{"id":377,"date":"2023-07-04T01:25:58","date_gmt":"2023-07-04T01:25:58","guid":{"rendered":"https:\/\/mathority.org\/id\/asimtot-vertikal\/"},"modified":"2023-07-04T01:25:58","modified_gmt":"2023-07-04T01:25:58","slug":"asimtot-vertikal","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/asimtot-vertikal\/","title":{"rendered":"Asimtot vertikal"},"content":{"rendered":"<p>Di sini Anda akan menemukan asimtot vertikal suatu fungsi (dengan contoh). Kami juga menjelaskan cara mencari asimtot vertikal suatu fungsi dan, sebagai tambahan, Anda akan dapat berlatih dengan latihan yang diselesaikan langkah demi langkah. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-una-asintota-vertical\"><\/span> Apa yang dimaksud dengan asimtot vertikal?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Asimtot vertikal suatu fungsi adalah garis vertikal yang grafiknya mendekati tak terhingga tanpa pernah melintasinya.<\/strong> Oleh karena itu, persamaan asimtot vertikal adalah <em>x=k<\/em> , dengan <em>k<\/em> adalah nilai asimtot vertikal.<\/p>\n<p> Artinya, <strong><em>k<\/em> adalah asimtot vertikal jika limit fungsi ketika <em>x<\/em> mendekati <em>k<\/em> tidak terhingga.<\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/asymptote-verticale.webp\" alt=\"apa itu asimtot vertikal\" class=\"wp-image-1281\" width=\"320\" height=\"255\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-calcular-la-asintota-vertical-de-una-funcion\"><\/span> Cara menghitung asimtot vertikal suatu fungsi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Untuk menghitung asimtot vertikal suatu fungsi, langkah-langkah berikut harus diikuti:<\/p>\n<ol style=\"color:#FF8A05; font-weight: bold;border:\">\n<li style=\"margin-bottom:12px\"> <span style=\"color:#101010;font-weight: normal;\">Temukan domain dari fungsi tersebut. Jika semua titik berada dalam domain, fungsi tersebut tidak memiliki asimtot vertikal.<\/span><\/li>\n<li style=\"margin-bottom:12px\"> <span style=\"color:#101010;font-weight: normal;\">Hitung limit fungsi pada titik-titik yang tidak berada dalam domain.<\/span><\/li>\n<li> <span style=\"color:#101010;font-weight: normal;\">Asimtot vertikal dari fungsi tersebut adalah semua nilai yang limitnya memberikan tak terhingga.<\/span><\/li>\n<\/ol>\n<p> Perhatikan bahwa suatu fungsi dapat memiliki lebih dari satu asimtot vertikal. Misalnya, <u style=\"text-decoration-color:#FF9B28;\">grafik fungsi tangen memiliki banyak asimtot vertikal yang tak terhingga banyaknya.<\/u><\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Lihat :<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/id\/fungsi-tangen\/\">ciri-ciri fungsi tangen<\/a><\/span> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-asintota-vertical\"><\/span> Contoh asimtot vertikal<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Sebagai contoh, kita akan menemukan semua asimtot dari fungsi rasional berikut sehingga Anda dapat melihat cara kerjanya:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0425f9cc254c22f6e28ad2186732cfdf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)=\\cfrac{1}{x-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"101\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Secara umum, titik-titik yang terdapat asimtot vertikal tidak termasuk dalam domain fungsi. Oleh karena itu, pertama-tama kita akan menghitung domain dari fungsi tersebut.<\/p>\n<p> Ini adalah fungsi rasional, jadi kita melihat saat penyebutnya hilang untuk menentukan titik-titik yang tidak termasuk dalam domain:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e0aacb848a27943fc0e8fba70f545d78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x-2=0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"73\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c657687cbbf5ea9a7545edb42190e592_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, domain dari fungsi tersebut adalah semua bilangan real kecuali x=2:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-298deba50795b5fc3979441d68ef3ed8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R} - \\{2\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"138\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Jadi <strong>x=2 bisa menjadi asimtot vertikal dari fungsi tersebut.<\/strong> Untuk memverifikasi ini, kita harus menghitung limit fungsi pada titik ini:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-acc5425df8da5bffaa5ee31c29284a86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 2} \\frac{1}{x-2}=\\frac{1}{2-2}=\\frac{1}{0}=\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"220\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Dalam hal ini kita telah memperoleh ketidakpastian suatu bilangan antara nol dan oleh karena itu, untuk menyelesaikan limitnya kita harus menghitung limit lateralnya untuk mengetahui apakah bilangan tersebut plus tak terhingga, dikurangi tak terhingga, atau limitnya tidak ada. Akan tetapi, ketika kita menghitung asimtot vertikal, kita tidak perlu melakukan batas lateral, namun memperoleh ketidakpastian ini sudah cukup untuk mengatakan bahwa ini adalah asimtot vertikal.<\/p>\n<p> Singkatnya, karena limit fungsi ketika x mendekati 2 menghasilkan tak terhingga, <strong>x=2 adalah asimtot vertikal.<\/strong><\/p>\n<p> Di bawah ini adalah fungsi yang direpresentasikan secara grafis. Seperti yang Anda lihat, garis tersebut sangat dekat dengan garis x=2 (dari kiri dan kanan) namun tidak pernah berpotongan karena merupakan asimtot vertikal: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-dasymptote-verticale.webp\" alt=\"contoh asimtot vertikal\" class=\"wp-image-1294\" width=\"431\" height=\"382\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Selain itu, kita dapat menyimpulkan dari grafik batas lateral fungsi di titik x=2: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bae3e5d8a91ed8bfd4d59e8cf2b2e046_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 2^-} \\frac{1}{x-2} = -\\infty \\qquad  \\lim_{x \\to 2^+} \\frac{1}{x-2} = +\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"320\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-asintotas-verticales\"><\/span> Memecahkan masalah asimtot vertikal<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Latihan 1<\/h3>\n<p> Hitung asimtot vertikal dari fungsi rasional berikut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-911fac1ac9244ceb5c6bff7e4bd14633_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=\\frac{3x-1}{2x-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"110\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Tidak ada rumus untuk menghitung asimtot vertikal suatu fungsi, tetapi Anda harus mencari domain fungsi tersebut dan melihat di titik mana fungsi tersebut tidak terdefinisi, limitnya memberikan tak terhingga.<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, kita menetapkan penyebut fungsi rasional sama dengan 0 untuk mencari titik-titik yang tidak termasuk dalam domain: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-eda4c745b07ad63c3060964038aebf0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x -1 =0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"82\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0323089c11e731c307ef7664ecb6710b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x= 1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"51\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-971df94c9decb86065329338ff4b81ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x = \\cfrac{1}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"45\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi, domain dari fungsi tersebut adalah semua bilangan real kecuali x=1\/2:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d45cfed65d2da3a61311dce298a529a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R} - \\left\\{ \\cfrac{1}{2} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"149\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi x=1\/2 bisa menjadi asimtot vertikal. Untuk memeriksanya, kami menghitung limit fungsi pada titik ini:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-55047465393cc2a65a7214fa64eac93d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to \\frac{1}{2} } \\cfrac{3x-1}{2x-1} = \\cfrac{3\\cdot\\cfrac{1}{2}-1}{2\\cdot\\cfrac{1}{2}-1} = \\cfrac{ \\cfrac{3}{2} -1 }{\\cfrac{2}{2} -1 } = \\cfrac{ \\cfrac{1}{2} }{1-1}=\\cfrac{\\cfrac{1}{2}}{0} =\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"84\" width=\"383\" style=\"vertical-align: -39px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi <strong>x=1\/2 adalah asimtot vertikal<\/strong> , karena limit fungsi pada titik ini menghasilkan tak terhingga.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> Latihan 2<\/h3>\n<p> Temukan semua asimtot vertikal dari fungsi pecahan berikut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cc3badbfcece4b7976d30989606ca685_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=\\frac{2x+1}{x^2-9}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"110\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Pertama, kita atur penyebut pecahan menjadi nol untuk melihat nilai mana yang tidak berada dalam domain fungsi:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ce55adbc277e9378607d68bce8ef19fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2-9=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"81\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Kami memecahkan persamaan kuadrat tidak lengkap: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-05112cb5a98f653cd1920fb40e5ef9a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2=9\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"50\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0505454de5d542ace3e698cb903893ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\pm 3\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"57\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, domain dari fungsi rasional adalah:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c91231eb4c883e8c625dba58f070307f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R} - \\left\\{3, -3\\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"168\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi, untuk menentukan mana dari dua nilai ini yang merupakan asimtot vertikal, kita mencari limit fungsi di setiap titik: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1a56d9ceafa2628b7a80603109ceafc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 3}\\frac{2x+1}{x^2-9}=\\frac{2\\cdot3+1}{3^2-9}=\\frac{7}{9-9}=\\frac{7}{0}=\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"317\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-944d84ad3ab51829df2623a4467cc16a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to -3}\\frac{2x+1}{x^2-9}=\\frac{2\\cdot(-3)+1}{(-3)^2-9}=\\frac{-5}{9-9}=\\frac{-5}{0}=\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"369\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Kedua limit tersebut menghasilkan tak terhingga, jadi <strong>x=3 dan x=-3 adalah dua asimtot vertikal dari fungsi soal<\/strong> .<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> Latihan 3<\/h3>\n<p> Temukan, jika Anda punya, semua asimtot vertikal dari fungsi rasional berikut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1dd8356a2f682824a334f15826b31c89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)=\\frac{x+3}{x^2+2x-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"150\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Lihat:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/id\/nol-antara-nol-0-0-ketidakpastian\/\">nol di antara nol ketidakpastian<\/a><\/span> <\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E6F9EF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E6F9EF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Pertama, kita selesaikan persamaan penyebut kuadrat untuk mencari nilai yang menghilangkan penyebut pecahan: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d5c5fd813f4a2456efa315766ad90ced_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+2x-3=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"122\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9b2170358d5d1719077695aba5afa02e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\displaystyle x&amp;=\\cfrac{-b\\pm\\sqrt{b^2-4ac}}{2a}=\\cfrac{-2\\pm\\sqrt{2^2-4\\cdot1\\cdot(-3)}}{2\\cdot1}=\\\\[3ex]\\displaystyle &amp;=\\cfrac{-2\\pm\\sqrt{16}}{2}=\\cfrac{-2\\pm 4}{2}=\\begin{cases}\\cfrac{-2+4}{2}=1\\\\[3ex]\\cfrac{-2-4}{2}=-3\\end{cases}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"172\" width=\"396\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi domain fungsinya adalah:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fd230a1caa7456bca8746870a6d0264a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R} - \\left\\{1, -3\\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"168\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi, pertama-tama kita hitung limit fungsi tersebut di x=1:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3784526cad2b36766a213c13a5938c6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 1}\\frac{x+3}{x^2+2x-3}=\\frac{1+3}{1^2+2\\cdot 1-3}=\\frac{4}{0}=\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"328\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan sebaliknya, kita menyelesaikan limit fungsi ketika x cenderung ke -3:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f0e96a48986cd110e04058e3545290a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}\\displaystyle\\lim_{x \\to -3}\\frac{x+3}{x^2+2x-3}=\\frac{-3+3}{(-3)^2+2\\cdot(-3)-3}=\\frac{0}{0}=\\\\[3ex]\\displaystyle =\\lim_{x \\to -3}\\frac{\\cancel{x+3}}{(x-1)\\cancel{(x+3)}}=\\lim_{x \\to -3}\\frac{1}{x-1}=\\frac{1}{-3-1}=-\\frac{1}{4}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"94\" width=\"413\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Limit sebelumnya memberikan bentuk tak tentu nol di antara nol, jadi untuk menyelesaikannya kita perlu memfaktorkan polinomialnya. <u style=\"text-decoration-color:#FF9B28;\">Jika Anda ragu tentang cara kami memecahkan batasan tersebut, Anda dapat melihat penjelasan lengkap tentang cara mengatasi ketidakpastian jenis ini di tautan ke pernyataan latihan.<\/u><\/p>\n<p class=\"has-text-align-left\"> Dalam hal ini, hanya limit fungsi di titik x=1 yang menghasilkan tak terhingga, jadi <strong>x=1 adalah satu-satunya asimtot vertikal fungsi tersebut<\/strong> .<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Di sini Anda akan menemukan asimtot vertikal suatu fungsi (dengan contoh). Kami juga menjelaskan cara mencari asimtot vertikal suatu fungsi dan, sebagai tambahan, Anda akan dapat berlatih dengan latihan yang diselesaikan langkah demi langkah. Apa yang dimaksud dengan asimtot vertikal? Asimtot vertikal suatu fungsi adalah garis vertikal yang grafiknya mendekati tak terhingga tanpa pernah melintasinya. &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/asimtot-vertikal\/\"> <span class=\"screen-reader-text\">Asimtot vertikal<\/span> Selengkapnya &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[43],"tags":[],"class_list":["post-377","post","type-post","status-publish","format-standard","hentry","category-batasan-fungsi"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Asimtot vertikal - Mathority<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/id\/asimtot-vertikal\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Asimtot vertikal - Mathority\" \/>\n<meta property=\"og:description\" content=\"Di sini Anda akan menemukan asimtot vertikal suatu fungsi (dengan contoh). 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Asimtot vertikal suatu fungsi adalah garis vertikal yang grafiknya mendekati tak terhingga tanpa pernah melintasinya. &hellip; Asimtot vertikal Selengkapnya &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/id\/asimtot-vertikal\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-04T01:25:58+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/asymptote-verticale.webp\" \/>\n<meta name=\"author\" content=\"Tim Mathority\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Ditulis oleh\" \/>\n\t<meta name=\"twitter:data1\" content=\"Tim Mathority\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimasi waktu membaca\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/id\/asimtot-vertikal\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/id\/asimtot-vertikal\/\"},\"author\":{\"name\":\"Tim Mathority\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38\"},\"headline\":\"Asimtot vertikal\",\"datePublished\":\"2023-07-04T01:25:58+00:00\",\"dateModified\":\"2023-07-04T01:25:58+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/id\/asimtot-vertikal\/\"},\"wordCount\":686,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/id\/#organization\"},\"articleSection\":[\"Batasan fungsi\"],\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/id\/asimtot-vertikal\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/id\/asimtot-vertikal\/\",\"url\":\"https:\/\/mathority.org\/id\/asimtot-vertikal\/\",\"name\":\"Asimtot vertikal - Mathority\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/id\/#website\"},\"datePublished\":\"2023-07-04T01:25:58+00:00\",\"dateModified\":\"2023-07-04T01:25:58+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathority.org\/id\/asimtot-vertikal\/#breadcrumb\"},\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathority.org\/id\/asimtot-vertikal\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathority.org\/id\/asimtot-vertikal\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathority.org\/id\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Asimtot vertikal\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathority.org\/id\/#website\",\"url\":\"https:\/\/mathority.org\/id\/\",\"name\":\"Mathority\",\"description\":\"Di mana rasa ingin tahu bertemu dengan perhitungan!\",\"publisher\":{\"@id\":\"https:\/\/mathority.org\/id\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathority.org\/id\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"id\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathority.org\/id\/#organization\",\"name\":\"Mathority\",\"url\":\"https:\/\/mathority.org\/id\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"id\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/mathority.org\/id\/wp-content\/uploads\/2023\/09\/mathority-logo.png\",\"contentUrl\":\"https:\/\/mathority.org\/id\/wp-content\/uploads\/2023\/09\/mathority-logo.png\",\"width\":703,\"height\":151,\"caption\":\"Mathority\"},\"image\":{\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/logo\/image\/\"}},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38\",\"name\":\"Tim Mathority\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"id\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"caption\":\"Tim Mathority\"},\"sameAs\":[\"http:\/\/mathority.org\/id\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Asimtot vertikal - Mathority","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":"https:\/\/mathority.org\/id\/asimtot-vertikal\/","og_locale":"id_ID","og_type":"article","og_title":"Asimtot vertikal - Mathority","og_description":"Di sini Anda akan menemukan asimtot vertikal suatu fungsi (dengan contoh). 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