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Videoda ayrıca kısa bir süre Görkem Şahin adında bir kimyacı da yer almaktadır.","Video, fonksiyonların limitleri konusunu detaylı olarak ele almaktadır. İlk olarak parçalı fonksiyonların limitleri, kritik noktalar ve sağdan-soldan yaklaşma kavramları anlatılmakta, ardından mutlak değerli fonksiyonların limitleri, trigonometrik fonksiyonlarda limit hesaplamaları ve genişletilmiş reel sayılarda limit kavramı açıklanmaktadır. Son bölümde ise sayı bölü sıfır ve sayı bölü sonsuz durumları incelenmektedir.","Videoda ÖSYM sınavlarında çıkabilecek soru tipleri örneklerle gösterilmekte ve çözüm stratejileri sunulmaktadır. Video sonunda öğrencilere Limit Türev İntegral kitabından sayfa 19'dan 38'e kadar ödev verilmekte ve bir sonraki videoda belirsizlikler konusunun işleneceği belirtilmektedir."]},"endTime":2049,"title":"Matematik Dersinde Fonksiyonların Limitleri","beginTime":0}],"fullResult":[{"index":0,"title":"Parçalı Fonksiyonların Limiti","list":{"type":"unordered","items":["Limit mantığı, bir noktaya yaklaştığında fonksiyonun aldığı değerlerdir.","Parçalı fonksiyonlarda kritik nokta, fonksiyonun parçalandığı noktadır.","Kritik noktada limit sorulduğunda sağdan ve soldan yaklaşma yapılır, limit varsa o değerdir; yoksa limit yoktur."]},"beginTime":3,"endTime":93,"href":"/video/preview/17724041870828594463?parent-reqid=1769685927070540-12168944028472787275-balancer-l7leveler-kubr-yp-sas-43-BAL&text=Edit2Limit&t=3&ask_summarization=1"},{"index":1,"title":"Örnek Sorular","list":{"type":"unordered","items":["İlk örnekte f(x) fonksiyonu x²+7 (x>0) ve 2x-4 (x\u003c0) şeklinde parçalanmış, x→0 sağdan limiti 7, soldan limiti -4 olduğundan limit yoktur.","x→3 limiti 16, x→-2 limiti -8 olarak hesaplanmıştır.","x→1 sağdan limiti -9, soldan limiti -9 olduğundan limit vardır ve -9'dur."]},"beginTime":93,"endTime":329,"href":"/video/preview/17724041870828594463?parent-reqid=1769685927070540-12168944028472787275-balancer-l7leveler-kubr-yp-sas-43-BAL&text=Edit2Limit&t=93&ask_summarization=1"},{"index":2,"title":"Fonksiyon Değerleri ve Kritik Noktalar","list":{"type":"unordered","items":["x→2 limiti -7, x→-6 limiti -6 olarak hesaplanmıştır.","f(1) değeri, x=1 için fonksiyonun değerini verir ve -9'dur.","Limit her yerde varsa, kritik noktada sağdan ve soldan limitler eşit olmalıdır."]},"beginTime":329,"endTime":454,"href":"/video/preview/17724041870828594463?parent-reqid=1769685927070540-12168944028472787275-balancer-l7leveler-kubr-yp-sas-43-BAL&text=Edit2Limit&t=329&ask_summarization=1"},{"index":3,"title":"Kritik Noktada Limit Sorusu","list":{"type":"unordered","items":["f(x) = x² - ax (x≤1) ve 2x - 7 (x>1) şeklinde parçalanmış bir fonksiyonda limitin tüm reel sayılar için olması için a değeri bulunmalıdır.","Kritik nokta x=1'dir ve limitin var olması için x→1 soldan ve x→1 sağdan limitler eşit olmalıdır.","x→1 soldan limiti 2x-7 = x² - ax denkleminden a = 6 olarak bulunmuştur."]},"beginTime":454,"endTime":549,"href":"/video/preview/17724041870828594463?parent-reqid=1769685927070540-12168944028472787275-balancer-l7leveler-kubr-yp-sas-43-BAL&text=Edit2Limit&t=454&ask_summarization=1"},{"index":4,"title":"Parçalı Fonksiyonların Limiti","list":{"type":"unordered","items":["Fonksiyonun tüm reel sayılarda limit olduğuna göre, kritik noktalara (1 ve 3) bakılmalıdır.","Kritik noktalarda limit var olduğundan, x=1 için 2a+b=8 denklemi, x=3 için 9+7=9-3b denklemi kurulur.","Denklemler çözülerek a=17/6 ve b=-7/3 bulunur, a+b toplamı 1,5 olarak hesaplanır."]},"beginTime":552,"endTime":726,"href":"/video/preview/17724041870828594463?parent-reqid=1769685927070540-12168944028472787275-balancer-l7leveler-kubr-yp-sas-43-BAL&text=Edit2Limit&t=552&ask_summarization=1"},{"index":5,"title":"Mutlak Değerli Fonksiyonların Limiti","list":{"type":"unordered","items":["Mutlak değerli fonksiyonlar da parçalı fonksiyonların limitindeki mantıkla çözülür.","Kritik noktada limit sorulursa sağdan ve soldan limitler eşitse limit vardır, eşit değilse limit yoktur.","Kritik nokta dışında soruluyorsa, fonksiyon doğrudan yerine yazılabilir."]},"beginTime":726,"endTime":796,"href":"/video/preview/17724041870828594463?parent-reqid=1769685927070540-12168944028472787275-balancer-l7leveler-kubr-yp-sas-43-BAL&text=Edit2Limit&t=726&ask_summarization=1"},{"index":6,"title":"Mutlak Değerli Fonksiyonların Limit Örnekleri","list":{"type":"unordered","items":["Doğrusal ifadelerde (rasyonel olmayan) limit sorulduğunda, kritik nokta olmasa bile doğrudan yerine yazılabilir.","Mutlak değerli ifadelerde, kritik noktaya sağdan yaklaşıldığında mutlak değer içi pozitif olur, soldan yaklaşıldığında negatif olur.","Paydada mutlak değer varsa ve kritik noktada sağdan ve soldan limitler farklı çıkarsa, limit yoktur."]},"beginTime":796,"endTime":1166,"href":"/video/preview/17724041870828594463?parent-reqid=1769685927070540-12168944028472787275-balancer-l7leveler-kubr-yp-sas-43-BAL&text=Edit2Limit&t=796&ask_summarization=1"},{"index":7,"title":"Mutlak Değerli Limit Problemleri","list":{"type":"unordered","items":["Mutlak değerli ifadelerde limit hesaplaması yaparken önce mutlak değer içindeki ifadenin işaretini belirlemek gerekir.","Soldan yaklaşma durumunda mutlak değer içindeki ifade negatif olur ve mutlak değer işareti çıkarılır.","Sağdan yaklaşma durumunda mutlak değer içindeki ifade pozitif olur ve mutlak değer işareti çıkarılmaz."]},"beginTime":1175,"endTime":1325,"href":"/video/preview/17724041870828594463?parent-reqid=1769685927070540-12168944028472787275-balancer-l7leveler-kubr-yp-sas-43-BAL&text=Edit2Limit&t=1175&ask_summarization=1"},{"index":8,"title":"Trigonometrik Fonksiyonlarda Limit","list":{"type":"unordered","items":["Trigonometrik fonksiyonlarda sağdan ve soldan yaklaşma, birim çemberde açıların hangi bölgeden yaklaştığına bağlıdır.","Saatin yönü sağdan yaklaşma, saatin ters yönü soldan yaklaşma olarak ifade edilebilir.","Trigonometrik fonksiyonlarda limit hesaplaması yaparken önce hangi bölgeden yaklaşıldığına göre işaret belirlenir."]},"beginTime":1325,"endTime":1642,"href":"/video/preview/17724041870828594463?parent-reqid=1769685927070540-12168944028472787275-balancer-l7leveler-kubr-yp-sas-43-BAL&text=Edit2Limit&t=1325&ask_summarization=1"},{"index":9,"title":"Genişletilmiş Reel Sayılarda Limit","list":{"type":"unordered","items":["Genişletilmiş reel sayılarda limit hesaplamasında, sonsuza bir sayı eklenildiğinde veya çıkarıldığında sonuç yine sonsuz olur.","Bir sayının sıfıra bölümü, sayının işaretine göre değişir: pozitif sayı sıfıra sağdan yaklaşırsa artı sonsuz, soldan yaklaşırsa eksi sonsuz olur.","Negatif sayı sıfıra soldan yaklaşırsa eksi sonsuz, sağdan yaklaşırsa artı sonsuz olur."]},"beginTime":1642,"endTime":1820,"href":"/video/preview/17724041870828594463?parent-reqid=1769685927070540-12168944028472787275-balancer-l7leveler-kubr-yp-sas-43-BAL&text=Edit2Limit&t=1642&ask_summarization=1"},{"index":10,"title":"Sonsuz Limit Kavramı","list":{"type":"unordered","items":["Sayı bölü sonsuz her zaman sıfırdır çünkü sıfırın bir işareti yoktur.","Pozitif sayı artı sonsuza bölünmesi artı sonsuz, negatif sayı eksi sonsuza bölünmesi eksi sonsuz sonucunu verir.","Sıfıra sağdan yaklaşıldığında sayı bölü sıfır sonsuz olur ve x pozitif olduğu için artı sonsuz sonucu elde edilir."]},"beginTime":1822,"endTime":1873,"href":"/video/preview/17724041870828594463?parent-reqid=1769685927070540-12168944028472787275-balancer-l7leveler-kubr-yp-sas-43-BAL&text=Edit2Limit&t=1822&ask_summarization=1"},{"index":11,"title":"İşaretlere Göre Limit Hesaplamaları","list":{"type":"unordered","items":["Sıfıra soldan yaklaşıldığında sayı bölü sıfır sonsuz olur ve eksi işaretli olduğu için eksi sonsuz sonucu elde edilir.","Sonsuza yaklaşıldığında sayı bölü sonsuz sonsuz olur, ancak bir eklenildiğinde sonuç sıfır olur.","Eksi sonsuz yerine yazıldığında, eksi işaretli sayılar artı işaretli olur ve sonuç artı sonsuza döner."]},"beginTime":1873,"endTime":1961,"href":"/video/preview/17724041870828594463?parent-reqid=1769685927070540-12168944028472787275-balancer-l7leveler-kubr-yp-sas-43-BAL&text=Edit2Limit&t=1873&ask_summarization=1"},{"index":12,"title":"Ödev Bilgileri","list":{"type":"unordered","items":["Ödev olarak limit türev integral kitabından sayfa 19'dan 38'e kadar çözülmelidir.","Bir sonraki videoda belirsizlikler konusu ele alınacaktır.","Limit konusunun sonraki kısımları sonsuza, belirsizlikler ve süreklilik kısımlarıdır."]},"beginTime":1961,"endTime":2046,"href":"/video/preview/17724041870828594463?parent-reqid=1769685927070540-12168944028472787275-balancer-l7leveler-kubr-yp-sas-43-BAL&text=Edit2Limit&t=1961&ask_summarization=1"}],"linkTemplate":"/video/preview/17724041870828594463?parent-reqid=1769685927070540-12168944028472787275-balancer-l7leveler-kubr-yp-sas-43-BAL&text=Edit2Limit&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"62) AYT Matematik - Limit 2 - İlyas Güneş 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Limit Türkiye geneli 2. TYT deneme sınavı Fizik soru ve çözümleri bu videoda @alfafizik / alfafizik46 #limityayınları #türkiyegenelideneme #tytfiziksoruçözümleri PDF...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/1788581/3412d3a05a8ece6c0222a50aaf57889d/564x318_1"},"target":"_self","position":"13","reqid":"1769685927070540-12168944028472787275-balancer-l7leveler-kubr-yp-sas-43-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769685927070540-12168944028472787275-balancer-l7leveler-kubr-yp-sas-43-BAL&text=videoid:16189321057322767126","teaser":[{"list":{"type":"unordered","items":["Bu video, bir fizik öğretmeninin Limit Yayınları'nın Türkiye geneli deneme sınavının sorularını çözdüğü eğitim içeriğidir. Öğretmen, tahtada görsel materyaller kullanarak konuları açıklamaktadır.","Videoda çeşitli fizik konuları ele alınmaktadır: yüzey gerilimi, sıvı basıncı, kaldırma kuvveti, elektrik devreleri, Ohm yasası, sürtünmeler, yayın geri çağırıcı kuvveti, mekanik enerji korunumu, merceklerin ışık akısına etkisi, su dalgalarının kırılması ve suyun kaynama noktasının yükseklikteki değişimi. Her soru için detaylı açıklamalar yapılarak doğru cevaplar bulunmakta ve çözüm yöntemleri gösterilmektedir.","Öğretmen, sınav sonrası cevapların kontrol edilmesi ve yanlışların irdelenmesi gerektiğini vurgulamakta, günlük hayattan örnekler vererek konuları pekiştirmektedir. Video, öğrencilere sınav başarıları dilekleriyle sonlanmaktadır."]},"endTime":1084,"title":"Fizik Dersi: Limit Yayınları Deneme Sınavı Çözümleri","beginTime":0}],"fullResult":[{"index":0,"title":"Limit Yayınları Deneme Sınavı Çözümü","list":{"type":"unordered","items":["Alfa, Limit Yayınları'nın Mayıs ayında yapılan Türkiye geneli deneme sınavının sorularını çözecek.","Sınav genel bir prova niteliğindeydi ve Türkiye geneli olması nedeniyle bu soruların çözümüne geçilecek.","Çözümler açıklayıcı olacak ve önemli olan yapamadığınız soruların doğrusunun nasıl olduğunu öğrenmektir."]},"beginTime":7,"endTime":35,"href":"/video/preview/16189321057322767126?parent-reqid=1769685927070540-12168944028472787275-balancer-l7leveler-kubr-yp-sas-43-BAL&text=Edit2Limit&t=7&ask_summarization=1"},{"index":1,"title":"Sınav Sonrası Değerlendirme","list":{"type":"unordered","items":["Sınavdan sonra cevaplarınızı kontrol edip neden yanlış yaptığınızı irdelemiyorsanız o sınavın çok fazla faydası olmayacaktır.","Yanlışlarınızı mutlaka irdeleyerek yeniden düşünmeniz, yeniden çözümünü dinlemeniz ve doğrusunu öğrenmeniz oldukça önemlidir."]},"beginTime":35,"endTime":55,"href":"/video/preview/16189321057322767126?parent-reqid=1769685927070540-12168944028472787275-balancer-l7leveler-kubr-yp-sas-43-BAL&text=Edit2Limit&t=35&ask_summarization=1"},{"index":2,"title":"Birinci Soru - Yüzey Gerilimi Deneyi","list":{"type":"unordered","items":["Kerem, alüminyum folyoyu suya yüzecek şekilde bırakıp çentikli kısmına deterjan damlattığında folyonun hareket ettiğini gözlemliyor.","Aynı deneyi yağ ve süt damlatarak tekrarladığında folyonun hareket etmediğini gözlemliyor.","Bu deney yüzey geriliminin etkisini gözlemek için yapılmıştır, deterjan suyun yüzey gerilimini azaltır ve alüminyum folyonun hareket etmesine neden olur.","Bazı sıvılar (yağ ve süt) suyun yüzey gerilimini pek değiştirmez."]},"beginTime":55,"endTime":174,"href":"/video/preview/16189321057322767126?parent-reqid=1769685927070540-12168944028472787275-balancer-l7leveler-kubr-yp-sas-43-BAL&text=Edit2Limit&t=55&ask_summarization=1"},{"index":3,"title":"İkinci Soru - Sıvı İçinde Dengede Kalan Cisim","list":{"type":"unordered","items":["Düşey kesiti kesik konu şeklinde olan içi dolu K cismi sıvı içinde tamamen batacak biçimde dengede kalmaktadır.","Cismin özkütlesi sıvının özkütlesine eşittir çünkü askıda kalıyor.","A yüzeyine uygulanan sıvı basınç kuvveti cismin ağırlığına eşit büyüklüktedir ifadesi yanlıştır çünkü yan yüzeylere de uygulanan basınç kuvvetleri dikkate alınmalıdır."]},"beginTime":174,"endTime":298,"href":"/video/preview/16189321057322767126?parent-reqid=1769685927070540-12168944028472787275-balancer-l7leveler-kubr-yp-sas-43-BAL&text=Edit2Limit&t=174&ask_summarization=1"},{"index":4,"title":"Üçüncü Soru - Elektrik Devresi","list":{"type":"unordered","items":["İç direnci önemsiz, üreteç 10 ohm ve 90 ohmluk dirençler ile R direnci ile elektrik devresi kurulmuştur.","S anahtarı açık iken ampermetre bir değer gösteriyor, kapatıldığında ampermetrenin gösterdiği değer iki katına çıktığına göre R direnci 14 ohmdur.","Akımın iki katına çıkabilmesi için eşdeğer direncin yarıya inmesi gerekir."]},"beginTime":298,"endTime":411,"href":"/video/preview/16189321057322767126?parent-reqid=1769685927070540-12168944028472787275-balancer-l7leveler-kubr-yp-sas-43-BAL&text=Edit2Limit&t=298&ask_summarization=1"},{"index":5,"title":"Fizik Problemi Çözümü","list":{"type":"unordered","items":["Bir yayın geri çağırıcı kuvveti, hareket doğrultusuna dik olduğu için iş yapmaz.","Ağırlık kuvvetinin hareket doğrultusuna paralel bileşeni iş yapar.","Sürtünmeler önemsiz olduğunda, mekanik enerji korunur ve sabit kalır."]},"beginTime":420,"endTime":580,"href":"/video/preview/16189321057322767126?parent-reqid=1769685927070540-12168944028472787275-balancer-l7leveler-kubr-yp-sas-43-BAL&text=Edit2Limit&t=420&ask_summarization=1"},{"index":6,"title":"Mercekler ve Işık Akısı","list":{"type":"unordered","items":["İnce kenarlı mercek (yakınsak mercek) ışınları asal eksene doğru kırar.","Kalın kenarlı mercek ışınları asal eksenden uzaklaşacak şekilde dağıtır.","Mercek konulduğunda, daha önce perdeye uğramayan ışınların bir kısmı perdeye çarpacağı için ışık akısı artar, daha önce perdeye çarpan ışınların bir kısmı perdeye çarpmayacağı için ışık akısı azalır."]},"beginTime":580,"endTime":727,"href":"/video/preview/16189321057322767126?parent-reqid=1769685927070540-12168944028472787275-balancer-l7leveler-kubr-yp-sas-43-BAL&text=Edit2Limit&t=580&ask_summarization=1"},{"index":7,"title":"Su Dalgalarının Kırılması","list":{"type":"unordered","items":["Fizik öğretmeni, su dalgalarının kırılmasını askerlerin çamur ortamına geçişine benzeterek anlatır.","Askerlerin çamur ortamına geçtiğinde hızlarının azaldığı ve ilerleme doğrultusunun değiştiği gösterilir.","Bu görsel, su dalgalarının kırılmasını daha iyi anlamak için kullanılır."]},"beginTime":727,"endTime":743,"href":"/video/preview/16189321057322767126?parent-reqid=1769685927070540-12168944028472787275-balancer-l7leveler-kubr-yp-sas-43-BAL&text=Edit2Limit&t=727&ask_summarization=1"},{"index":8,"title":"Su Dalgalarının Kırılması","list":{"type":"unordered","items":["Dalga tepelerinin görüldüğü su dalgalarının kırılması konusunda, dalgaları ayıran yüzeye geliş doğrultusuyla normal arasındaki açı gelme açısıdır.","Dalga tepesinin ortamları ayıran yüzeyle yaptığı açı ise kırılma açısıdır ve bu açılar birer kenarları birbirine dik olan açıların eşitliği kuralına göre eşittir.","Gelme açısı kırılma açısından büyükse, derin ortamdan sığ ortama geldiğini ve ilerleme doğrultusunun normale yaklaştığını 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