-08T02:10:52","date_gmt":"2025-07-07T19:10:52","guid":{"rendered":"https:\/\/www.ckconitsha.com\/vn\/?p=21049"},"modified":"2025-07-09T17:05:58","modified_gmt":"2025-07-09T10:05:58","slug":"cong-thuc-dao-ham-nang-cao-11-va-tuyet-chieu-giai-bai-tap-cuc-dinh-hoc-sinh-nen-biet","status":"publish","type":"post","link":"https:\/\/www.ckconitsha.com\/vn\/cong-thuc-dao-ham-nang-cao-11-va-tuyet-chieu-giai-bai-tap-cuc-dinh-hoc-sinh-nen-biet\/","title":{"rendered":"C\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m n\u00e2ng cao 11 v\u00e0 tuy\u1ec7t chi\u00eau gi\u1ea3i b\u00e0i t\u1eadp c\u1ef1c \u0111\u1ec9nh h\u1ecdc sinh n\u00ean bi\u1ebft"},"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\/cong-thuc-dao-ham-nang-cao-11-va-tuyet-chieu-giai-bai-tap-cuc-dinh-hoc-sinh-nen-biet\/#Dao_ham_tien_tien_la_gi\" >\u0110\u1ea1o h\u00e0m ti\u00ean ti\u1ebfn l\u00e0 g\u00ec?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.ckconitsha.com\/vn\/cong-thuc-dao-ham-nang-cao-11-va-tuyet-chieu-giai-bai-tap-cuc-dinh-hoc-sinh-nen-biet\/#Toan_hoc_va_giai_phap_toan_nang_cao\" >To\u00e1n h\u1ecdc v\u00e0 gi\u1ea3i ph\u00e1p to\u00e1n n\u00e2ng cao<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.ckconitsha.com\/vn\/cong-thuc-dao-ham-nang-cao-11-va-tuyet-chieu-giai-bai-tap-cuc-dinh-hoc-sinh-nen-biet\/#Mau_1_Tim_so\" >M\u1eabu 1: T\u00ecm s\u1ed1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.ckconitsha.com\/vn\/cong-thuc-dao-ham-nang-cao-11-va-tuyet-chieu-giai-bai-tap-cuc-dinh-hoc-sinh-nen-biet\/#Mau_2_Dao_ham_nang_cao\" >M\u1eabu 2: \u0110\u1ea1o h\u00e0m n\u00e2ng cao<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.ckconitsha.com\/vn\/cong-thuc-dao-ham-nang-cao-11-va-tuyet-chieu-giai-bai-tap-cuc-dinh-hoc-sinh-nen-biet\/#Mau_3_Tinh_dao_ham_cua_ham_tai_x0\" >M\u1eabu 3: T\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m t\u1ea1i x0<\/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\/cong-thuc-dao-ham-nang-cao-11-va-tuyet-chieu-giai-bai-tap-cuc-dinh-hoc-sinh-nen-biet\/#Mau_4_Dao_ham_cua_noi_dung_luong_giac_nang_cao\" >M\u1eabu 4: \u0110\u1ea1o h\u00e0m c\u1ee7a n\u1ed9i dung l\u01b0\u1ee3ng gi\u00e1c n\u00e2ng cao<\/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\/cong-thuc-dao-ham-nang-cao-11-va-tuyet-chieu-giai-bai-tap-cuc-dinh-hoc-sinh-nen-biet\/#Mau_5_Dao_ham_kep_nang_cao\" >M\u1eabu 5: \u0110\u1ea1o h\u00e0m k\u00e9p n\u00e2ng cao<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.ckconitsha.com\/vn\/cong-thuc-dao-ham-nang-cao-11-va-tuyet-chieu-giai-bai-tap-cuc-dinh-hoc-sinh-nen-biet\/#Mau_6_Giai_cac_phuong_trinh_chuc_nang_nang_cao\" >M\u1eabu 6: Gi\u1ea3i c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh ch\u1ee9c n\u0103ng n\u00e2ng cao<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/www.ckconitsha.com\/vn\/cong-thuc-dao-ham-nang-cao-11-va-tuyet-chieu-giai-bai-tap-cuc-dinh-hoc-sinh-nen-biet\/#Mau_7_Phuong_trinh_tiep_tuyen_cua_do_thi\" >M\u1eabu 7: Ph\u01b0\u01a1ng tr\u00ecnh ti\u1ebfp tuy\u1ebfn c\u1ee7a \u0111\u1ed3 th\u1ecb<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/www.ckconitsha.com\/vn\/cong-thuc-dao-ham-nang-cao-11-va-tuyet-chieu-giai-bai-tap-cuc-dinh-hoc-sinh-nen-biet\/#Bai_tap_toan_hoc_nang_cao_TOAN_11_tu_dong\" >B\u00e0i t\u1eadp to\u00e1n h\u1ecdc n\u00e2ng cao TO\u00c1N 11 t\u1ef1 \u0111\u1ed9ng<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/www.ckconitsha.com\/vn\/cong-thuc-dao-ham-nang-cao-11-va-tuyet-chieu-giai-bai-tap-cuc-dinh-hoc-sinh-nen-biet\/#Ket_luan\" >K\u1ebft lu\u1eadn<\/a><\/li><\/ul><\/nav><\/div>\n<\/p>\n<p>D\u1eabn xu\u1ea5t n\u00e2ng cao l\u00e0 ki\u1ebfn \u200b\u200bth\u1ee9c kh\u00e1 kh\u00f3 kh\u0103n cho h\u1ecdc sinh l\u1edbp 11 tham gia v\u00e0o c\u00e1c h\u1ecdc sinh xu\u1ea5t s\u1eafc, k\u1ef3 thi c\u1ea5p t\u1ec9nh v\u00e0 qu\u1ed1c gia v\u00e0 th\u1eadm ch\u00ed trong c\u00e1c k\u1ef3 thi trung h\u1ecdc v\u00e0 \u0111\u1ea1i h\u1ecdc. V\u00ec v\u1eady, \u0111\u1ec3 gi\u00fap h\u1ecdc sinh th\u1ef1c hi\u1ec7n b\u00e0i t\u1eadp n\u00e0y t\u1ed1t, h\u00e3y \u0111\u1ec3 kh\u1ec9 t\u00ecm hi\u1ec3u c\u00f4ng th\u1ee9c ch\u1ee9c n\u0103ng n\u00e2ng cao v\u00e0 gi\u1ea3i ph\u00e1p chi ti\u1ebft trong b\u00e0i vi\u1ebft sau.<\/p>\n<p>                                    <\/p>\n<h2><span class=\"ez-toc-section\" id=\"Dao_ham_tien_tien_la_gi\"><\/span>\u0110\u1ea1o h\u00e0m ti\u00ean ti\u1ebfn l\u00e0 g\u00ec?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Trong ch\u01b0\u01a1ng tr\u00ecnh \u0111\u1ea1i s\u1ed1 l\u1edbp 11, h\u1ecd s\u1ebd l\u00e0m quen v\u00e0 h\u1ecdc ki\u1ebfn \u200b\u200bth\u1ee9c ph\u00e1i sinh n\u00e2ng cao. V\u1ec1 b\u1ea3n ch\u1ea5t, \u0111\u00e2y l\u00e0 m\u1ed9t ki\u1ebfn \u200b\u200bth\u1ee9c n\u00e2ng cao h\u01a1n v\u1ec1 to\u00e1n h\u1ecdc to\u00e1n h\u1ecdc c\u01a1 b\u1ea3n.<\/p>\n<p>N\u1ebfu \u0111\u1ea1o h\u00e0m c\u01a1 b\u1ea3n l\u00e0 m\u1ed9t h\u00e0m m\u00f4 t\u1ea3 bi\u1ebfn th\u1ec3 c\u1ee7a ch\u00fang t\u1ea1i m\u1ed9t \u0111i\u1ec3m nh\u1ea5t \u0111\u1ecbnh, c\u00f9ng v\u1edbi m\u1ed9t t\u00edch ph\u00e2n \u0111\u1ec3 t\u1ea1o th\u00e0nh c\u00e1c ho\u1ea1t \u0111\u1ed9ng ng\u01b0\u1ee3c l\u1ea1i th\u01b0\u1eddng \u1edf c\u1ea5p 1.<\/p>\n<p>\u0110\u1ed1i v\u1edbi \u0111\u1ee9c t\u00ednh ti\u00ean ti\u1ebfn, c\u00f2n \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 d\u1eabn xu\u1ea5t cao, th\u01b0\u1eddng c\u00f3 l\u1ee3i cho vi\u1ec7c t\u00ednh to\u00e1n \u0111\u1ea1o h\u00e0m c\u1ee7a c\u1ea5p 2, t\u1eeb 3 \u0111\u1ebfn c\u1ea5p. <\/p>\n<p><img decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/dao-ham-nang-cao-1.png\" alt=\"\u0110\u1ea1o h\u00e0m cao l\u00e0 ki\u1ebfn \u200b\u200bth\u1ee9c kh\u00e1 kh\u00f3 kh\u0103n. (\u1ea2nh: B\u1ed9 s\u01b0u t\u1eadp Internet)\" width=\"100%\"><\/p>\n<p>\u0110\u1ecbnh ngh\u0129a chi ti\u1ebft:<\/p>\n<p><em>Gi\u1ea3 s\u1eed h\u00e0m y = f (x) c\u00f3 m\u1ed9t \u0111\u1ea1o h\u00e0m f &#039;(x)<\/em><\/p>\n<p><em>\u0110\u1ea1o h\u00e0m c\u1ee7a h\u00e0m f &#039;(x), n\u1ebfu c\u00f3, \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u0111\u1ea1o h\u00e0m th\u1ee9 c\u1ea5p c\u1ee7a h\u00e0m f (x), k\u00fd hi\u1ec7u l\u00e0 y&#039; &#039;ho\u1eb7c f&#039; &#039;(x).<\/em><\/p>\n<p><em>\u0110\u1ea1o h\u00e0m c\u1ee7a h\u00e0m f &#039;&#039; (x), n\u1ebfu c\u00f3, \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 d\u1eabn xu\u1ea5t c\u1ee7a tr\u01b0\u1eddng trung h\u1ecdc c\u1ee7a h\u00e0m f (x), bi\u1ec3u t\u01b0\u1ee3ng l\u00e0 y &#039;&#039; ho\u1eb7c f &#039;&#039; (x).<\/em><\/p>\n<p><em>T\u01b0\u01a1ng t\u1ef1, \u0111\u1ea1o h\u00e0m c\u1ee7a \u0111\u1ea1o h\u00e0m c\u1ea5p t\u00ednh (N-1) \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 h\u00e0m n c\u1ea5p n c\u1ee7a h\u00e0m y = f (x), k\u00fd hi\u1ec7u l\u00e0 y (n) ho\u1eb7c f (n) (x).<\/em><\/p>\n<p><em>f (n) (x) =[f(n\u22121)(x)]\u2032, V\u1edbi n thu\u1ed9c v\u1ec1 z v\u00e0 n&gt; = 2<\/em><\/p>\n<p>C\u00f4ng th\u1ee9c ch\u1ee9c n\u0103ng n\u00e2ng cao 11 Chi ti\u1ebft<\/p>\n<p>\u0110\u1ec3 c\u00f3 th\u1ec3 gi\u1ea3i quy\u1ebft c\u00e1c v\u1ea5n \u0111\u1ec1 ph\u00e1i sinh cao n\u00e0y, n\u00f3 \u0111\u00f2i h\u1ecfi sinh vi\u00ean ph\u1ea3i nh\u1edb, ghi nh\u1edb v\u00e0 l\u00e0m ch\u1ee7 c\u00f4ng th\u1ee9c chi ti\u1ebft sau \u0111\u00e2y:<\/p>\n<p><em>\u0110\u1eb7t h\u00e0m y = f (x) c\u00f3 k\u00fd hi\u1ec7u N-1 d\u1eabn xu\u1ea5t f (n-1) (x) (n \u2208 N, n \u2265 4).<\/em><\/p>\n<p><em>N\u1ebfu f (n-1) (x) c\u00f3 \u0111\u1ea1o h\u00e0m, ch\u1ee9c n\u0103ng c\u1ee7a n\u00f3 \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 ninoa ch\u1ee9c n\u0103ng c\u1ee7a y = f (x), y (n) ho\u1eb7c f (n) (x).<\/em><\/p>\n<p><em>f (n) (x) = [f (n-1)(x)]&#039;<\/em><\/p>\n<p>C\u00f4ng th\u1ee9c ph\u00e1i sinh l\u1edbp cao:<\/p>\n<ul>\n<li>(xm) (n) = m (m &#8211; 1) (m &#8211; 2) &#8230; (m &#8211; n + 1) .xm &#8211; n (n\u1ebfu m \u2265 n)<\/li>\n<li>(xm) (n) = 0 (n\u1ebfu m \u2264 n)<\/li>\n<li>(lnx) (n) = (1) n &#8211; 1 (n &#8211; 1)! \/ xn.<\/li>\n<li>(ax) (n) = ax.lnna, v\u1edbi a&gt; 0.<\/li>\n<li>(sinx) (n) = sin (x+n.\u03c0\/2).<\/li>\n<li>(cosx) (n) = cos (x+n.\u03c0\/2).<\/li>\n<li>(ex) (n) = Ex.<\/li>\n<li>(1\/x) (n) = ( &#8211; 1) nn!<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Toan_hoc_va_giai_phap_toan_nang_cao\"><\/span>To\u00e1n h\u1ecdc v\u00e0 gi\u1ea3i ph\u00e1p to\u00e1n n\u00e2ng cao<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Ngo\u00e0i vi\u1ec7c ghi nh\u1edb v\u00e0 ghi nh\u1edb \u0111\u1ecbnh ngh\u0129a, c\u00f4ng th\u1ee9c khi nghi\u00ean c\u1ee9u s\u1ef1 m\u1edf r\u1ed9ng c\u1ee7a ch\u1ee9c n\u0103ng l\u00e0 kh\u00f4ng \u0111\u1ee7. B\u00ean c\u1ea1nh \u0111\u00f3, h\u1ecd c\u1ea7n x\u00e1c \u0111\u1ecbnh c\u00e1c lo\u1ea1i b\u00e0i t\u1eadp li\u00ean quan \u0111\u1ec3 bi\u1ebft c\u00e1ch \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c \u0111\u1ec3 t\u00ednh to\u00e1n t\u01b0\u01a1ng \u1ee9ng.<\/p>\n<p>V\u00ec v\u1eady, \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 lo\u1ea1i to\u00e1n h\u1ecdc to\u00e1n h\u1ecdc v\u1edbi ki\u1ebfn \u200b\u200bth\u1ee9c n\u00e2ng cao \u0111\u1ec3 m\u1ecdi ng\u01b0\u1eddi c\u00f3 th\u1ec3 tham kh\u1ea3o:<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Mau_1_Tim_so\"><\/span>M\u1eabu 1: T\u00ecm s\u1ed1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><img decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/dao-ham-nang-cao-3.png\" alt=\"\" width=\"100%\"><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Mau_2_Dao_ham_nang_cao\"><\/span>M\u1eabu 2: \u0110\u1ea1o h\u00e0m n\u00e2ng cao<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><img decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/dao-ham-nang-cao-4.png\" alt=\"\" width=\"100%\"><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Mau_3_Tinh_dao_ham_cua_ham_tai_x0\"><\/span>M\u1eabu 3: T\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m t\u1ea1i x0<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><img decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/dao-ham-nang-cao-5.png\" alt=\"\" width=\"100%\"><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Mau_4_Dao_ham_cua_noi_dung_luong_giac_nang_cao\"><\/span>M\u1eabu 4: \u0110\u1ea1o h\u00e0m c\u1ee7a n\u1ed9i dung l\u01b0\u1ee3ng gi\u00e1c n\u00e2ng cao<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><img decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/dao-ham-nang-cao-6.png\" alt=\"\" width=\"100%\"><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Mau_5_Dao_ham_kep_nang_cao\"><\/span>M\u1eabu 5: \u0110\u1ea1o h\u00e0m k\u00e9p n\u00e2ng cao<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Lo\u1ea1i 1. T\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m f (x) b\u1eb1ng f1 (x) khi x kh\u00e1c v\u1edbi x0 v\u00e0 b\u1eb1ng f2 (x) khi x = x0.<\/p>\n<p><img decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/dao-ham-nang-cao-7.png\" alt=\"\" width=\"100%\"><\/p>\n<p>Lo\u1ea1i 2. T\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m f (x) b\u1eb1ng f1 (x) khi x \u2265 x0 v\u00e0 b\u1eb1ng f2 (x) khi x<\/p>\n<p><img decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/dao-ham-nang-cao-8.png\" alt=\"\" width=\"100%\"><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Mau_6_Giai_cac_phuong_trinh_chuc_nang_nang_cao\"><\/span>M\u1eabu 6: Gi\u1ea3i c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh ch\u1ee9c n\u0103ng n\u00e2ng cao<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Lo\u1ea1i 1. V\u00f4 c\u00f9ng \/ c\u1ef1c k\u1ef3: Quy t\u1eafc x\u1ed5 s\u1ed1.<\/p>\n<p><img decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/dao-ham-nang-cao-9.png\" alt=\"\" width=\"100%\"><\/p>\n<p>Lo\u1ea1i 2. S\u1eed d\u1ee5ng \u0111\u1ea1o h\u00e0m trong v\u1ea5n \u0111\u1ec1 gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh v\u00e0 b\u1ea5t b\u00ecnh \u0111\u1eb3ng.<\/p>\n<p><img decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/dao-ham-nang-cao-10.png\" alt=\"\" width=\"100%\"><\/p>\n<p>Lo\u1ea1i 3.<\/p>\n<p>Trong lo\u1ea1i ch\u1ee9c n\u0103ng n\u00e2ng cao n\u00e0y, n\u00f3 s\u1ebd ph\u1ea3i \u00e1p d\u1ee5ng c\u00e1c c\u00f4ng th\u1ee9c \u0111\u1ec3 ti\u1ebfn h\u00e0nh t\u00ecm ki\u1ebfm ph\u00e1i sinh, sau \u0111\u00f3 ti\u1ebfn h\u00e0nh thay th\u1ebf bi\u1ec3u th\u1ee9c \u0111\u1ec3 thay \u0111\u1ed5i v\u00e0 t\u00ecm hi\u1ec3u k\u1ebft qu\u1ea3.<\/p>\n<p><img decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/dao-ham-nang-cao-11.png\" alt=\"\" width=\"100%\"><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Mau_7_Phuong_trinh_tiep_tuyen_cua_do_thi\"><\/span>M\u1eabu 7: Ph\u01b0\u01a1ng tr\u00ecnh ti\u1ebfp tuy\u1ebfn c\u1ee7a \u0111\u1ed3 th\u1ecb<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Trong h\u00ecnh th\u1ee9c n\u00e0y s\u1ebd \u0111\u01b0\u1ee3c chia th\u00e0nh 3 lo\u1ea1i b\u00e0i t\u1eadp ph\u1ed5 bi\u1ebfn nh\u01b0:<\/p>\n<p>Lo\u1ea1i 1. Ph\u01b0\u01a1ng tr\u00ecnh ti\u1ebfp tuy\u1ebfn khi bi\u1ebft li\u00ean h\u1ec7 m (x0; y0).<\/p>\n<p><img decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/dao-ham-nang-cao-12.png\" alt=\"\" width=\"100%\"><\/p>\n<p>Lo\u1ea1i 2. Vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh ti\u1ebfp tuy\u1ebfn khi bi\u1ebft h\u1ec7 s\u1ed1 g\u00f3c k.<\/p>\n<p><img decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/dao-ham-nang-cao-13.png\" alt=\"\" width=\"100%\"><\/p>\n<p>Lo\u1ea1i 3. Ph\u01b0\u01a1ng tr\u00ecnh ti\u1ebfp tuy\u1ebfn \u0111i qua \u0111i\u1ec3m A (x1; y1).<\/p>\n<p><img decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/dao-ham-nang-cao-14.png\" alt=\"\" width=\"100%\"><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Bai_tap_toan_hoc_nang_cao_TOAN_11_tu_dong\"><\/span>B\u00e0i t\u1eadp to\u00e1n h\u1ecdc n\u00e2ng cao TO\u00c1N 11 t\u1ef1 \u0111\u1ed9ng<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>V\u1edbi th\u00f4ng tin tr\u00ean, b\u1ea1n c\u00f3 th\u1ec3 th\u1ea5y c\u00e1c h\u00ecnh th\u1ee9c to\u00e1n h\u1ecdc khi nghi\u00ean c\u1ee9u c\u00e1c d\u1eabn xu\u1ea5t cao c\u1ea5p kh\u00e1 nhi\u1ec1u. Do \u0111\u00f3, \u0111\u1ec3 c\u00f3 th\u1ec3 chinh ph\u1ee5c ch\u00fang ch\u1ec9 theo c\u00e1ch l\u00e0 th\u1ef1c h\u00e0nh v\u00e0 th\u1ef1c hi\u1ec7n c\u00e1c b\u00e0i t\u1eadp v\u1ec1 ch\u00fang th\u01b0\u1eddng xuy\u00ean.<\/p>\n<p>V\u00ec v\u1eady, \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 b\u00e0i t\u1eadp li\u00ean quan \u0111\u1ebfn c\u00e1c lo\u1ea1i to\u00e1n h\u1ecdc tr\u00ean \u0111\u1ec3 ch\u00fang c\u00f3 th\u1ec3 th\u1ef1c h\u00e0nh nhi\u1ec1u h\u01a1n:<\/p>\n<p><img decoding=\"async\" class=\"lazyload\" src=\"https:\/\/external-content.duckduckgo.com\/iu\/?u=https:\/\/vnmedia2.monkeyuni.net\/upload\/web\/img\/dao-ham-nang-cao-15.png\" alt=\"(Ngu\u1ed3n: T\u00f3m t\u1eaft)\" width=\"100%\"><\/p>\n<p>Xem th\u00eam: \u0110\u1ec1 xu\u1ea5t m\u1ed9t c\u00f4ng th\u1ee9c nhanh ch\u00f3ng \u0111\u1ec3 gi\u00fap t\u00ednh to\u00e1n nhanh ch\u00f3ng, d\u1ec5 d\u00e0ng v\u00e0 ch\u00ednh x\u00e1c<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Ket_luan\"><\/span>K\u1ebft lu\u1eadn<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Tr\u00ean \u0111\u00e2y l\u00e0 m\u1ed9t b\u1ea3n t\u00f3m t\u1eaft ki\u1ebfn \u200b\u200bth\u1ee9c \u0111\u1ec3 gi\u00fap tr\u1ebb em hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 ch\u1ee9c n\u0103ng n\u00e2ng cao. Do \u0111\u00f3, c\u00f3 th\u1ec3 th\u1ea5y r\u1eb1ng \u0111i\u1ec1u n\u00e0y kh\u00f4ng d\u1ec5 d\u00e0ng, v\u00ec v\u1eady m\u1ecdi ng\u01b0\u1eddi c\u1ea7n bi\u1ebft c\u00f4ng th\u1ee9c, h\u00ecnh th\u1ee9c to\u00e1n h\u1ecdc v\u00e0 th\u1ef1c h\u00e0nh th\u01b0\u1eddng xuy\u00ean \u0111\u1ec3 chinh ph\u1ee5c ch\u00fang 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>D\u1eabn xu\u1ea5t n\u00e2ng cao l\u00e0 ki\u1ebfn \u200b\u200bth\u1ee9c kh\u00e1 kh\u00f3 kh\u0103n cho h\u1ecdc sinh l\u1edbp 11 tham gia v\u00e0o c\u00e1c h\u1ecdc sinh xu\u1ea5t s\u1eafc, k\u1ef3 thi c\u1ea5p t\u1ec9nh v\u00e0 qu\u1ed1c gia v\u00e0 th\u1eadm ch\u00ed trong c\u00e1c k\u1ef3 thi trung h\u1ecdc v\u00e0 \u0111\u1ea1i h\u1ecdc. V\u00ec v\u1eady, \u0111\u1ec3 gi\u00fap h\u1ecdc sinh th\u1ef1c hi\u1ec7n b\u00e0i t\u1eadp n\u00e0y t\u1ed1t, h\u00e3y&#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-21049","post","type-post","status-publish","format-standard","hentry","category-kien-thuc"],"_links":{"self":[{"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/posts\/21049","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=21049"}],"version-history":[{"count":2,"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/posts\/21049\/revisions"}],"predecessor-version":[{"id":25709,"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/posts\/21049\/revisions\/25709"}],"wp:attachment":[{"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/media?parent=21049"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/categories?post=21049"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ckconitsha.com\/vn\/wp-json\/wp\/v2\/tags?post=21049"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}