{"id":23,"date":"2023-09-17T11:07:18","date_gmt":"2023-09-17T11:07:18","guid":{"rendered":"https:\/\/mathority.org\/id\/jenis-diskontinuitas\/"},"modified":"2023-09-17T11:07:18","modified_gmt":"2023-09-17T11:07:18","slug":"jenis-diskontinuitas","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/jenis-diskontinuitas\/","title":{"rendered":"Jenis diskontinuitas"},"content":{"rendered":"<p>Di sini Anda akan mengetahui jenis diskontinuitas yang ada. Selain itu, Anda akan dapat melihat contoh semua jenis diskontinuitas dan Anda akan dapat berlatih dengan latihan yang diselesaikan tentang jenis-jenis diskontinuitas fungsi. <\/p>\n<p><strong><\/strong><\/p>\n<p><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-104\"><strong> <\/strong><\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcuales-son-todos-los-tipos-de-discontinuidades\"><\/span> Apa saja jenis diskontinuitas?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Ada tiga jenis diskontinuitas, yaitu:<\/p>\n<ul>\n<li> <strong>Diskontinuitas yang dapat dihindari<\/strong> : Batas lateral suatu fungsi pada suatu titik tidak berimpit dengan nilai fungsi tersebut.<\/li>\n<li> <strong>Diskontinuitas loncatan hingga yang tak terhindarkan<\/strong> : Batas lateral suatu fungsi pada suatu titik berbeda-beda.<\/li>\n<li> <strong>Diskontinuitas lompatan tak terhingga yang tak terelakkan<\/strong> : salah satu batas lateral fungsi memberikan tak terhingga atau tidak ada.<\/li>\n<\/ul>\n<p> Untuk menyelesaikan pemahaman konsepnya, kami akan menjelaskan masing-masing jenis diskontinuitas secara lebih rinci dan melihat contoh fungsi dengan ketiga jenis diskontinuitas tersebut.<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"discontinuidad-evitable\"><\/span> Diskontinuitas yang dapat dihindari <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-105\"><strong> <\/strong><\/div>\n<\/div>\n<p><strong>Diskontinuitas yang dapat dihindari<\/strong> adalah jenis diskontinuitas yang mempunyai fungsi pada suatu titik jika batasnya ada pada titik tersebut tetapi tidak berimpit dengan nilai fungsi atau bayangan fungsi tersebut tidak ada. <\/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-c26b9be97568ba85e1f8f22b568a2354_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\exists \\lim_{x \\to a} f(x) \\neq f(a) \\qquad | \\qquad \\displaystyle \\exists\\lim_{x \\to a} f(x) \\text{ y } \\ \\cancel{\\exists} \\ f(a)\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"367\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-columns are-vertically-aligned-top is-layout-flex wp-container-99\">\n<div class=\"wp-block-column is-vertically-aligned-top is-layout-flow\">\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/discontinuite-evitable-d-une-fonction.webp\" alt=\"diskontinuitas suatu fungsi yang dapat dihindari\" class=\"wp-image-1400\" width=\"276\" height=\"259\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<p> Batas lateral fungsi ini sama satu sama lain, tetapi berbeda dengan nilai fungsi pada titik tersebut. Oleh karena itu, fungsi tersebut menghadirkan diskontinuitas yang dapat dihindari. <\/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-ac5bdc61d377477ddcc788b7230bcfbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left. \\begin{array}{l}\\displaystyle \\lim_{x \\to a^-} f(x) =b \\\\[3ex] \\displaystyle \\lim_{x \\to a^+} f(x)=b \\end{array} \\right\\} \\ \\bm{\\longrightarrow} \\ \\lim_{x \\to a} f(x)=b\" title=\"Rendered by QuickLaTeX.com\" height=\"76\" width=\"276\" 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-9f61efde161e83828572db200f128ced_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\lim_{x \\to a} f(x)=b \\qquad f(a)=c\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"198\" 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-de211758fe99134c01f6eec8ea7c6348_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\exists \\lim_{x \\to a} f(x) \\neq f(a)\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"135\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-vertically-aligned-top is-layout-flow\">\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/discontinuite-evitable-d-une-fonction-sans-image.webp\" alt=\"diskontinuitas yang dapat dihindari dari suatu fungsi tanpa gambar\" class=\"wp-image-1401\" width=\"276\" height=\"259\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<p class=\"has-text-align-left\"> Fungsi pada contoh sebelumnya mempunyai diskontinuitas yang dapat dihindari karena batas lateral di x=a mempunyai nilai yang sama, namun bayangan fungsi pada titik tersebut tidak ada.<\/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-ac5bdc61d377477ddcc788b7230bcfbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left. \\begin{array}{l}\\displaystyle \\lim_{x \\to a^-} f(x) =b \\\\[3ex] \\displaystyle \\lim_{x \\to a^+} f(x)=b \\end{array} \\right\\} \\ \\bm{\\longrightarrow} \\ \\lim_{x \\to a} f(x)=b\" title=\"Rendered by QuickLaTeX.com\" height=\"76\" width=\"276\" 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-87531b3fbfb53b42e79af5a7305ffc37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\lim_{x \\to a} f(x)=b \\qquad \\cancel{\\exists} \\ f(a)\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"181\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Lihat:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/id\/batas-lateral\/\">batas lateral suatu fungsi<\/a><\/span> <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"discontinuidad-inevitable-de-salto-finito\"><\/span> Diskontinuitas lompatan terbatas yang tak terelakkan <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-106\"><strong> <\/strong><\/div>\n<p><strong><br \/><\/strong><\/p>\n<\/div>\n<p><strong>Diskontinuitas lompatan hingga yang tak terhindarkan<\/strong> adalah jenis diskontinuitas yang menampilkan suatu fungsi pada suatu titik ketika batas lateral fungsi pada titik tersebut tidak sama.<\/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-66fd7a55b2fad1a91622d738925d3304_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to a^-} f(x) \\neq \\lim_{x \\to a^+} f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"175\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> Misalnya, batas lateral dari fungsi terdefinisi sepotong-sepotong berikutnya pada titik perubahan definisi berbeda, sehingga fungsi tersebut mempunyai diskontinuitas lompatan hingga yang tak terelakkan pada titik tersebut. <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/saut-fini-inevitable-discontinuite.webp\" alt=\"diskontinuitas yang tak terhindarkan dari lompatan terbatas\" class=\"wp-image-1406\" width=\"275\" height=\"258\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4f7173f197ec50976b07e8ab608ec4aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\lim_{x \\to a^-} f(x)=b \\qquad  \\lim_{x \\to a^+} f(x)=c\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"254\" style=\"vertical-align: -14px;\"><\/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-66fd7a55b2fad1a91622d738925d3304_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to a^-} f(x) \\neq \\lim_{x \\to a^+} f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"175\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> Jenis diskontinuitas ini umumnya muncul dalam fungsi yang didefinisikan secara sepotong-sepotong (atau sepotong-sepotong).<\/p>\n<p> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Lihat:<\/strong> <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/id\">kesinambungan fungsi sepotong-sepotong<\/a><\/span> <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"discontinuidad-inevitable-de-salto-infinito\"><\/span> Lompatan tak terbatas Diskontinuitas yang tak terelakkan <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-107\"><strong> <\/strong><\/div>\n<\/div>\n<p><strong>Diskontinuitas lompatan tak hingga yang tak terelakkan<\/strong> adalah jenis diskontinuitas yang mempunyai fungsi pada saat salah satu batas lateral pada titik tersebut tak terhingga atau tidak ada. <\/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-a67f3a84bbd7cc965e932b0cb681912a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to a^-} f(x) = \\pm \\infty \\qquad \\lim_{x \\to a^+} f(x)= \\pm \\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"301\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-102\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<p> Limit kiri fungsi berikut menghasilkan bilangan real, sedangkan limit kanan menghasilkan tak terhingga. Oleh karena itu, fungsi tersebut menghadirkan diskontinuitas lompatan tak terbatas yang tak terelakkan. <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/saut-infini-discontinuite.webp\" alt=\"diskontinuitas lompatan tak terbatas\" class=\"wp-image-1411\" width=\"276\" height=\"259\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9e12509ad0839664b52f4224f0fc2e56_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\lim_{x \\to a^-} f(x)=b \\qquad \\lim_{x \\to a^+} f(x)=+\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"277\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow\">\n<p class=\"has-text-align-left\"> Di bawah ini Anda dapat melihat grafik fungsi yang kedua batas sisinya memberikan tak terhingga dan oleh karena itu fungsi tersebut memiliki diskontinuitas lompatan tak terhingga yang tak terelakkan. <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/discontinuite-infinie.webp\" alt=\"diskontinuitas yang tak terbatas\" class=\"wp-image-1412\" width=\"276\" height=\"259\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-99099617bca8a79ef975169f06f5c14e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\lim_{x \\to a^-} f(x)=-\\infty \\qquad \\lim_{x \\to a^+} f(x)=+\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"301\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p> Diskontinuitas jenis ini biasanya terjadi pada <span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/id\/fungsi-rasional\/\">fungsi rasional (atau pecahan)<\/a><\/span> . <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-tipos-de-discontinuidades\"><\/span> Latihan soal jenis diskontinuitas<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Latihan 1 <\/h3>\n<p><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-108\"><strong> <\/strong><\/div>\n<p><strong><br \/><\/strong><\/p>\n<\/div>\n<p>Tentukan jenis diskontinuitas fungsi sepotong-sepotong berikut di titik x=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-8185827ad36ab3921bb96eb5a6da21a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)= \\left\\{ \\begin{array}{lcl} -2x+1 &amp;  \\text{si} &amp;  x\\leq 3 \\\\[2ex] 4x - 5 &amp; \\text{si} &amp; x > 3 \\end{array} \\right.&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;65&#8243; width=&#8221;232&#8243; style=&#8221;vertical-align: 0px;&#8221;><\/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 solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Domain elemen pertama dari fungsi tersebut,<\/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-490b7f67d1b8735fc34485932796cef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-2x+1\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"61\" style=\"vertical-align: -2px;\"><\/p>\n<p> , seperti bagian kedua,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-82dafeb4abb94d9f10e1603d00cc3d59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4x-5\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"49\" style=\"vertical-align: 0px;\"><\/p>\n<p> , semuanya bilangan real karena merupakan fungsi polinomial.<\/p>\n<p class=\"has-text-align-left\"> Jadi, satu-satunya titik di mana fungsi tersebut dapat diskontinu adalah titik perhentian fungsi sepotong-sepotong. Oleh karena itu kami akan menghitung batas lateral pada tahap 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-e5aa03a9198a249e6cb09793b67754f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\lim_{x \\to 3^-} f(x)=\\lim_{x \\to 3} (-2x+1) = -2\\cdot 3+1=-5\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"349\" style=\"vertical-align: -14px;\"><\/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-c8e29ea20c018b8936dca674ada7590a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\lim_{x \\to 3^+} f(x)=\\lim_{x \\to 3}(4x-5)=4\\cdot 3-5=7\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"308\" style=\"vertical-align: -14px;\"><\/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-ffa1cc3d456b55bfef8f4a5999e072e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 3^-} f(x) \\neq \\lim_{x \\to 3^+} f(x)\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"174\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dua batas lateral di x=3 memberikan hasil yang berbeda. Oleh karena itu, titik x=3 merupakan diskontinuitas lompatan berhingga yang tidak dapat dihindari.<\/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 jenis diskontinuitas yang terdapat pada fungsi rasional berikut pada titik-titik yang tidak termasuk dalam domainnya: <\/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-44d5d873cde7d3365fc55943c61e78f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(x)= \\cfrac{x^2-4}{x+2}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"109\" style=\"vertical-align: -14px;\"><\/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 solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Logikanya, untuk menyelesaikan latihan ini, Anda harus mencari domain fungsinya terlebih dahulu. Jadi, karena ini adalah fungsi rasional, kita atur penyebutnya menjadi 0 dan selesaikan persamaan yang dihasilkan: <\/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-24e301fa7ea2e8d9f0041192d9a84927_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x+2=0\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"73\" 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-01f282abd343bbe6b83c45e54b86c6ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=-2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" 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-fbd5fe607cd89a42b4db6e52bc047c56_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=\"152\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, fungsi tersebut kontinu di semua titik kecuali x=-2, jadi mari kita lihat jenis diskontinuitas di titik x=-2. Untuk melakukan ini, kita menghitung limit fungsi di 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-bf6f3ceb66dcd630224097f54365ef24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -2} \\cfrac{x^2-4}{x+2} = \\cfrac{ (-2)^2-4}{-2+2}= \\cfrac{0}{0}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"227\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Tapi kita mendapatkan nol ketidakpastian antara nol, jadi kita memfaktorkan polinomial pembilang dan penyebutnya dan menyederhanakannya:<\/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-e939f4fee6ac399b046fa809daab31c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -2} \\cfrac{x^2-4}{x+2}=\\lim_{x \\to -2} \\cfrac{ (x-2)\\cancel{(x+2)}}{\\cancel{x+2}}  =\\lim_{x \\to -2} (x-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"385\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita selesaikan batasannya:<\/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-5e05e20f45a4d8b2fbe26bb0d3ae5091_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -2} (x-2) =-2-2=-4\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"217\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Akibatnya, limit fungsi di titik x=-2 memang ada dan menghasilkan -4. Sekarang mari kita periksa apakah itu ada <\/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-80b84d482e50cebc375313e005736c97_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(-2):\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"56\" style=\"vertical-align: -5px;\"><\/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-c58a37ec90f203b24b790c7cfacaf2c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(-2)=\\cfrac{(-2)^2-4}{-2+2}= \\cfrac{4-4}{0} = \\cfrac{0}{0} \\quad \\bm{\\longrightarrow} \\quad \\cancel{\\exists} \\ f(2)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"359\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dalam menghitung gambaran suatu fungsi, ketidakpastian 0\/0 tidak dapat disederhanakan dan tidak mempunyai penyelesaian. JADI<\/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-7ee53c0d0a8e84c09c63d946334cd34b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"47\" style=\"vertical-align: -5px;\"><\/p>\n<p> tidak ada.<\/p>\n<p class=\"has-text-align-left\"> Kesimpulannya, limit fungsi di x=-2 ada, tetapi<\/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-7ee53c0d0a8e84c09c63d946334cd34b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f(-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"47\" style=\"vertical-align: -5px;\"><\/p>\n<p> Tidak. Oleh karena itu, x=-2 adalah diskontinuitas yang dapat dihindari.<\/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><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-110\"><strong> <\/strong><\/div>\n<p><strong><br \/><\/strong><\/p>\n<\/div>\n<p>Analisislah kontinuitas 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-59ee18262fd6f3427ebab6ceabb22868_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x)= \\frac{2}{x-5}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"101\" 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 solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Untuk mengetahui apakah suatu fungsi kontinu, pertama-tama kita harus menghitung domainnya. Oleh karena itu, kami menetapkan penyebut fungsi rasional sama dengan nol untuk melihat titik mana 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-845b4cbd750afedb8e09b0ed6a9809c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x-5=0\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" 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-8ddab230605c435eb8b7408a736d3e77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=5\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" 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-96a28ea816d10d62e90dd13ad1aa79c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{Dom } f = \\mathbb{R} - \\{5\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"138\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, fungsi tersebut kontinu di semua titik kecuali x=5. Jadi mari kita lihat jenis diskontinuitas x=5 dengan menghitung limit 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-976747f92d549df73e0cf24ee4ff2953_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 5} \\frac{2}{x-5} = \\frac{2}{5-5} = \\frac{2}{0} = \\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"220\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Kita mendapati diri kita dihadapkan pada ketidakpastian suatu bilangan dibagi 0. Oleh karena itu, kita menghitung batas lateral fungsi tersebut di x=5: <\/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-98edca328c2637f8b7ae59dde1789f44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 5^{-}} \\frac{2}{x-5}=\\frac{2}{4,999-5}=\\frac{2}{-0}= \\bm{-\\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"292\" style=\"vertical-align: -16px;\"><\/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-378f3bdf00d4375069e68f4fc8547ca0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 5^{+}} \\frac{2}{x-5}=\\frac{2}{5,001-5}=\\frac{2}{+0}=\\bm{+\\infty}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"292\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Limit kiri fungsi di x=5 menghasilkan minus tak terhingga dan limit kanan menghasilkan plus tak terhingga. Oleh karena itu, fungsi tersebut memiliki diskontinuitas lompatan tak terhingga pada x = 5, karena setidaknya satu batas lateral pada titik ini cenderung tak terhingga.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> Latihan 4<\/h3>\n<p> Tentukan semua diskontinuitas fungsi sepotong-sepotong yang ditunjukkan pada grafik berikut: <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercice-resolu-discontinuites-de-fonctions.webp\" alt=\"latihan menyelesaikan diskontinuitas fungsi\" class=\"wp-image-1433\" width=\"400\" height=\"344\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\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 solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Untuk menggambar fungsinya Anda harus menaikkan pensil di x=-2, di x=1 dan di x=4. Oleh karena itu, fungsinya terputus-putus pada ketiga titik ini.<\/p>\n<p class=\"has-text-align-left\"> Pada x=-2, limit ruas kirinya adalah +\u221e dan limit ruas kanannya adalah 3. Jadi, karena salah satu limit sisinya tak terhingga, fungsi tersebut mempunyai diskontinuitas lompat tak terhingga pada 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-eff79ace33659ceb8203e6e27f38fe35_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -2^-} f(x) = +\\infty \\ \\neq \\ \\lim_{x \\to -2^+} f(x) = 3\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"296\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Limit fungsi di x=1 adalah 0 dan, sebaliknya, nilai fungsi di x=1 sama dengan 2. Oleh karena itu, fungsi tersebut menyajikan diskontinuitas yang dapat dihindari 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-3a616cc5210984ffeed3525a219dd53a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 1^-} f(x) =   \\lim_{x \\to 1^+} f(x) = 0 \\ \\bm{\\longrightarrow} \\ \\lim_{x \\to 1} f(x) = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"350\" style=\"vertical-align: -14px;\"><\/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-9a3aea29db1a67d08d91d510033ffd1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 1} f(x) =  0 \\neq  f(1) = 2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"187\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Pada x = 4, limit ruas kirinya adalah -3 dan limit ruas kanannya adalah 1. Oleh karena itu, karena kedua limit sisi tersebut berbeda dan tidak ada satu pun yang menghasilkan tak terhingga, maka fungsi tersebut pasti memiliki diskontinuitas lompatan berhingga di x =4. <\/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-b758745a987f927350b2d885009c3a87_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 4^-} f(x) = -3 \\ \\neq \\ \\lim_{x \\to 4^+} f(x) = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"265\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Latihan 5<\/h3>\n<p> Temukan semua asimtot dan diskontinuitas fungsi yang ditunjukkan pada grafik berikut: <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercice-resolu-types-de-discontinuites-d-une-fonction.webp\" alt=\"menyelesaikan latihan tentang jenis-jenis diskontinuitas suatu fungsi\" class=\"wp-image-1435\" width=\"537\" height=\"453\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\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 solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> <strong><span style=\"text-decoration: underline;\">Asimtot<\/span><\/strong><\/p>\n<p class=\"has-text-align-left\"> Fungsinya sangat dekat dengan garis vertikal x=3 tetapi tidak pernah menyentuhnya. Selain itu, batas lateral kiri di x=3 adalah +\u221e dan batas lateral kanan adalah -\u221e. Oleh karena itu, x=3 adalah asimtot vertikal.<\/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-89bdb1598b6153cec4e9efce7b0927b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 3^-} f(x)=+\\infty \\qquad \\lim_{x \\to 3^+} f(x)=-\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"300\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Hal yang sama terjadi pada garis horizontal y=-1, fungsinya sangat dekat dengan y=-1 tetapi tidak pernah melintasinya. Selain itu, limit fungsi ketika x mendekati +\u221e dan -\u221e adalah -1. Oleh karena itu, y=-1 adalah asimtot horizontal.<\/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-d0f0ee09aaa4a3bfa4fcb77ecc84640a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to +\\infty} f(x)=-1 \\qquad \\lim_{x \\to -\\infty} f(x)=-1\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"297\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> <strong><span style=\"text-decoration: underline;\">Diskontinuitas<\/span><\/strong><\/p>\n<p class=\"has-text-align-left\"> Pada x=6 fungsinya terputus karena ada titik terbuka. Limit saat x mendekati 6 adalah -1,4 tetapi f(6)=1. Oleh karena itu, fungsi tersebut mempunyai diskontinuitas yang dapat dihindari pada x=6 karena nilai limitnya tidak sesuai dengan nilai 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-33612be383c71fea04c8c886710f7f10_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left. \\begin{array}{l} \\displaystyle \\lim_{x \\to 6^-} f(x)=-1,4\\\\[3ex] \\displaystyle \\lim_{x \\to 6^+} f(x)=-1,4 \\end{array} \\right\\} \\bm{\\longrightarrow} \\lim_{x \\to 6} f(x)=-1,4\" title=\"Rendered by QuickLaTeX.com\" height=\"76\" width=\"326\" 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-647b9aea6cc8b605d7e8bc7d5e83ee64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\lim_{x \\to 6} f(x)=-1,4 \\neq f(6)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"217\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Pada x=-3 batas lateralnya tidak berimpit dan tidak ada yang menghasilkan tak terhingga. Oleh karena itu, fungsi tersebut memiliki diskontinuitas lompatan terbatas yang tak terelakkan pada x=-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-3f7d2a2c7abbc525adfcc7576b449f1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to -3^-} f(x)=-2 \\neq \\lim_{x \\to -3^+} f(x)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"275\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan yang terakhir, fungsi tersebut mempunyai diskontinuitas lompatan tak terhingga pada x = 3, karena setidaknya satu batas lateral pada titik ini menghasilkan tak terhingga. <\/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-89bdb1598b6153cec4e9efce7b0927b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lim_{x \\to 3^-} f(x)=+\\infty \\qquad \\lim_{x \\to 3^+} f(x)=-\\infty\" title=\"Rendered by QuickLaTeX.com\" height=\"28\" width=\"300\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<p><strong><\/strong><\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-109\"><strong> <\/strong><\/div>\n<p><strong><br \/><\/strong><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Di sini Anda akan mengetahui jenis diskontinuitas yang ada. Selain itu, Anda akan dapat melihat contoh semua jenis diskontinuitas dan Anda akan dapat berlatih dengan latihan yang diselesaikan tentang jenis-jenis diskontinuitas fungsi. Apa saja jenis diskontinuitas? Ada tiga jenis diskontinuitas, yaitu: Diskontinuitas yang dapat dihindari : Batas lateral suatu fungsi pada suatu titik tidak berimpit &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/jenis-diskontinuitas\/\"> <span class=\"screen-reader-text\">Jenis diskontinuitas<\/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-23","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>\u25b7 Apa saja jenis diskontinuitas?<\/title>\n<meta name=\"description\" content=\"Kami menjelaskan semua jenis diskontinuitas (lompatan terbatas yang dapat dihindari, tak terelakkan, dan tak terbatas). \u2705 Latihan terpecahkan untuk semua jenis diskontinuitas. \u2705\" \/>\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\/jenis-diskontinuitas\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Apa saja jenis diskontinuitas?\" \/>\n<meta property=\"og:description\" content=\"Kami menjelaskan semua jenis diskontinuitas (lompatan terbatas yang dapat dihindari, tak terelakkan, dan tak terbatas). \u2705 Latihan terpecahkan untuk semua jenis diskontinuitas. \u2705\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/id\/jenis-diskontinuitas\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-09-17T11:07:18+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c26b9be97568ba85e1f8f22b568a2354_l3.png\" \/>\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=\"5 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/id\/jenis-diskontinuitas\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/id\/jenis-diskontinuitas\/\"},\"author\":{\"name\":\"Tim Mathority\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38\"},\"headline\":\"Jenis diskontinuitas\",\"datePublished\":\"2023-09-17T11:07:18+00:00\",\"dateModified\":\"2023-09-17T11:07:18+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/id\/jenis-diskontinuitas\/\"},\"wordCount\":1039,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/id\/#organization\"},\"articleSection\":[\"Batasan fungsi\"],\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/id\/jenis-diskontinuitas\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/id\/jenis-diskontinuitas\/\",\"url\":\"https:\/\/mathority.org\/id\/jenis-diskontinuitas\/\",\"name\":\"\u25b7 Apa saja jenis diskontinuitas?\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/id\/#website\"},\"datePublished\":\"2023-09-17T11:07:18+00:00\",\"dateModified\":\"2023-09-17T11:07:18+00:00\",\"description\":\"Kami menjelaskan semua jenis diskontinuitas (lompatan terbatas yang dapat dihindari, tak terelakkan, dan tak terbatas). \u2705 Latihan terpecahkan untuk semua jenis diskontinuitas. \u2705\",\"breadcrumb\":{\"@id\":\"https:\/\/mathority.org\/id\/jenis-diskontinuitas\/#breadcrumb\"},\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathority.org\/id\/jenis-diskontinuitas\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathority.org\/id\/jenis-diskontinuitas\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathority.org\/id\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Jenis diskontinuitas\"}]},{\"@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":"\u25b7 Apa saja jenis diskontinuitas?","description":"Kami menjelaskan semua jenis diskontinuitas (lompatan terbatas yang dapat dihindari, tak terelakkan, dan tak terbatas). \u2705 Latihan terpecahkan untuk semua jenis diskontinuitas. \u2705","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\/jenis-diskontinuitas\/","og_locale":"id_ID","og_type":"article","og_title":"\u25b7 Apa saja jenis diskontinuitas?","og_description":"Kami menjelaskan semua jenis diskontinuitas (lompatan terbatas yang dapat dihindari, tak terelakkan, dan tak terbatas). \u2705 Latihan terpecahkan untuk semua jenis diskontinuitas. \u2705","og_url":"https:\/\/mathority.org\/id\/jenis-diskontinuitas\/","article_published_time":"2023-09-17T11:07:18+00:00","og_image":[{"url":"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c26b9be97568ba85e1f8f22b568a2354_l3.png"}],"author":"Tim Mathority","twitter_card":"summary_large_image","twitter_misc":{"Ditulis oleh":"Tim Mathority","Estimasi waktu membaca":"5 menit"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathority.org\/id\/jenis-diskontinuitas\/#article","isPartOf":{"@id":"https:\/\/mathority.org\/id\/jenis-diskontinuitas\/"},"author":{"name":"Tim Mathority","@id":"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38"},"headline":"Jenis diskontinuitas","datePublished":"2023-09-17T11:07:18+00:00","dateModified":"2023-09-17T11:07:18+00:00","mainEntityOfPage":{"@id":"https:\/\/mathority.org\/id\/jenis-diskontinuitas\/"},"wordCount":1039,"commentCount":0,"publisher":{"@id":"https:\/\/mathority.org\/id\/#organization"},"articleSection":["Batasan fungsi"],"inLanguage":"id","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathority.org\/id\/jenis-diskontinuitas\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathority.org\/id\/jenis-diskontinuitas\/","url":"https:\/\/mathority.org\/id\/jenis-diskontinuitas\/","name":"\u25b7 Apa saja jenis diskontinuitas?","isPartOf":{"@id":"https:\/\/mathority.org\/id\/#website"},"datePublished":"2023-09-17T11:07:18+00:00","dateModified":"2023-09-17T11:07:18+00:00","description":"Kami menjelaskan semua jenis diskontinuitas (lompatan terbatas yang dapat dihindari, tak terelakkan, dan tak terbatas). \u2705 Latihan terpecahkan untuk semua jenis diskontinuitas. \u2705","breadcrumb":{"@id":"https:\/\/mathority.org\/id\/jenis-diskontinuitas\/#breadcrumb"},"inLanguage":"id","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathority.org\/id\/jenis-diskontinuitas\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathority.org\/id\/jenis-diskontinuitas\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathority.org\/id\/"},{"@type":"ListItem","position":2,"name":"Jenis diskontinuitas"}]},{"@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"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/posts\/23","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/comments?post=23"}],"version-history":[{"count":0,"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/posts\/23\/revisions"}],"wp:attachment":[{"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/media?parent=23"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/categories?post=23"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/tags?post=23"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}