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Welcome to AYT Math Camp. Our AYT Math Camp topics will be completed in a...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/4521119/5ac1cd36161345190bf5a2e92e4ca324/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/_E2wQgIAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"1","reqid":"1769211112467483-10366714487739187384-balancer-l7leveler-kubr-yp-sas-145-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769211112467483-10366714487739187384-balancer-l7leveler-kubr-yp-sas-145-BAL&text=videoid:6761378592904580617","teaser":[{"list":{"type":"unordered","items":["Bu video, Selim Hoca tarafından sunulan AYT matematik dersinin onuncu bölümüdür. Öğretmen, öğrencilere hitap ederek limit ve belirsizlikler konusunu anlatmaktadır.","Videoda trigonometrik sıfır bölü sıfır belirsizliği, limit hesaplamaları ve çeşitli belirsizlik durumları detaylı olarak ele alınmaktadır. Öğretmen önce teorik bilgileri açıklamakta, ardından sinüs ve tanjant fonksiyonlarının limit özelliklerini kullanarak örnek sorular çözmektedir. Ayrıca grafiksel yöntemlerle x'in sonsuza ve eksi sonsuza giderken limit değerlerini incelemektedir.","Video, müfredatta olup olmama arasındaki konuları da içermekte ve ÖSYM sınavlarında çıkabilecek zorlu limit problemlerini içermektedir. Özellikle \"bir sayı bölü x\", \"bir basit kesrin sonsuzuncu kuvveti\" ve \"sonsuz bölü sonsuz\" gibi belirsizlik durumlarında limitin nasıl hesaplanacağı detaylı olarak açıklanmaktadır. Dersin sonunda süreklilik konusuna geçileceği belirtilmektedir."]},"endTime":2356,"title":"AYT Matematik Dersi: Limit ve Belirsizlikler","beginTime":0}],"fullResult":[{"index":0,"title":"Limit Dersinin Önemi","list":{"type":"unordered","items":["Limit dersinin onuncu derse devam ediliyor ve AYT matematik için önemli bir konu olarak vurgulanıyor.","Limit, türev ve integral konularında soru kaçırmamak için detaylı anlatımlar yapılacak.","Bu videoda müfredatta olup olmama arasındaki konular ele alınacak ve trigonometrik sıfır bölü sıfır belirsizliği konusu işlenecek."]},"beginTime":0,"endTime":108,"href":"/video/preview/6761378592904580617?parent-reqid=1769211112467483-10366714487739187384-balancer-l7leveler-kubr-yp-sas-145-BAL&text=10+Hour+Limit+-+Topic&t=0&ask_summarization=1"},{"index":1,"title":"Trigonometrik Sıfır Bölü Sıfır Belirsizliği","list":{"type":"unordered","items":["Bu videodan sonra limit sorularının testi bitirilecek ve sonraki derste süreklilik konusuna başlanacak.","Trigonometrik sıfır bölü sıfır belirsizliği için kalıplar var ve bu kalıplar varsa soruların içerisinde direkt kolay bir yöntem bulunuyor.","Kalıplar: Limit x sıfıra giderken sinüs ax bölü sinüs bx şeklinde bir şey çıkarsa veya limit x sıfıra giderken ax bölü sinüs bx şeklinde bir şey çıkarsa, cevap a bölü b'dir."]},"beginTime":108,"endTime":215,"href":"/video/preview/6761378592904580617?parent-reqid=1769211112467483-10366714487739187384-balancer-l7leveler-kubr-yp-sas-145-BAL&text=10+Hour+Limit+-+Topic&t=108&ask_summarization=1"},{"index":2,"title":"Kalıbın Uygulanması","list":{"type":"unordered","items":["Yukarıda sinüs, aşağıda sinüs veya yukarıda x'li bir durum, aşağıda sinüslü veya yukarıda sinüslü aşağıda xli bir şey varsa, cevap a bölü b'dir.","Sinüs x bölü x belirsizliği için cevap 1'dir çünkü sinüs x'in katsayısı 1'dir.","Tanjant için de aynı kalıp geçerlidir: Limit x sıfıra giderken tanjant ax bölü tanjant bx şeklinde bir şey çıkarsa veya limit x sıfıra giderken ax bölü tanjant b şeklinde bir şey çıkarsa, cevap a bölü b'dir."]},"beginTime":215,"endTime":334,"href":"/video/preview/6761378592904580617?parent-reqid=1769211112467483-10366714487739187384-balancer-l7leveler-kubr-yp-sas-145-BAL&text=10+Hour+Limit+-+Topic&t=215&ask_summarization=1"},{"index":3,"title":"Özel Durumlar","list":{"type":"unordered","items":["Kareköklü ifadelerde de bu özellik kullanılabilir, örneğin limit x sıfıra giderken sinüs karekök x bölü tanjant beş karekök x şeklinde bir şey çıkarsa, cevap 3/5'tir.","Sinüs ve tanjant aynı anda varsa da özellik uygulanabilir, örneğin limit x sıfıra giderken tanjant x bölü x, tanjant ax bölü tanjant bx veya tanjant x bölü tanjant b şeklinde bir şey çıkarsa, cevap a bölü b'dir.","Sorularda bu tanımlar verilip cevap sorulabilir."]},"beginTime":334,"endTime":435,"href":"/video/preview/6761378592904580617?parent-reqid=1769211112467483-10366714487739187384-balancer-l7leveler-kubr-yp-sas-145-BAL&text=10+Hour+Limit+-+Topic&t=334&ask_summarization=1"},{"index":4,"title":"Örnek Sorular","list":{"type":"unordered","items":["Örnek 84'te x sıfıra giderken üç farklı belirsizlik çözülüyor ve cevap -3/2 olarak bulunuyor.","Örnek 85'te sinüs küp 2x ifadesi sinüs 2x çarpı sinüs 2x çarpı sinüs 2x şeklinde parçalanarak kalıba benzetiliyor ve cevap 8/3 olarak bulunuyor.","Örnek 86'da tanjant 4x ifadesi için, toplam durumunda olduğu için her iki ifade de x'e bölünerek çözüm yapılıyor."]},"beginTime":435,"endTime":668,"href":"/video/preview/6761378592904580617?parent-reqid=1769211112467483-10366714487739187384-balancer-l7leveler-kubr-yp-sas-145-BAL&text=10+Hour+Limit+-+Topic&t=435&ask_summarization=1"},{"index":5,"title":"Limit Problemlerinin Çözümü","list":{"type":"unordered","items":["Limit problemlerinde, sinüs ve tanjant fonksiyonlarının x'e bölünmesi durumunda, limit değeri hesaplanabilir.","Limit hesaplamasında, sinüs ve tanjant fonksiyonlarının katsayıları ve x'in sıfıra yaklaşması durumunda limit değeri bulunabilir.","Limit problemlerinde, sinüs ve tanjant fonksiyonlarının katsayıları ve x'in sıfıra yaklaşması durumunda limit değeri hesaplanabilir."]},"beginTime":669,"endTime":742,"href":"/video/preview/6761378592904580617?parent-reqid=1769211112467483-10366714487739187384-balancer-l7leveler-kubr-yp-sas-145-BAL&text=10+Hour+Limit+-+Topic&t=669&ask_summarization=1"},{"index":6,"title":"Limit Özelliklerinin Kullanımı","list":{"type":"unordered","items":["Limit problemlerinde, sinüs ve tanjant fonksiyonlarının katsayıları ve x'in sıfıra yaklaşması durumunda limit değeri hesaplanabilir.","Limit problemlerinde, sinüs ve tanjant fonksiyonlarının katsayıları ve x'in sıfıra yaklaşması durumunda limit değeri hesaplanabilir.","Limit problemlerinde, sinüs ve tanjant fonksiyonlarının katsayıları ve x'in sıfıra yaklaşması durumunda limit değeri hesaplanabilir."]},"beginTime":742,"endTime":1043,"href":"/video/preview/6761378592904580617?parent-reqid=1769211112467483-10366714487739187384-balancer-l7leveler-kubr-yp-sas-145-BAL&text=10+Hour+Limit+-+Topic&t=742&ask_summarization=1"},{"index":7,"title":"Grafiksel Limit Problemleri","list":{"type":"unordered","items":["Grafiksel limit problemlerinde, x'in sonsuza giderken fonksiyonun limiti grafik üzerinden görülebilir.","Grafiksel limit problemlerinde, x'in eksi sonsuza giderken fonksiyonun limiti grafik üzerinden görülebilir.","Grafiksel limit problemlerinde, x'in sıfıra giderken fonksiyonun limiti grafik üzerinden görülebilir."]},"beginTime":1043,"endTime":1166,"href":"/video/preview/6761378592904580617?parent-reqid=1769211112467483-10366714487739187384-balancer-l7leveler-kubr-yp-sas-145-BAL&text=10+Hour+Limit+-+Topic&t=1043&ask_summarization=1"},{"index":8,"title":"Limit Problemlerinin Çözümü","list":{"type":"unordered","items":["Grafiksel limit problemlerinde, x'in sıfıra giderken fonksiyonun limiti grafik üzerinden görülebilir.","Grafiksel limit problemlerinde, x'in eksi sonsuza giderken fonksiyonun limiti grafik üzerinden görülebilir.","Grafiksel limit problemlerinde, x'in artı sonsuza giderken fonksiyonun limiti grafik üzerinden görülebilir."]},"beginTime":1166,"endTime":1254,"href":"/video/preview/6761378592904580617?parent-reqid=1769211112467483-10366714487739187384-balancer-l7leveler-kubr-yp-sas-145-BAL&text=10+Hour+Limit+-+Topic&t=1166&ask_summarization=1"},{"index":9,"title":"Limit Değerlerinin Hesaplanması","list":{"type":"unordered","items":["x değerleri eksi sonsuza doğru giderken, grafiğin eksi iki noktasına yaklaştığı görülmektedir.","x değerleri artı sonsuza doğru giderken, sonuçların sıfır olduğu yere yaklaştığı gözlemlenmektedir.","x=-3 ve x=2 noktalarındaki limit değerleri hesaplanırken, sağdan ve soldan yaklaşımların aynı olduğu için limit değerleri doğru olarak belirlenmiştir."]},"beginTime":1258,"endTime":1335,"href":"/video/preview/6761378592904580617?parent-reqid=1769211112467483-10366714487739187384-balancer-l7leveler-kubr-yp-sas-145-BAL&text=10+Hour+Limit+-+Topic&t=1258&ask_summarization=1"},{"index":10,"title":"Müfredatta Muallak Konular","list":{"type":"unordered","items":["Müfredatta olup olmaması muallak olan bir durum anlatılacaktır.","Eskiden müfredatta sonucu sonsuz olan limitler vardı, ancak şimdi müfredat bunu bırakmıştır.","Sonsuz limitlerde x değerleri sonsuza giderken sonucun 3, -5 gibi gerçel sayı olduğu durumlar muallak olarak bırakılmıştır."]},"beginTime":1335,"endTime":1402,"href":"/video/preview/6761378592904580617?parent-reqid=1769211112467483-10366714487739187384-balancer-l7leveler-kubr-yp-sas-145-BAL&text=10+Hour+Limit+-+Topic&t=1335&ask_summarization=1"},{"index":11,"title":"Sonsuz Limitlerde Limit Hesaplamaları","list":{"type":"unordered","items":["x değerleri sonsuza giderken limitleri hesaplanırken, sonucu sonsuz olmayanlara bakılacaktır.","Bir sayıyı sonsuz büyüklükte bir şeye böldüğünüzde limit olarak sıfıra yaklaşır.","x sonsuza giderken bir sayı bölü x gibi bir şey çıkarsa sonucu sıfırdır."]},"beginTime":1402,"endTime":1527,"href":"/video/preview/6761378592904580617?parent-reqid=1769211112467483-10366714487739187384-balancer-l7leveler-kubr-yp-sas-145-BAL&text=10+Hour+Limit+-+Topic&t=1402&ask_summarization=1"},{"index":12,"title":"Basit Kesirlerin Sonsuz Kuvvetleri","list":{"type":"unordered","items":["Bir basit kesrin (0,1 arasında bir sayının) sonsuzuncu kuvvetini aldığınızda limit olarak sıfıra yaklaşır.","Bileşik kesirlerin (örneğin 250x) sonsuz kuvveti alındığında limit sonsuz olacağı için bu durum ilgilendirmez.","Sonsuza giderken limitlerde bir sayı bölü x belirsizliği karşımıza gelirse, bir sayıyı sonsuz büyüklükte bir sayıya böldüğümüzde limit olarak sıfıra yaklaşır."]},"beginTime":1527,"endTime":1715,"href":"/video/preview/6761378592904580617?parent-reqid=1769211112467483-10366714487739187384-balancer-l7leveler-kubr-yp-sas-145-BAL&text=10+Hour+Limit+-+Topic&t=1527&ask_summarization=1"},{"index":13,"title":"Trigonometrik Limit Hesaplamaları","list":{"type":"unordered","items":["x yerine sonsuz yazıldığında, sinüs 5 çarpı sonsuz şeklinde bir ifade elde edilir.","Sinüs sonsuz değeri, sinüsün eksi bir ile bir aralığında bir sayı olması nedeniyle bir sayıdır.","Bir sayıyı sonsuza böldüğünüzde cevabınız sıfıra yaklaşır."]},"beginTime":1715,"endTime":1782,"href":"/video/preview/6761378592904580617?parent-reqid=1769211112467483-10366714487739187384-balancer-l7leveler-kubr-yp-sas-145-BAL&text=10+Hour+Limit+-+Topic&t=1715&ask_summarization=1"},{"index":14,"title":"Sonsuz Limit Problemleri","list":{"type":"unordered","items":["Basit kesirlerin sonsuzuncu kuvveti sıfıra yaklaşır çünkü gittikçe kuvvetlerini aldıkça basit kesirler küçülür.","Eksi 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