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Deneme PDF...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3370152/352682d2ae4b3ac22de913a1b1bef933/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/LD3cIQIAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"12","reqid":"1765307410326478-12454964806554249617-balancer-l7leveler-kubr-yp-vla-80-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1765307410326478-12454964806554249617-balancer-l7leveler-kubr-yp-vla-80-BAL&text=videoid:12203498088954688165","teaser":[{"list":{"type":"unordered","items":["Bu video, Zikri Sezgin tarafından sunulan bir matematik eğitim içeriğidir. Öğretmen, öğrencilere hitap ederek limit, türev ve integral konularındaki soruları adım adım çözmektedir.","Videoda toplam dokuz farklı matematik sorusu çözülmektedir. İlk bölümde limit, türev ve integral konularından sorular ele alınırken, devamında türev alma kuralları, polinomlar, türevin geometrik yorumu, belirli integral hesaplamaları ve alan bulma yöntemleri anlatılmaktadır. Her soru için farklı çözüm yolları gösterilmekte ve ÖSYM sınavlarında çıkabilecek soru tipleri açıklanmaktadır.","Video sonunda öğretmen, bir sonraki derste trigonometri konusunu ele alacağını belirtmektedir. Ayrıca izleyicilere PDF çıktısını alıp denemeyi çözmelerini ve yapamadıkları soruları incelemelerini önermektedir."]},"endTime":2319,"title":"Matematik Dersi: Limit, Türev ve İntegral","beginTime":0}],"fullResult":[{"index":0,"title":"Limit, Türev ve İntegral Denemesi Tanıtımı","list":{"type":"unordered","items":["Videoda dokuz sorudan oluşan mini bir limit, türev ve integral denemesi bulunmaktadır.","Denemede iki limit, üç türev ve dört integral sorusu bulunmaktadır.","Türevin geometrik yorumu ve integralde alan konularında sorular bulunmaktadır."]},"beginTime":0,"endTime":43,"href":"/video/preview/12203498088954688165?parent-reqid=1765307410326478-12454964806554249617-balancer-l7leveler-kubr-yp-vla-80-BAL&text=Zikri+Sezgin+ile+Matematik&t=0&ask_summarization=1"},{"index":1,"title":"Fonksiyonun Sürekli Olması","list":{"type":"unordered","items":["Bir fonksiyonun sürekli olabilmesi için o noktada limitin olması ve görüntüsünün limit değerine eşit olması gerekir.","Parçalı bir fonksiyonun sürekli olması için limit değerlerinin eşit olması ve fonksiyonun o noktadaki değerinin limit değerine eşit olması gerekir.","Köklü fonksiyonun tanım kümesinde kökün içindeki ifadenin pozitif olması gerekir."]},"beginTime":43,"endTime":301,"href":"/video/preview/12203498088954688165?parent-reqid=1765307410326478-12454964806554249617-balancer-l7leveler-kubr-yp-vla-80-BAL&text=Zikri+Sezgin+ile+Matematik&t=43&ask_summarization=1"},{"index":2,"title":"Belirsizlik Sorusu","list":{"type":"unordered","items":["Belirsizliklerde önce limitin belirsiz olup olmadığını anlamak için x yerine değer yazmak gerekir.","Belirsizlik durumunda iki kare farkı özdeşliği kullanılarak belirsizlik ortadan kaldırılabilir.","Belirsizlik sorusunda b=4 ve c=3 değerleri bulunmuş, b+c toplamı 8 olarak hesaplanmıştır."]},"beginTime":301,"endTime":504,"href":"/video/preview/12203498088954688165?parent-reqid=1765307410326478-12454964806554249617-balancer-l7leveler-kubr-yp-vla-80-BAL&text=Zikri+Sezgin+ile+Matematik&t=301&ask_summarization=1"},{"index":3,"title":"Polinom ve Türev Sorusu","list":{"type":"unordered","items":["Soruda ikinci dereceden bir polinom fonksiyonu verilmiş ve P(1) = 21, P(2) = 24 bilgileri kullanılarak polinomun katsayıları bulunuyor.","Polinom fonksiyonu P(x) = ax² + bx + c şeklinde yazılabilir ve verilen bilgilere göre 3a = 3 ve a = 3 olarak bulunuyor.","Sorunun cevabı P(x) polinomunun en yüksek dereceli terimin katsayısı olan a'nın 3 olduğu."]},"beginTime":505,"endTime":660,"href":"/video/preview/12203498088954688165?parent-reqid=1765307410326478-12454964806554249617-balancer-l7leveler-kubr-yp-vla-80-BAL&text=Zikri+Sezgin+ile+Matematik&t=505&ask_summarization=1"},{"index":4,"title":"Türevin Geometrik Yorumu","list":{"type":"unordered","items":["Türevin geometrik yorumu, bir eğrinin bir noktasındaki teğetin eğimini türev değerinin verdiği bilgisidir.","Soruda m ve n katsayılı ikinci dereceden bir parabol fonksiyonu verilmiş ve (1,4) noktasından çizilen teğet doğrusunun y eksenini 2 noktasında kestiği belirtilmiştir.","Parabolün denklemi f(x) = x² + 2x + 6 olarak bulunmuş ve f(4) değeri -8 olarak hesaplanmıştır."]},"beginTime":660,"endTime":940,"href":"/video/preview/12203498088954688165?parent-reqid=1765307410326478-12454964806554249617-balancer-l7leveler-kubr-yp-vla-80-BAL&text=Zikri+Sezgin+ile+Matematik&t=660&ask_summarization=1"},{"index":5,"title":"Türev ile İlgili Yorum Sorusu","list":{"type":"unordered","items":["Soruda İcornt düzleminde gerçek sayılar kümesi üzerinde tanımlı ve türevlenebilir f ve g fonksiyonlarının grafikleri verilmiş, bunlara bağlı olarak h(x) = f(x)g(x) fonksiyonu tanımlanmıştır.","h'(1) değerini bulmak için çarpım türevi uygulanarak h'(1) = f'(1)g(1) + f(1)g'(1) formülü elde edilmiştir.","f azalan bir fonksiyon olduğu için f'(1) \u003c 0, g artan bir fonksiyon olduğu için g'(1) > 0 olarak belirlenmiş ve h'(1) > 0 olarak sonuçlanmıştır."]},"beginTime":943,"endTime":1184,"href":"/video/preview/12203498088954688165?parent-reqid=1765307410326478-12454964806554249617-balancer-l7leveler-kubr-yp-vla-80-BAL&text=Zikri+Sezgin+ile+Matematik&t=943&ask_summarization=1"},{"index":6,"title":"Belirli İntegral Sorusu","list":{"type":"unordered","items":["Belirli integral sorusunda ∫₁⁴ (x/(x+a))/√x dx integrali verilmiş ve a değeri bulunması istenmiştir.","İntegral, ∫₁⁴ (x/√x) + ∫₁⁴ (a/√x) dx şeklinde parçalanmıştır.","İntegral hesaplanarak a = 2 olarak bulunmuştur."]},"beginTime":1184,"endTime":1459,"href":"/video/preview/12203498088954688165?parent-reqid=1765307410326478-12454964806554249617-balancer-l7leveler-kubr-yp-vla-80-BAL&text=Zikri+Sezgin+ile+Matematik&t=1184&ask_summarization=1"},{"index":7,"title":"Tanım Sorusu","list":{"type":"unordered","items":["Tanım sorusunda f(x) fonksiyonu x/5 sayısının tam kısmı olarak tanımlanmıştır.","f(8) = 1, f(15) = 3, f(16) = 3, f(17) = 3, f(18) = 3, f(19) = 3, f(20) = 4 şeklinde değerler verilmiştir.","f(x) fonksiyonunun grafiği çizilerek 2'den 32'ye kadar f(x) dx integralinin değeri bulunması istenmiştir."]},"beginTime":1459,"endTime":1672,"href":"/video/preview/12203498088954688165?parent-reqid=1765307410326478-12454964806554249617-balancer-l7leveler-kubr-yp-vla-80-BAL&text=Zikri+Sezgin+ile+Matematik&t=1459&ask_summarization=1"},{"index":8,"title":"İntegral ile Alan Hesaplama","list":{"type":"unordered","items":["İntegralin değeri, f(x) fonksiyonu ile x ekseninin altında kalan alanın integral değerine eşittir.","İntegral hesaplaması için alan, dikdörtgenler şeklinde parçalara ayrılır ve her dikdörtgenin alanı hesaplanır.","İntegral hesaplamasında, fonksiyonun grafiğini çizebilme ve x ekseni ile grafik arasında kalan alanlar yardımıyla integral değerini bulabilme becerisi önemlidir."]},"beginTime":1676,"endTime":1850,"href":"/video/preview/12203498088954688165?parent-reqid=1765307410326478-12454964806554249617-balancer-l7leveler-kubr-yp-vla-80-BAL&text=Zikri+Sezgin+ile+Matematik&t=1676&ask_summarization=1"},{"index":9,"title":"Fonksiyon Dönüşümüyle İntegral Hesaplama","list":{"type":"unordered","items":["f(2x) fonksiyonu için integral hesaplaması, değişken değiştirme yöntemiyle veya fonksiyon dönüşümü yöntemiyle yapılabilir.","Değişken değiştirme yöntemiyle integral hesaplanırken, sınırlar ve fonksiyon değerleri değiştirilir.","Fonksiyon dönüşümü yöntemiyle integral hesaplanırken, f(x) fonksiyonunun grafiği f(2x) fonksiyonuna göre nasıl değiştiğini analiz ederek integral değeri bulunur."]},"beginTime":1850,"endTime":2139,"href":"/video/preview/12203498088954688165?parent-reqid=1765307410326478-12454964806554249617-balancer-l7leveler-kubr-yp-vla-80-BAL&text=Zikri+Sezgin+ile+Matematik&t=1850&ask_summarization=1"},{"index":10,"title":"Riemann Toplamı ile Alan Hesaplama","list":{"type":"unordered","items":["Riemann toplamı, bir fonksiyonun grafiğini küçük dikdörtgenlere bölerek alanı hesaplamak için kullanılan bir yöntemdir.","Riemann toplamı, dikdörtgenlerin alanları toplamı olarak hesaplanır ve bu toplam, fonksiyonun gerçek alanına yaklaşır.","f(4) + f(8) toplamının en büyük değeri, Riemann toplamı kullanılarak 9'dan küçük 8 olarak bulunur."]},"beginTime":2139,"endTime":2281,"href":"/video/preview/12203498088954688165?parent-reqid=1765307410326478-12454964806554249617-balancer-l7leveler-kubr-yp-vla-80-BAL&text=Zikri+Sezgin+ile+Matematik&t=2139&ask_summarization=1"},{"index":11,"title":"Dersin Özeti","list":{"type":"unordered","items":["Ders boyunca limit, türev ve integral konuları üzerinden dokuz soru çözülmüştür.","Bir sonraki denemede trigonometri konusu ele alınacak ve yaklaşık beş soru çözülecektir.","Bu denemeler, eksiklerin kapatılması için faydalı olacaktır."]},"beginTime":2281,"endTime":2314,"href":"/video/preview/12203498088954688165?parent-reqid=1765307410326478-12454964806554249617-balancer-l7leveler-kubr-yp-vla-80-BAL&text=Zikri+Sezgin+ile+Matematik&t=2281&ask_summarization=1"}],"linkTemplate":"/video/preview/12203498088954688165?parent-reqid=1765307410326478-12454964806554249617-balancer-l7leveler-kubr-yp-vla-80-BAL&text=Zikri+Sezgin+ile+Matematik&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"AYT Matematik Denemesi 2-Limit Türev İntegral /Zikri Sezgin ile Matematik","related_orig_text":"Zikri Sezgin ile Matematik","related_porno":false,"related_less_3m_off":true,"client":"d2d","no_cnt":1,"related_src":"serp","related":"{\"porno\":false,\"vfp\":1,\"orig_text\":\"Zikri Sezgin ile 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Video, AYT matematik sınavına hazırlanan öğrenciler için geometri konusunda pratik yapmak isteyenler için faydalı olabilir."]},"endTime":1681,"title":"AYT Matematik Geometri Denemesi Çözümü","beginTime":0}],"fullResult":[{"index":0,"title":"Geometri Denemesi Tanıtımı","list":{"type":"unordered","items":["AYT matematik denemesinin ardından 10 soruluk geometri denemesi sunuluyor.","Denemede üçgenler ve üçgen açıları konularında sorular bulunmaktadır.","İzleyicilerden kanala abone olmaları, videoyu beğenmeleri ve yorum yapmaları isteniyor."]},"beginTime":0,"endTime":45,"href":"/video/preview/16687205130058749111?parent-reqid=1765307410326478-12454964806554249617-balancer-l7leveler-kubr-yp-vla-80-BAL&text=Zikri+Sezgin+ile+Matematik&t=0&ask_summarization=1"},{"index":1,"title":"Üçgen Açı Sorusu","list":{"type":"unordered","items":["İlk soruda bir üçgenin bir köşesi etrafında döndürülerek ikizkenar üçgen elde ediliyor.","İkizkenar üçgenin açıları hesaplanarak cevap bulunuyor.","Üçgende açı 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döndürüldüğünde oluşan durum inceleniyor.","Pisagor teoremi kullanılarak çubukların uzunlukları hesaplanıyor.","Çubukların arasındaki mesafe bulunarak cevap elde ediliyor."]},"beginTime":807,"endTime":900,"href":"/video/preview/16687205130058749111?parent-reqid=1765307410326478-12454964806554249617-balancer-l7leveler-kubr-yp-vla-80-BAL&text=Zikri+Sezgin+ile+Matematik&t=807&ask_summarization=1"},{"index":6,"title":"Otopark Bariyer Sorusu","list":{"type":"unordered","items":["Otoparkın girişindeki bariyerin döndürülmesi durumunda oluşan geometrik ilişkiler inceleniyor.","Bariyerin yere uzaklığı hesaplanıyor.","Bariyerin iki durum arasındaki mesafe bulunarak cevap elde ediliyor."]},"beginTime":900,"endTime":1086,"href":"/video/preview/16687205130058749111?parent-reqid=1765307410326478-12454964806554249617-balancer-l7leveler-kubr-yp-vla-80-BAL&text=Zikri+Sezgin+ile+Matematik&t=900&ask_summarization=1"},{"index":7,"title":"Pisagor Sorusu","list":{"type":"unordered","items":["Birim karelere 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