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Matematiğin tüm konularını #öğrenbitsin ile kamp kamp bitiriyoruz. Sıra geldi Limit konusuna. oluyor. Telegram Grubumuza Aşağıdaki Linkten Ulaşabilirsin↙️ https://t.me/rehber_matem...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/2238828/99379a6709055f3ad199b85273e5d2d3/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/vjQv9QEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"2","reqid":"1769514051874146-11411995624285502602-balancer-l7leveler-kubr-yp-klg-278-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769514051874146-11411995624285502602-balancer-l7leveler-kubr-yp-klg-278-BAL&text=videoid:12183751211292253248","teaser":[{"list":{"type":"unordered","items":["Bu video, Mehmet Hoca olarak hitap edilen bir matematik öğretmeninin \"Limit 7\" kampının son dersini sunduğu eğitim içeriğidir. Öğretmen, \"RM tayfa\" olarak adlandırdığı öğrencilere hitap etmektedir.","Videoda fonksiyonların sürekliliği konusu detaylı şekilde ele alınmaktadır. Öğretmen, mutlak değerli fonksiyonların sürekliliği, parçalı fonksiyonların sürekliliği, köklü ifadelerin sürekliliği, rasyonel ifadelerin sürekliliği ve logaritma fonksiyonlarının sürekliliği gibi konuları örneklerle açıklamaktadır. Ayrıca, fonksiyonların süreksizlik noktalarını bulma, sağdan ve soldan limit hesaplamaları ve süreklilik aralıklarını belirleme teknikleri gösterilmektedir.","Video, ÖSYM sınavlarında çıkabilecek zorlu soruların çözüm yöntemlerini içermekte ve bir sonraki derste türev konusunun ele alınacağı belirtilmektedir. Öğretmen, mutlak değerli fonksiyonların en geniş tanım aralığını bulma, toplam ve çarpım fonksiyonlarının sürekliliği, bileşke fonksiyonların sürekliliği gibi konuları da örneklerle pekiştirmektedir."]},"endTime":2140,"title":"Limit Kampı Son Dersi: Fonksiyonların Sürekliliği","beginTime":0}],"fullResult":[{"index":0,"title":"Limit Kampının Sonu","list":{"type":"unordered","items":["Limit, türev ve integral kampının sonuna gelinmiş bulunuyor.","Bu kamp, bugüne kadar yapılan en sağlam limit kampı olarak değerlendiriliyor.","Kamp boyunca en zor ÖSYM soruları çözülmüş ve öğrenciler terletilmiş."]},"beginTime":0,"endTime":49,"href":"/video/preview/12183751211292253248?parent-reqid=1769514051874146-11411995624285502602-balancer-l7leveler-kubr-yp-klg-278-BAL&text=Limi7edDesigns&t=0&ask_summarization=1"},{"index":1,"title":"Limitin Yedinci ve Son Videosu","list":{"type":"unordered","items":["Limitin yedinci ve son videosunda en önemli noktalarda muhteşem sorularla ders bitirilecek.","Ayrılık şarkısı dersin sonunda yer alacak ve ardından yeni bir kamp başlayacak.","Bazı öğrenciler limiti hakkını vere vere bitirdiklerini ve karşılarına gelebilecek zor sorulara baktıklarını belirtmişler."]},"beginTime":49,"endTime":93,"href":"/video/preview/12183751211292253248?parent-reqid=1769514051874146-11411995624285502602-balancer-l7leveler-kubr-yp-klg-278-BAL&text=Limi7edDesigns&t=49&ask_summarization=1"},{"index":2,"title":"Mutlak Değer Fonksiyonunun Sürekliliği","list":{"type":"unordered","items":["Son kez limitte başlıklar mutlak değer fonksiyonunun sürekliliğinden bahsedilecek.","Mutlak değer ifadeleri aslında parçalı fonksiyonlar olarak yazılabiliyor.","Mutlak değerde limitte problem olabildiği noktalar, içerisini sıfır yapan değerlerdir."]},"beginTime":93,"endTime":166,"href":"/video/preview/12183751211292253248?parent-reqid=1769514051874146-11411995624285502602-balancer-l7leveler-kubr-yp-klg-278-BAL&text=Limi7edDesigns&t=93&ask_summarization=1"},{"index":3,"title":"Fonksiyonun Sürekliliği Örneği","list":{"type":"unordered","items":["Fonksiyonun sürekli olduğu durumda en geniş tanım aralığı bulunması isteniyor.","İçerisini sıfır yapan değer 4 olarak bulunuyor.","Fonksiyon parçalı fonksiyon şeklinde yazıldığında, x değeri 4'ten büyük eşit olduğunda içerisi pozitif, 4'ten küçük olduğunda içerisi negatif oluyor."]},"beginTime":166,"endTime":214,"href":"/video/preview/12183751211292253248?parent-reqid=1769514051874146-11411995624285502602-balancer-l7leveler-kubr-yp-klg-278-BAL&text=Limi7edDesigns&t=166&ask_summarization=1"},{"index":4,"title":"Fonksiyonların Sürekliliği","list":{"type":"unordered","items":["Bir fonksiyonun sürekliliğini kontrol etmek için kritik noktada sürekliliği incelemek gerekir.","Fonksiyonun bir noktada sürekli olması için sağdan, soldan limitlerin ve o noktadaki fonksiyon değerinin birbirine eşit olması gerekir.","Parçalı fonksiyonlarda kritik noktada sürekliliğin olabilmesi için sağdan, soldan limitlerin ve o noktadaki fonksiyon değerinin birbirine eşit olması gerekir."]},"beginTime":215,"endTime":281,"href":"/video/preview/12183751211292253248?parent-reqid=1769514051874146-11411995624285502602-balancer-l7leveler-kubr-yp-klg-278-BAL&text=Limi7edDesigns&t=215&ask_summarization=1"},{"index":5,"title":"Süreklilik Problemleri","list":{"type":"unordered","items":["Bir fonksiyonun bir noktada sürekli olması için sağdan, soldan limitlerin ve o noktadaki fonksiyon değerinin birbirine eşit olması gerekir.","Köklü ifadelerde mutlak değer kullanılarak limit hesaplanabilir.","Rasyonel ifadelerde sürekliliği bozan yer paydayı sıfır yapan değerlerdir."]},"beginTime":281,"endTime":536,"href":"/video/preview/12183751211292253248?parent-reqid=1769514051874146-11411995624285502602-balancer-l7leveler-kubr-yp-klg-278-BAL&text=Limi7edDesigns&t=281&ask_summarization=1"},{"index":6,"title":"Süreksizlik Noktaları","list":{"type":"unordered","items":["Mutlak değerli ifadelerde payda sıfır olamaz, bu durumda süreksizlik oluşur.","Fonksiyonun grafiğinde süreksizlik noktaları, paydayı sıfır yapan değerlerdir.","Fonksiyonun sağdan ve soldan limitleri farklı olduğunda, o noktada süreksizlik oluşur."]},"beginTime":536,"endTime":811,"href":"/video/preview/12183751211292253248?parent-reqid=1769514051874146-11411995624285502602-balancer-l7leveler-kubr-yp-klg-278-BAL&text=Limi7edDesigns&t=536&ask_summarization=1"},{"index":7,"title":"Köklü İfadelerde Süreklilik","list":{"type":"unordered","items":["Köklü ifadelerde kökün derecesi tekse, fonksiyon bütün reel sayılarda tanımlıdır ve süreklidir.","Kökün derecesi çiftse, kökün içindeki ifade sıfırdan büyük eşit olmalıdır, aksi takdirde süreksizlik oluşur."]},"beginTime":811,"endTime":840,"href":"/video/preview/12183751211292253248?parent-reqid=1769514051874146-11411995624285502602-balancer-l7leveler-kubr-yp-klg-278-BAL&text=Limi7edDesigns&t=811&ask_summarization=1"},{"index":8,"title":"Fonksiyonların Sürekliliği","list":{"type":"unordered","items":["Fonksiyonun sürekli olması için öncelikle köklü ifadenin tanım aralığına uyması gerekir.","Köklü ifadenin tanım aralığı için 16-x² ≥ 0 denkleminin çözümü x ∈ [-4, 4] kapalı aralığıdır.","Çift dereceli köklü ifadelerde, kökün içindeki ifade sıfırdan büyük eşit olmalıdır."]},"beginTime":841,"endTime":947,"href":"/video/preview/12183751211292253248?parent-reqid=1769514051874146-11411995624285502602-balancer-l7leveler-kubr-yp-klg-278-BAL&text=Limi7edDesigns&t=841&ask_summarization=1"},{"index":9,"title":"Mutlak Değerli Fonksiyonların Sürekliliği","list":{"type":"unordered","items":["Mutlak değerli fonksiyonların sürekliliğini kontrol etmek için limit değerleri hesaplanır.","Mutlak değer dışarı atıldığında, fonksiyonun sürekli olduğu noktalar belirlenir.","Mutlak değerli fonksiyonların sürekliliğini kontrol etmek için alternatif olarak, x ekseninin altında kalan kısımların x eksenine göre simetri alınması da mümkündür."]},"beginTime":947,"endTime":1261,"href":"/video/preview/12183751211292253248?parent-reqid=1769514051874146-11411995624285502602-balancer-l7leveler-kubr-yp-klg-278-BAL&text=Limi7edDesigns&t=947&ask_summarization=1"},{"index":10,"title":"Logaritma Fonksiyonlarının Sürekliliği","list":{"type":"unordered","items":["Logaritma fonksiyonlarının tanım aralığı için üç koşul sağlanmalıdır: logaritmanın tabanı sıfırdan büyük ve birden farklı olmalı, logaritmanın içindeki ifade sıfırdan büyük olmalıdır.","Verilen logaritma fonksiyonunun tanımlı ve sürekli olduğu tam sayı değerleri için x > 2, x ≠ 3 ve 17 > x koşulları uygulanır.","Bu koşullara uygun 13 tam sayı değeri bulunur."]},"beginTime":1261,"endTime":1354,"href":"/video/preview/12183751211292253248?parent-reqid=1769514051874146-11411995624285502602-balancer-l7leveler-kubr-yp-klg-278-BAL&text=Limi7edDesigns&t=1261&ask_summarization=1"},{"index":11,"title":"Fonksiyon Problemi Çözümü","list":{"type":"unordered","items":["Fonksiyon probleminde \"bıdı bıdı bıdı\" ifadesini sağlayan en küçük üç tam sayının toplamı isteniyor.","x'in alabileceği en küçük üç tam sayı 4, 5 ve 6 olarak bulunuyor ve toplamları 15'tir."]},"beginTime":1355,"endTime":1420,"href":"/video/preview/12183751211292253248?parent-reqid=1769514051874146-11411995624285502602-balancer-l7leveler-kubr-yp-klg-278-BAL&text=Limi7edDesigns&t=1355&ask_summarization=1"},{"index":12,"title":"Süreklilik Kavramı","list":{"type":"unordered","items":["Gerçek sayılarda tanımlı f ve g fonksiyonlarının x=m noktasında süreklidir.","f(x) + 2g(x) fonksiyonunun limiti, f(m) + 2g(m) değerine eşittir.","f(x) × 2g(x) fonksiyonunun limiti de f(m) × 2g(m) değerine eşittir."]},"beginTime":1420,"endTime":1591,"href":"/video/preview/12183751211292253248?parent-reqid=1769514051874146-11411995624285502602-balancer-l7leveler-kubr-yp-klg-278-BAL&text=Limi7edDesigns&t=1420&ask_summarization=1"},{"index":13,"title":"Bileşke Fonksiyonun Sürekliliği","list":{"type":"unordered","items":["f bileşke g(x) fonksiyonunun limiti, önce g(x) fonksiyonunun limitinin bulunması gerekir.","f(g(x)) fonksiyonunun limiti, f(g(x))'nin varlığından haberdar olunduğunda hesaplanabilir."]},"beginTime":1591,"endTime":1684,"href":"/video/preview/12183751211292253248?parent-reqid=1769514051874146-11411995624285502602-balancer-l7leveler-kubr-yp-klg-278-BAL&text=Limi7edDesigns&t=1591&ask_summarization=1"},{"index":14,"title":"Mutlak Değerli Fonksiyonun Sürekliliği","list":{"type":"unordered","items":["|f(x)| fonksiyonu x ≤ 2 için süreklidir.","x = -2 noktasında mutlak değer fonksiyonu sürekli çünkü soldan ve sağdan limit değerleri aynıdır.","x = 2 noktasında fonksiyon tanımsız olduğu için sürekli değildir."]},"beginTime":1684,"endTime":1781,"href":"/video/preview/12183751211292253248?parent-reqid=1769514051874146-11411995624285502602-balancer-l7leveler-kubr-yp-klg-278-BAL&text=Limi7edDesigns&t=1684&ask_summarization=1"},{"index":15,"title":"Limit Hesaplama","list":{"type":"unordered","items":["x → 1+ için f(x) - 1 limiti hesaplanıyor.","x → 0'+ için f(x) limiti hesaplanıyor.","İki limitin toplamı 3 olarak bulunuyor."]},"beginTime":1781,"endTime":1890,"href":"/video/preview/12183751211292253248?parent-reqid=1769514051874146-11411995624285502602-balancer-l7leveler-kubr-yp-klg-278-BAL&text=Limi7edDesigns&t=1781&ask_summarization=1"},{"index":16,"title":"Fonksiyonun Sürekliliği","list":{"type":"unordered","items":["Fonksiyonun x=1 noktasındaki sürekliliği inceleniyor, sağdan limit alındığında limit 1'e eşit olmadığı için fonksiyon süreksizdir.","Logaritma fonksiyonunda x=1 noktasında limit 3/4 olarak bulunuyor, ancak f(1) değeri 1'e eşit olduğu için fonksiyon sürekli değildir.","Fonksiyonun x=1 noktasında limiti var ancak f(1) değeri ile eşit olmadığı için süreksizdir."]},"beginTime":1893,"endTime":1954,"href":"/video/preview/12183751211292253248?parent-reqid=1769514051874146-11411995624285502602-balancer-l7leveler-kubr-yp-klg-278-BAL&text=Limi7edDesigns&t=1893&ask_summarization=1"},{"index":17,"title":"Fonksiyonun Süreksiz Olduğu Noktalar","list":{"type":"unordered","items":["Fonksiyonun süreksiz olduğu iki nokta vardır: x=1 ve logaritma fonksiyonunun tanım kümesindeki sınır noktaları.","Logaritma fonksiyonunun tanım kümesinde x=-2, x=-1,5 ve x=-3 kökleri vardır.","Fonksiyonun toplam üç noktada süreksiz olduğu belirlenmiştir."]},"beginTime":1954,"endTime":2028,"href":"/video/preview/12183751211292253248?parent-reqid=1769514051874146-11411995624285502602-balancer-l7leveler-kubr-yp-klg-278-BAL&text=Limi7edDesigns&t=1954&ask_summarization=1"},{"index":18,"title":"Kampın Sonu ve Türev Kampı","list":{"type":"unordered","items":["Eğitmen, son soruyu izleyicilerden çözümünü beklediğini belirtiyor.","Limit kampı sona eriyor ve eğitmen bu kampı kendisi için efsane bir kamp olarak tanımlıyor.","Türev kampının daha sert, ayrıntılı ve zor sorularla karşılaşılacağı, sınavda çıkan türev sorularının zor olduğu vurgulanıyor."]},"beginTime":2028,"endTime":2115,"href":"/video/preview/12183751211292253248?parent-reqid=1769514051874146-11411995624285502602-balancer-l7leveler-kubr-yp-klg-278-BAL&text=Limi7edDesigns&t=2028&ask_summarization=1"}],"linkTemplate":"/video/preview/12183751211292253248?parent-reqid=1769514051874146-11411995624285502602-balancer-l7leveler-kubr-yp-klg-278-BAL&text=Limi7edDesigns&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Limit 7 | AYT Matematik Kampi 86.gün | Rehber 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Konu Anlatımı Video Dersi Limit 7 (Süreklilik) | Ali Ahsen Akti www.aliahsenakti.com Öğrenmek İstiyorsan Matematik Ali Hocadan Al Taktik Hem Ekonomik Hem Pratik Ali Matematik...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/1520265/a7ad595b8bcf8c968b3d374d96a944c0/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/feWMPgAAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"3","reqid":"1769514051874146-11411995624285502602-balancer-l7leveler-kubr-yp-klg-278-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769514051874146-11411995624285502602-balancer-l7leveler-kubr-yp-klg-278-BAL&text=videoid:13955468832559722014","teaser":[{"list":{"type":"unordered","items":["Bu video, bir matematik öğretmeninin öğrencilere süreklilik konusunu anlattığı eğitim içeriğidir. Öğretmen, Taha, Mustafa, Semih ve Alper adlı öğrencilerle etkileşim halindedir.","Videoda süreklilik kavramı detaylı olarak ele alınmaktadır. Süreklilik için gerekli şartlar (sağdan limit, soldan limit ve limitin görüntüsüne eşit olması) anlatılmakta, parçalı fonksiyonlar üzerinden örnekler çözülmektedir. Ayrıca, R'de sürekli fonksiyonların paydasını sıfır yapan değerlerin olmaması gerektiği ve ikinci dereceden denklemlerin delta değerinin bu durumda nasıl hesaplanacağı açıklanmaktadır.","Video, süreksizlik noktalarının nasıl tespit edileceğini, limitin var olup olmadığına ve limitin var olmasına rağmen süreklilik olup olmadığına göre noktaları sınıflandırarak açıklamaktadır. Video sonunda, konunun pekiştirilmesi için örnek sorular çözülmekte ve türev konusuna geçileceği bilgisi verilmektedir."]},"endTime":1315,"title":"Matematik Dersinde Süreklilik Konusu","beginTime":0}],"fullResult":[{"index":0,"title":"Süreklilik Kavramı","list":{"type":"unordered","items":["Süreklilik için bir fonksiyonun limitinin var olması gerekir.","Fonksiyonun sürekli olması için sağdan limitin soldan limite eşit olması ve bu limitin görüntüsüne eşit olması gerekir.","Limit yoksa fonksiyon otomatikman sürekli değildir."]},"beginTime":8,"endTime":59,"href":"/video/preview/13955468832559722014?parent-reqid=1769514051874146-11411995624285502602-balancer-l7leveler-kubr-yp-klg-278-BAL&text=Limi7edDesigns&t=8&ask_summarization=1"},{"index":1,"title":"Parçalı Fonksiyon Örneği","list":{"type":"unordered","items":["Parçalı bir fonksiyonun R'de sürekli olması için kritik noktada sağdan limitin soldan limite eşit olması ve bu limitin görüntüsüne eşit olması gerekir.","Örnekte x=-4 noktasındaki sağdan limit 8, soldan limit -4+a ve görüntü -4 olduğundan a=12 bulunur.","a+b toplamı 20 olarak hesaplanır."]},"beginTime":59,"endTime":251,"href":"/video/preview/13955468832559722014?parent-reqid=1769514051874146-11411995624285502602-balancer-l7leveler-kubr-yp-klg-278-BAL&text=Limi7edDesigns&t=59&ask_summarization=1"},{"index":2,"title":"Süreksizlik Örnekleri","list":{"type":"unordered","items":["Fonksiyonun süreksiz olabilmesi için paydayı sıfır yapan değerler ve kritik noktalar incelenmelidir.","Paydayı sıfır yapan değerler tanımsız olduğu için otomatikman sürekli değildir.","Kritik noktada sağdan limitin soldan limite eşit olmadığı durumlarda limit yoktur ve fonksiyon süreksizdir."]},"beginTime":251,"endTime":451,"href":"/video/preview/13955468832559722014?parent-reqid=1769514051874146-11411995624285502602-balancer-l7leveler-kubr-yp-klg-278-BAL&text=Limi7edDesigns&t=251&ask_summarization=1"},{"index":3,"title":"R'de Sürekli Fonksiyon","list":{"type":"unordered","items":["Bir fonksiyonun R'de sürekli olması için tüm reel sayılarda sağdan limitin soldan limite eşit olması ve bu limitin görüntüsüne eşit olması gerekir.","Örnekte x=3 noktasındaki sağdan limit ve soldan limit 6 olarak bulunur.","Fonksiyonun sürekli olması için f(3)=3+a=6 olduğu için a=3 olarak hesaplanır."]},"beginTime":451,"endTime":624,"href":"/video/preview/13955468832559722014?parent-reqid=1769514051874146-11411995624285502602-balancer-l7leveler-kubr-yp-klg-278-BAL&text=Limi7edDesigns&t=451&ask_summarization=1"},{"index":4,"title":"Fonksiyonların Sürekliliği","list":{"type":"unordered","items":["Bir fonksiyon R'de sürekli ise, paydayı sıfır yapan hiçbir değer olmamalıdır.","Paydayı sıfır yapan bir değer olduğunda fonksiyon tanımsız olur ve sürekliliği bozulur.","Fonksiyonun her noktada sürekli olması için ikinci dereceden denklemin kökü olmamalıdır, bu da delta'nın sıfırdan küçük olması anlamına gelir."]},"beginTime":627,"endTime":811,"href":"/video/preview/13955468832559722014?parent-reqid=1769514051874146-11411995624285502602-balancer-l7leveler-kubr-yp-klg-278-BAL&text=Limi7edDesigns&t=627&ask_summarization=1"},{"index":5,"title":"Süreklilik Durumları","list":{"type":"unordered","items":["Tek noktada süreksizlik için ikinci dereceden denklemin bir kökü olmalı ve bu kökler birbirine eşit olmalıdır, bu da delta'nın sıfıra eşit olması anlamına gelir.","İki noktada süreksizlik için ikinci dereceden denklemin iki farklı kökü olmalıdır, bu da delta'nın sıfırdan büyük olması anlamına gelir.","Fonksiyonun sürekli olması için üç şart vardır: limitin olması, sağdan limitin soldan limite eşit olması ve görüntüsünün dolu olması."]},"beginTime":811,"endTime":965,"href":"/video/preview/13955468832559722014?parent-reqid=1769514051874146-11411995624285502602-balancer-l7leveler-kubr-yp-klg-278-BAL&text=Limi7edDesigns&t=811&ask_summarization=1"},{"index":6,"title":"Grafikte Süreklilik","list":{"type":"unordered","items":["Süreksiz olduğu noktaları bulmak için içi boş olan yerlere ve limitin olmadığı yerlere bakılmalıdır.","Limiti olduğu ama süreksiz olduğu noktalar için hem limitin olması hem de görüntünün dolu olması gerekir.","Limiti var ama içi boş olan noktalar süreksizdir, çünkü sürekli olabilmesi için hem limitin olması hem de görüntünün dolu olması gerekir."]},"beginTime":965,"endTime":1153,"href":"/video/preview/13955468832559722014?parent-reqid=1769514051874146-11411995624285502602-balancer-l7leveler-kubr-yp-klg-278-BAL&text=Limi7edDesigns&t=965&ask_summarization=1"},{"index":7,"title":"Süreksiz Noktaların Bulunması","list":{"type":"unordered","items":["Süreksiz noktalar, limit olmayan veya limiti olan ancak içi boş olan noktalardır.","Eksi üç noktasında limit olmadığı için sürekli değildir.","Eksi bir noktasında limit var ancak sürekli 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