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Yaklaşım","list":{"type":"unordered","items":["x değişkeni 2 sayısına sağdan yaklaşırken f fonksiyonu 7'ye yaklaşır.","x değişkeni 2 sayısına soldan yaklaşırken f fonksiyonu da 7'ye yaklaşır.","Bu durumda limit x→2'de f(x) = 7 olarak ifade edilir."]},"beginTime":216,"endTime":382,"href":"/video/preview/7311325274580852999?parent-reqid=1769772085206810-15809777932751184288-balancer-l7leveler-kubr-yp-sas-29-BAL&text=Mert.&t=216&ask_summarization=1"},{"index":4,"title":"Limitin Varlığı","list":{"type":"unordered","items":["Bir fonksiyonun bir noktada limitinin olabilmesi için o noktanın sağındaki ve solundaki limitlerin var olması ve birbirine eşit olması gerekir.","Eğer bir noktada sağdaki limit ve soldaki limit birbirine eşit değilse, o noktada limit yoktur.","Bir fonksiyonun her yerde limitinin olması gerekmez, örneğin f fonksiyonunun 3'teki limiti yoktur."]},"beginTime":382,"endTime":518,"href":"/video/preview/7311325274580852999?parent-reqid=1769772085206810-15809777932751184288-balancer-l7leveler-kubr-yp-sas-29-BAL&text=Mert.&t=382&ask_summarization=1"},{"index":5,"title":"Limit Kavramı ve Uç Noktalarda Limit","list":{"type":"unordered","items":["Limit hesaplamasında, bir noktaya sağdan ve soldan yaklaşarak limitin aynı değere gittiği durumda, o noktadaki limit o değere eşittir.","Uç noktalarda (a ve b) sağdan veya soldan yaklaşılamadığı için, limit hesaplaması için sadece yaklaşılabilen yönden limit alınır.","Limit hesaplamasında fonksiyonun o noktada tanımlı olup olmadığı önemli değildir, çünkü limit bir sayıya yaklaşımdır ve o sayıya hiçbir zaman varılmaz."]},"beginTime":520,"endTime":712,"href":"/video/preview/7311325274580852999?parent-reqid=1769772085206810-15809777932751184288-balancer-l7leveler-kubr-yp-sas-29-BAL&text=Mert.&t=520&ask_summarization=1"},{"index":6,"title":"Tanımsız Noktalarda Limit","list":{"type":"unordered","items":["Tanımsız noktalarda (örneğin asimptot doğruları) fonksiyonun o noktada tanımlı olmadığı için limit hesaplaması yapılamaz.","Tanımsız noktalarda sağdan ve soldan yaklaşıldığında fonksiyonun değerleri farklı olabilir (örneğin eksi sonsuza veya artı sonsuza).","Normalde eksi sonsuz ve artı sonsuz çıkan limitler müfredatta yoktur, ancak bu yaklaşım metodu diğer sorularda da kullanılabilir."]},"beginTime":712,"endTime":802,"href":"/video/preview/7311325274580852999?parent-reqid=1769772085206810-15809777932751184288-balancer-l7leveler-kubr-yp-sas-29-BAL&text=Mert.&t=712&ask_summarization=1"},{"index":7,"title":"Bileşke Fonksiyonlarda Limit","list":{"type":"unordered","items":["Bileşke fonksiyonlarda limit hesaplaması yaparken, önce iç fonksiyonun limiti bulunur ve bu değer dış fonksiyonun limit hesaplamasında kullanılır.","Bileşke fonksiyonlarda limitin varlığı için, iç fonksiyonun limiti ile dış fonksiyonun limitinin eşit olması gerekir.","Bileşke fonksiyonlarda limit hesaplaması yaparken, iç fonksiyonun limitinin hangi yönden yaklaşıldığı önemlidir ve bu bilgi dış fonksiyonun limit hesaplamasında kullanılır."]},"beginTime":802,"endTime":1105,"href":"/video/preview/7311325274580852999?parent-reqid=1769772085206810-15809777932751184288-balancer-l7leveler-kubr-yp-sas-29-BAL&text=Mert.&t=802&ask_summarization=1"},{"index":8,"title":"Limit Özellikleri","list":{"type":"unordered","items":["Limit özellikleri, limit sorularında özellikle öncüllü sorularda işe yarar.","Herhangi sabit bir fonksiyonun herhangi bir noktadaki limiti yine sabit fonksiyonun kendisidir.","Limitte sabit bir sayı yanında fonksiyon varsa, o sayı dışarı çıkarılabilir."]},"beginTime":1110,"endTime":1187,"href":"/video/preview/7311325274580852999?parent-reqid=1769772085206810-15809777932751184288-balancer-l7leveler-kubr-yp-sas-29-BAL&text=Mert.&t=1110&ask_summarization=1"},{"index":9,"title":"Limit Özellikleri (Devam)","list":{"type":"unordered","items":["Limitte 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girebilir."]},"beginTime":1282,"endTime":1377,"href":"/video/preview/7311325274580852999?parent-reqid=1769772085206810-15809777932751184288-balancer-l7leveler-kubr-yp-sas-29-BAL&text=Mert.&t=1282&ask_summarization=1"},{"index":11,"title":"Parçalı Fonksiyonlarda Limit Hesabı","list":{"type":"unordered","items":["Parçalı fonksiyonlarda limit hesabı yaparken kritik noktalara dikkat edilir.","Kritik noktada fonksiyonun limiti yoksa, sağdan ve soldan limitler farklı çıkabilir.","Polinom fonksiyonları her yerde limitlidir, bu nedenle kritik nokta dışındaki her yerde limiti vardır."]},"beginTime":1378,"endTime":1465,"href":"/video/preview/7311325274580852999?parent-reqid=1769772085206810-15809777932751184288-balancer-l7leveler-kubr-yp-sas-29-BAL&text=Mert.&t=1378&ask_summarization=1"},{"index":12,"title":"Mutlak Değer Fonksiyonlarında Limit","list":{"type":"unordered","items":["Mutlak değer fonksiyonunda kritik noktada limit ararken sağdan ve soldan yaklaşıp mutlak değeri artı ve eksi 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Sassuolo kariyeriyle A Milli Takım'a kadar yükselen, Mert Müldür Fenerbahçe'nin oyununa ne...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3905608/25d5fda19b2fea4db08ea92f6e93a984/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/xaVLRgIAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"7","reqid":"1769772085206810-15809777932751184288-balancer-l7leveler-kubr-yp-sas-29-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769772085206810-15809777932751184288-balancer-l7leveler-kubr-yp-sas-29-BAL&text=videoid:9441966035908193920","teaser":[{"list":{"type":"unordered","items":["Bu video, \"Analiz Departmanı\" programının bir bölümü olup, sunucu Furkan ve konuk Melih tarafından Fenerbahçe'nin yeni transferi Mert Müldür hakkında detaylı bir değerlendirme sunulmaktadır.","Videoda Mert Müldür'ün teknik özellikleri, oyun tarzı ve Fenerbahçe'ye katkıları ele alınmaktadır. 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Şarkıda bir kişi aşk acısını ve hayal kırıklığını anlatmaktadır.","Şarkının ana teması aşk acısı, hasret ve hayal kırıklığıdır. Sözlerde \"göz değil nakış mübarek bendeki aşk değil ibadet\", \"seyrelmiş, beyhude oldum, serseri oldum diyarda zalim\" gibi ifadeler kullanılarak duygusal bir atmosfer yaratılmaktadır. Şarkı, tekrarlanan nakaratlar ve benzer temalarla ilerlemektedir."]},"endTime":317,"title":"Türkçe Şarkı Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Aşk ve İbadet","list":{"type":"unordered","items":["Kahkahasında bülbüller ve kirpiği kapkara tüller anlatılıyor.","Göz değil nakış mübarek, aşk değil ibadet olarak ifade ediliyor.","Elleri sevdi nihayet ben ebedi saa şeklinde bir duygusal ifade yapılıyor."]},"beginTime":48,"endTime":102,"href":"/video/preview/11316164316882551806?parent-reqid=1769772085206810-15809777932751184288-balancer-l7leveler-kubr-yp-sas-29-BAL&text=Mert.&t=48&ask_summarization=1"},{"index":1,"title":"Akşam ve Seyrelme","list":{"type":"unordered","items":["Akşam olmakta dostlar ve seyrelmiş, beyhude oldum, serseri oldum diyarda zalim ifadeleri kullanılıyor.","Genç yaşımda zalim senin allah'ın yar şeklinde bir acı ifade ediliyor.","Hasretin bahtsız, mecnun mevla'ya sığınan perişan halimi bende akşam olmakta dostlar seyrelmiş beyhude lafı şeklinde devam 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