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konusu tyt ayt dgs kpss ve ales yani kısacası tüm sınavların ortak konusudur ve her sınavda her yıl soru gelir dolayısıyla fonksiyonları adım adım detaylı bir şekilde konu anlatacağım...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/860261/444032192793973a4014877255b92e00/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/nejsJgIAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"13","reqid":"1769858522940326-9671839507046811744-balancer-l7leveler-kubr-yp-vla-224-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769858522940326-9671839507046811744-balancer-l7leveler-kubr-yp-vla-224-BAL&text=videoid:5055364925731724356","teaser":[{"list":{"type":"unordered","items":["Bu video, bir matematik eğitmeni tarafından sunulan, TYT, DGS, KPSS ve ALES sınavlarına hazırlanan öğrencilere yönelik bir eğitim içeriğidir.","Videoda fonksiyon çeşitleri detaylı olarak ele alınmaktadır. İlk olarak sabit fonksiyon ve birim fonksiyon tanımlanmakta, ardından birebir fonksiyon, örten fonksiyon ve içine fonksiyon kavramları şema ve grafiklerle görselleştirilmektedir. Eğitmen, her bir fonksiyon türünün özelliklerini örneklerle açıklamakta ve tanım kümesi ile görüntü kümesinin nasıl bulunacağını göstermektedir.","Video, öğrencilerin fonksiyon çeşitlerini kolayca anlayabilmeleri için basit ve anlaşılır bir dille hazırlanmıştır. Bir sonraki videoda doğrusal grafik, tek çift fonksiyon ve fonksiyon tersi konularının işleneceği belirtilmektedir."]},"endTime":1122,"title":"Fonksiyon Çeşitleri Eğitim Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Fonksiyon Çeşitleri","list":{"type":"unordered","items":["Bu videoda fonksiyon çeşitleri anlatılacak ve öğrencilerin en nefret ettiği bu konu kolay bir şekilde açıklanacak.","Sabit fonksiyon, aldığı her elemanı sabit bir reel sayıya götüren fonksiyondur ve f(x) = c şeklinde gösterilir.","Sabit fonksiyonun grafiğinde dışarıda x'li bir ifade olmaz ve her değer aynı sayıya götürülür."]},"beginTime":15,"endTime":41,"href":"/video/preview/5055364925731724356?parent-reqid=1769858522940326-9671839507046811744-balancer-l7leveler-kubr-yp-vla-224-BAL&text=%7ECemBer%7EFn&t=15&ask_summarization=1"},{"index":1,"title":"Sabit Fonksiyon Örnekleri","list":{"type":"unordered","items":["f(x) = 5000, f(x) = 3 gibi örnekler sabit fonksiyonlardır çünkü dışarıda x'li bir ifade yoktur.","Sabit fonksiyonda f(5) = 3, f(100) = 3, f(-6) = 3 gibi her değer aynı sayıya götürülür.","Sabit fonksiyonun grafiği doğrusal bir grafiktir."]},"beginTime":41,"endTime":110,"href":"/video/preview/5055364925731724356?parent-reqid=1769858522940326-9671839507046811744-balancer-l7leveler-kubr-yp-vla-224-BAL&text=%7ECemBer%7EFn&t=41&ask_summarization=1"},{"index":2,"title":"Sabit Fonksiyon Problemleri","list":{"type":"unordered","items":["Sabit fonksiyonda dışarıda x'li ifadeler varsa, bu ifadeler sıfır olmalıdır.","f(x) = ax² + bx + c sabit fonksiyonunda, a = 0, b = 0, c = 3 şeklinde değerler bulunur.","Sabit fonksiyonun özel durumları olarak sıfır fonksiyon ve birim fonksiyon vardır."]},"beginTime":110,"endTime":179,"href":"/video/preview/5055364925731724356?parent-reqid=1769858522940326-9671839507046811744-balancer-l7leveler-kubr-yp-vla-224-BAL&text=%7ECemBer%7EFn&t=110&ask_summarization=1"},{"index":3,"title":"Birim Fonksiyon","list":{"type":"unordered","items":["Birim fonksiyon, aldığı her elemanı kendisi ile eşleştiren fonksiyondur ve f(x) = x şeklinde gösterilir.","Birim fonksiyonda içi dışı aynıdır, yani f(5) = 5, f(Ali) = Ali gibi her değer kendisine eşittir.","Birim fonksiyonun grafiği y = x doğrusudur."]},"beginTime":179,"endTime":265,"href":"/video/preview/5055364925731724356?parent-reqid=1769858522940326-9671839507046811744-balancer-l7leveler-kubr-yp-vla-224-BAL&text=%7ECemBer%7EFn&t=179&ask_summarization=1"},{"index":4,"title":"Birim Fonksiyon Problemleri","list":{"type":"unordered","items":["Birim fonksiyonda içteki ifade dıştaki ifadeye eşittir, yani ax² + bx + c = 5x² + 7x + 2 şeklinde eşitlik kurulur.","Eşitlikte katsayılar birbirine eşit olmalıdır: a = 5, b = 7, c = -2.","Birim fonksiyonun karakterli olduğu, içi dışı aynı olduğu ve güvenilir olduğu vurgulanmaktadır."]},"beginTime":265,"endTime":358,"href":"/video/preview/5055364925731724356?parent-reqid=1769858522940326-9671839507046811744-balancer-l7leveler-kubr-yp-vla-224-BAL&text=%7ECemBer%7EFn&t=265&ask_summarization=1"},{"index":5,"title":"Sabit ve Birim Fonksiyon Uygulaması","list":{"type":"unordered","items":["f(x) sabit fonksiyon olduğunda, f(5) = c, f(10) = c, f(100-198) = c şeklinde her değer sabit c'ye eşittir.","g(x) birim fonksiyon olduğunda, g(5) = 5, g(-7) = -7 şeklinde her değer kendisine eşittir.","f(5) + 3g(2) = 14 denkleminde, f(5) = c = 4 ve g(2) = 2 olduğundan, c = 4 bulunur.","f(16) + 3g(5) = 16 + 3 × 5 = 19 olarak hesaplanır."]},"beginTime":358,"endTime":528,"href":"/video/preview/5055364925731724356?parent-reqid=1769858522940326-9671839507046811744-balancer-l7leveler-kubr-yp-vla-224-BAL&text=%7ECemBer%7EFn&t=358&ask_summarization=1"},{"index":6,"title":"Fonksiyon Türleri","list":{"type":"unordered","items":["Sabit fonksiyon ve birebir fonksiyon önemlidir, ancak detaylı bilgiye gerek yoktur.","Birebir fonksiyonda her eleman ayrı ayrı sadece bir yere gider, iki eleman aynı yere gidemez.","Örten fonksiyonda değer kümesinde boşta eleman kalmaz, tüm elemanlar eşleşir."]},"beginTime":531,"endTime":641,"href":"/video/preview/5055364925731724356?parent-reqid=1769858522940326-9671839507046811744-balancer-l7leveler-kubr-yp-vla-224-BAL&text=%7ECemBer%7EFn&t=531&ask_summarization=1"},{"index":7,"title":"Fonksiyon Türlerinin Örnekleri","list":{"type":"unordered","items":["İçine fonksiyon, örten olmayan fonksiyondur.","Bir fonksiyonun birebir olup olmadığını anlamak için her elemanın ayrı ayrı bir yere gittiğini kontrol etmek gerekir.","Bir fonksiyonun örten olup olmadığını anlamak için değer kümesinde boşta eleman kalmadığını kontrol etmek gerekir."]},"beginTime":641,"endTime":751,"href":"/video/preview/5055364925731724356?parent-reqid=1769858522940326-9671839507046811744-balancer-l7leveler-kubr-yp-vla-224-BAL&text=%7ECemBer%7EFn&t=641&ask_summarization=1"},{"index":8,"title":"Grafiklerde Fonksiyon Türlerini Belirleme","list":{"type":"unordered","items":["Bir fonksiyonun birebir olup olmadığını anlamak için x eksenine paralel doğrular çizilir ve bu doğrular grafiği sadece bir noktada kesiyorsa birebirdir.","Bir fonksiyonun örten olup olmadığını anlamak için x eksenine paralel doğrular çizilir ve bu doğrular grafiği en az bir noktada kesiyorsa örtendir.","TYT sınavlarında bu tür sorular daha çok gelmektedir."]},"beginTime":751,"endTime":920,"href":"/video/preview/5055364925731724356?parent-reqid=1769858522940326-9671839507046811744-balancer-l7leveler-kubr-yp-vla-224-BAL&text=%7ECemBer%7EFn&t=751&ask_summarization=1"},{"index":9,"title":"Fonksiyonun Özellikleri","list":{"type":"unordered","items":["Fonksiyonun tanım kümesi x ekseninde gösterilir ve bu örnekte -4 dahil değil, 5 dahil olmak üzere tanım kümesi (-4,5] şeklindedir.","Görüntü kümesi y ekseninde gösterilir ve bu örnekte -3 dahil değil, 8 dahil olmak üzere görüntü kümesi [-3,8] şeklindedir.","Fonksiyon birebir değildir çünkü yatay doğrular grafiği sadece bir noktada kesmez, ancak örten bir fonksiyondur."]},"beginTime":923,"endTime":1046,"href":"/video/preview/5055364925731724356?parent-reqid=1769858522940326-9671839507046811744-balancer-l7leveler-kubr-yp-vla-224-BAL&text=%7ECemBer%7EFn&t=923&ask_summarization=1"},{"index":10,"title":"Fonksiyonun Özellikleri ve Öneriler","list":{"type":"unordered","items":["Fonksiyonun en büyük değeri 8'dir çünkü f(5) değeri 8'dir.","DGS, KPSS ve ALES sınavlarında fonksiyon çeşitleri konusunda çok fazla detaya girmeye gerek yoktur.","TYT sınavında fonksiyonlarla ilgili test çözülmesi önerilmektedir."]},"beginTime":1046,"endTime":1087,"href":"/video/preview/5055364925731724356?parent-reqid=1769858522940326-9671839507046811744-balancer-l7leveler-kubr-yp-vla-224-BAL&text=%7ECemBer%7EFn&t=1046&ask_summarization=1"},{"index":11,"title":"Gelecek Videolar","list":{"type":"unordered","items":["Bir sonraki videoda doğrusal grafik ve tek çift fonksiyonlar ele alınacaktır.","Sonraki videoda fonksiyonun tersi konusu işlenecektir.","Fonksiyonlar her sene sınavlarda banko soru olarak gelmekte ve standart sapmaya katkı sağlamaktadır."]},"beginTime":1087,"endTime":1120,"href":"/video/preview/5055364925731724356?parent-reqid=1769858522940326-9671839507046811744-balancer-l7leveler-kubr-yp-vla-224-BAL&text=%7ECemBer%7EFn&t=1087&ask_summarization=1"}],"linkTemplate":"/video/preview/5055364925731724356?parent-reqid=1769858522940326-9671839507046811744-balancer-l7leveler-kubr-yp-vla-224-BAL&text=%7ECemBer%7EFn&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Fonksiyonlar 5. adım kavramak garanti ( 2021yks dgs kpss ales )#2021yks #2021dgs 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Bilgisayar, Mimari, Çizim, 2D, 3D, F fonksiyon tuşları, Snap, Grid, Ortho, F8, Object Snap, F3...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3304426/796e9c43e29c27ba3a65de60e40a1103/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/OKufHwEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"14","reqid":"1769858522940326-9671839507046811744-balancer-l7leveler-kubr-yp-vla-224-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769858522940326-9671839507046811744-balancer-l7leveler-kubr-yp-vla-224-BAL&text=videoid:3770722643963078814","teaser":[{"list":{"type":"unordered","items":["Bu video, AutoCAD programında hızlı erişim butonları ve fonksiyon tuşlarının kullanımını anlatan bir eğitim içeriğidir. Eğitmen, programın çalışma ekranının altında yer alan butonları ve bunların kısayol tuşlarını detaylı şekilde açıklamaktadır.","Video, AutoCAD'de en çok kullanılan fonksiyon tuşlarını (F3, F7, F8, F9, F10) ve bunların işlevlerini adım adım göstermektedir. Snap mode, grid display, orto, polar tracking ve object snap gibi temel özelliklerin nasıl aktif edileceği, nasıl kullanılacağı ve ayarlarının nasıl yapılacağı pratik örneklerle anlatılmaktadır. Özellikle object snap özelliğinin objelerin doğru şekilde yakalanmasını sağladığı ve snap modunun çizim yaparken nasıl etkili olduğu vurgulanmaktadır."]},"endTime":594,"title":"AutoCAD'de Hızlı Erişim Butonları ve Fonksiyon Tuşları Eğitimi","beginTime":0}],"fullResult":[{"index":0,"title":"AutoCAD'de Hızlı Erişim Butonları","list":{"type":"unordered","items":["AutoCAD'de katmanlar araç çubuğu, özellikler araç çubuğu ve özellikler araç çubuğu gibi ana ekranın altında yer alan hızlı erişim butonları bulunmaktadır.","Klavyedeki fonksiyon tuşlarına karşılık gelen snap grid, orto, object snap, çizgi kalınlığını göstergle ve quick properties gibi özellikler bu butonlarla erişilebilir.","Her AutoCAD çalışma ekranının altında bu fonksiyon tuşları mevcuttur ve klavyeden F3 tuşlayarak object snap'i, F8 tuşlayarak orto'yu gibi birçok F fonksiyon tuşuna buradan ulaşılabilir."]},"beginTime":2,"endTime":67,"href":"/video/preview/3770722643963078814?parent-reqid=1769858522940326-9671839507046811744-balancer-l7leveler-kubr-yp-vla-224-BAL&text=%7ECemBer%7EFn&t=2&ask_summarization=1"},{"index":1,"title":"Snap Modu ve Ayarları","list":{"type":"unordered","items":["Snap modu, AutoCAD'de objelerin belirli noktalarda yakalanmasını sağlayan bir özellik olup, aktif olduğunda mavi ışık, pasif olduğunda gri ışık yanar.","Snap modu açıkken, mouse'u belirli bir ölçüde (örneğin 10 birim) hareket ettirerek objelerin köşelerinden ilerleyebilirsiniz.","Snap modu pasif edildiğinde (F9 tuşuyla), mouse'u tüm düzlemde free bir şekilde hareket ettirebilirsiniz."]},"beginTime":67,"endTime":242,"href":"/video/preview/3770722643963078814?parent-reqid=1769858522940326-9671839507046811744-balancer-l7leveler-kubr-yp-vla-224-BAL&text=%7ECemBer%7EFn&t=67&ask_summarization=1"},{"index":2,"title":"Grid (Izgara) Özellikleri","list":{"type":"unordered","items":["AutoCAD'de okunurluğu artırmak için normal çizgili defterlerde olduğu gibi bir grid (ızgara) mevcuttur ve kısayol tuşu F7'dir.","Grid pasif olduğunda arka plan pürüzsüz bir beyaz kağıt gibi görünür, aktif olduğunda kareli bir defter haline gelir.","Snap ayarları (snap settings) kısmında snap boşlukları (snapspace) değiştirilebilir ve en önemli snap type'lar arasında rectanda snap (dikdörtgen düzlem) ve izometrik snap (30 derecelik açılı düzlem) bulunmaktadır."]},"beginTime":242,"endTime":335,"href":"/video/preview/3770722643963078814?parent-reqid=1769858522940326-9671839507046811744-balancer-l7leveler-kubr-yp-vla-224-BAL&text=%7ECemBer%7EFn&t=242&ask_summarization=1"},{"index":3,"title":"Orto ve Polar Tracking","list":{"type":"unordered","items":["Orto modu (kısayolu F8) dik çizmeye yarar ve mouse'un sağ kenarında 90°, 180°, 270° ve 360° değerleri görünür.","Polar tracking (kısayolu F10) objelerin polar bir şekilde referans alınmasına yardımcı 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Öğretmen, müfredat dışı konuları da ele alarak öğrencilere yardımcı olmaktadır.","Videoda süreklilik ve limit konusu detaylı olarak işlenmektedir. İlk olarak sürekliliğin temel tanımı ve dört şartı açıklanmakta, ardından süreksizlik çeşitleri (kaldırılabilir ve sıçrama süreksizliği) anlatılmaktadır. Daha sonra çeşitli fonksiyon grafikleri üzerinden süreklilik ve süreksizlik durumları örneklerle yorumlanmakta ve 55-62. örnekler adım adım çözülmektedir.","Video, üç günde beş video ve 66 örnekle tamamlanan bir serinin son bölümüdür. Öğretmen, parçalı tanımlı fonksiyonların sürekliliği, limit hesaplamaları ve fonksiyonların grafiksel temsilleri gibi konuları ele almaktadır. Video sonunda türev ve integral konularına geçiş yapılacağı belirtilmektedir."]},"endTime":2381,"title":"AYT Matematik 2023 Kampı: Süreklilik ve Limit Konusu","beginTime":0}],"fullResult":[{"index":0,"title":"Süreklilik Konusuna Giriş","list":{"type":"unordered","items":["İsmail Hoca, AYT Matematik 2023 kampında limit süreklilik konusuna geçiş yapıyor.","Süreklilik, limitle türev arasındaki ince köprüyü kurmamızı sağlayacak önemli bir konu.","Süreklilik tek videoda ele alınacak ve dikkatli dinlemek gerekiyor."]},"beginTime":0,"endTime":61,"href":"/video/preview/10730357591456006635?parent-reqid=1769858522940326-9671839507046811744-balancer-l7leveler-kubr-yp-vla-224-BAL&text=%7ECemBer%7EFn&t=0&ask_summarization=1"},{"index":1,"title":"Süreklilik Tanımı","list":{"type":"unordered","items":["Grafik tanımı olarak \"kalemi kaldırmadan çizebileceğimiz fonksiyon grafiği sürekli bir fonksiyona aittir\" denir ancak bu sürekliliği tanımlamaz.","Bir fonksiyonun a noktasında sürekli olması için üç şart gerekiyor: 1) Fonksiyon x=a'da tanımlı olmalı, 2) Fonksiyon x=a'da limitli olmalı, 3) Fonksiyonun x=a'daki limiti görüntüsüne eşit olmalı.","Fonksiyonun tanımsız olduğu bir noktada sürekliliği incelenmeyecek, tanımsız olduğu noktalarda fonksiyona süreksiz de diyemeyiz."]},"beginTime":61,"endTime":175,"href":"/video/preview/10730357591456006635?parent-reqid=1769858522940326-9671839507046811744-balancer-l7leveler-kubr-yp-vla-224-BAL&text=%7ECemBer%7EFn&t=61&ask_summarization=1"},{"index":2,"title":"Fonksiyon Grafiği Örnekleri","list":{"type":"unordered","items":["Altı farklı fonksiyon grafiği inceleniyor ve her birinin a noktasında sürekliliği değerlendiriliyor.","Fonksiyonun tanımlı olmadığı bir noktada sürekliliğine veya süreksizliğine yorum yapamadığımız için \"sürekli değil\" diyebiliriz, \"süreksiz\" demeyiz.","Fonksiyonun tanımlı olduğu bir noktada limiti yoksa, o noktada süreksizdir diyebiliriz."]},"beginTime":175,"endTime":505,"href":"/video/preview/10730357591456006635?parent-reqid=1769858522940326-9671839507046811744-balancer-l7leveler-kubr-yp-vla-224-BAL&text=%7ECemBer%7EFn&t=175&ask_summarization=1"},{"index":3,"title":"Asimptotlar ve Limitler","list":{"type":"unordered","items":["Düşey asimptotlar, fonksiyona sonsuzda teğet (hayali teğet) olarak geçer ve fonksiyonun grafiği doğruya artı veya eksi sonsuzda çok yakın yaklaşır.","Fonksiyonun a noktasında tanımsız olduğu durumda \"sürekli değil\" diyebiliriz.","Limitinin değeri sonsuz çıkan limitler için, normal şartlar altında limiti yoktur denirken, genişletilmiş reel sayılar kümesi kullanılarak limiti vardır da diyebiliriz."]},"beginTime":505,"endTime":665,"href":"/video/preview/10730357591456006635?parent-reqid=1769858522940326-9671839507046811744-balancer-l7leveler-kubr-yp-vla-224-BAL&text=%7ECemBer%7EFn&t=505&ask_summarization=1"},{"index":4,"title":"Süreksizlik Çeşitleri","list":{"type":"unordered","items":["Müfredat dışı olmasına rağmen süreksizlik çeşitleri konusu öğrencilere yardımcı olacak önemli bir konudur.","Fonksiyonların süreksizlikleri iki ana türde incelenir: kaldırılabilir süreksizlik ve sıçrama süreksizliği.","Kaldırılabilir süreksizlik, sadece bir reel sayı için tanım dışına çıkmış gibi duran ve limiti olan fonksiyonlardır.","Sıçrama süreksizliği ise limiti olmayan, sadece bir reel sayı için sapma gösteren süreksiz fonksiyonlardır."]},"beginTime":670,"endTime":857,"href":"/video/preview/10730357591456006635?parent-reqid=1769858522940326-9671839507046811744-balancer-l7leveler-kubr-yp-vla-224-BAL&text=%7ECemBer%7EFn&t=670&ask_summarization=1"},{"index":5,"title":"Süreklilik Örnekleri","list":{"type":"unordered","items":["Örnek 55'te verilen fonksiyonun grafiğinde A, C ve F noktalarında sürekli, B, C, D ve E noktalarında sürekli olmadığı belirlenmiştir.","Tanımsız olan noktalar (C ve E) için süreklilik veya süreksizlik hakkında yorum yapılamaz.","Örnek 56'da tüm gerçek sayılarda sürekli olan bir fonksiyon için kritik noktada sol ve sağ limitlerin eşit olması gerektiği gösterilmiştir."]},"beginTime":857,"endTime":1078,"href":"/video/preview/10730357591456006635?parent-reqid=1769858522940326-9671839507046811744-balancer-l7leveler-kubr-yp-vla-224-BAL&text=%7ECemBer%7EFn&t=857&ask_summarization=1"},{"index":6,"title":"Süreklilik Problemleri","list":{"type":"unordered","items":["Örnek 57'de x=2 noktasında sürekliliği sağlayan m değerlerinin çarpımı 3 olarak bulunmuştur.","Örnek 58'de rasyonel bir fonksiyonun sürekli olduğu en geniş kümesi, paydasını sıfır yapan noktalar hariç tüm reel sayılar olarak belirlenmiştir.","Süreksiz olduğu noktalar, tanımlı olup sürekli olmayan noktalar olarak açıklanmıştır."]},"beginTime":1078,"endTime":1216,"href":"/video/preview/10730357591456006635?parent-reqid=1769858522940326-9671839507046811744-balancer-l7leveler-kubr-yp-vla-224-BAL&text=%7ECemBer%7EFn&t=1078&ask_summarization=1"},{"index":7,"title":"Süreklilik Kavramı","list":{"type":"unordered","items":["Bir fonksiyonun tanım kümesinde olmayan noktalarda süreksizlik durumunda olamaz, çünkü fonksiyon o noktalarda tanımlı değildir.","Rasyonel bir fonksiyonun tüm gerçel sayılarda sürekli olması için paydanın reel kökü olmaması gerekir.","İkinci dereceden bir ifadenin reel kökü olmaması için delta (Δ) değeri sıfırdan küçük olmalıdır."]},"beginTime":1228,"endTime":1368,"href":"/video/preview/10730357591456006635?parent-reqid=1769858522940326-9671839507046811744-balancer-l7leveler-kubr-yp-vla-224-BAL&text=%7ECemBer%7EFn&t=1228&ask_summarization=1"},{"index":8,"title":"Süreklilik Problemleri","list":{"type":"unordered","items":["Bir fonksiyonun tanımlı olduğu en geniş aralıkta süreksiz olduğu noktalar, sadece limiti olmayan veya limiti var ancak görüntüye eşit olmayan noktalardır.","Paydayı sıfır yapan noktalar, fonksiyonun tanım kümesinde yoksa süreksizlik noktası olarak kabul edilemez.","Bir fonksiyonun sürekliliği için, limitin var olması ve limitin görüntüye eşit olması gerekir."]},"beginTime":1368,"endTime":1513,"href":"/video/preview/10730357591456006635?parent-reqid=1769858522940326-9671839507046811744-balancer-l7leveler-kubr-yp-vla-224-BAL&text=%7ECemBer%7EFn&t=1368&ask_summarization=1"},{"index":9,"title":"Limit ve Süreklilik Örnekleri","list":{"type":"unordered","items":["Limit ve süreklilik sorularında \"kesinlikle\" veya \"her zaman\" gibi kelimeler kullanıldığında, öncülü bulmak için aksine örnekler vermek gerekir.","Fonksiyonların sürekli olup olmadığı belirtilmediğinde, limitleri ve görüntüleri hakkında kesin sonuçlar çıkarılamaz.","Fonksiyonların toplamı, farkı veya çarpımı için limit özellikleri, fonksiyonların sürekli olup olmadığına bağlıdır."]},"beginTime":1513,"endTime":1861,"href":"/video/preview/10730357591456006635?parent-reqid=1769858522940326-9671839507046811744-balancer-l7leveler-kubr-yp-vla-224-BAL&text=%7ECemBer%7EFn&t=1513&ask_summarization=1"},{"index":10,"title":"Logaritma Fonksiyonu ve Süreklilik","list":{"type":"unordered","items":["Bir fonksiyonun tanım kümesindeki tüm reel sayılarda sürekli olması için, kritik noktalarda sol limitin sağ limitine eşit olması gerekir.","Logaritma fonksiyonunda kritik nokta, logaritmanın tabanının sıfırdan farklı olması ve logaritmanın içinin pozitif olması koşullarını sağlayacak değerdir.","Verilen örnekte, fonksiyonun sürekli olması için a değeri 8/3'tür."]},"beginTime":1861,"endTime":1907,"href":"/video/preview/10730357591456006635?parent-reqid=1769858522940326-9671839507046811744-balancer-l7leveler-kubr-yp-vla-224-BAL&text=%7ECemBer%7EFn&t=1861&ask_summarization=1"},{"index":11,"title":"Fonksiyon Grafiği Sorusu","list":{"type":"unordered","items":["Soruda f fonksiyonunun grafiği verilmiş ve y=f(3x) fonksiyonunun süreksiz olduğu noktaların apsisleri toplamının koordinatları toplamına oranı sorulmuş.","f(x) fonksiyonunun süreksiz olduğu noktaların apsisleri -3 ve 2, koordinatları (-3,1) ve (2,-2) olarak belirlenmiş.","-f(3x) fonksiyonunda içeriye 3 eklenmesiyle fonksiyon sola kaymış, dışarıdan -1 ile çarpılarak ordinatlar işaret değiştirmiş ve süreksiz noktaların apsisleri toplamı -5, koordinatları toplamı 1 olarak bulunmuş."]},"beginTime":1959,"endTime":2085,"href":"/video/preview/10730357591456006635?parent-reqid=1769858522940326-9671839507046811744-balancer-l7leveler-kubr-yp-vla-224-BAL&text=%7ECemBer%7EFn&t=1959&ask_summarization=1"},{"index":12,"title":"Bileşke Fonksiyon Sorusu","list":{"type":"unordered","items":["f ve g fonksiyonlarının grafikleri verilmiş ve g(f(x)) fonksiyonunun x=2 noktasında sürekli olduğu belirtilmiş.","g(f(2)) fonksiyonunun limitinin var olması için f(2) noktasının sol ve sağ limitlerinin g fonksiyonunda 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