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Sonuç olarak, limitin 2 olduğu bulunmuştur."]},"endTime":364,"title":"Matematik Dersinde Limit Hesaplama","beginTime":0}],"fullResult":[{"index":0,"title":"Sonsuz Limit Problemi","list":{"type":"unordered","items":["n yerine sonsuz yazıldığında çarpı sonsuz belirsizliği oluşuyor ve bu belirsizliği Lobital kuralı kullanarak çözemiyoruz.","Toplam sembolü kullanılarak integral hesaplanarak limit hesaplanacak.","Limit n sonsuza giderken 3 bölü n toplam k eşittir 0'dan 3n-1'e kadar şeklinde ifade ediliyor."]},"beginTime":7,"endTime":65,"href":"/video/preview/1169669755244487116?parent-reqid=1769394139125214-15140574026912942731-balancer-l7leveler-kubr-yp-klg-155-BAL&text=Integral+Limited&t=7&ask_summarization=1"},{"index":1,"title":"Toplam Sembolünün Oluşturulması","list":{"type":"unordered","items":["Değişen kısım k değişkeni olup, kök içinde n bölü (n+3) çarpı k şeklinde ifade ediliyor.","K yerine 0, 1, 2, ..., n-1 değerleri yazarak terimler tek tek elde edilebiliyor.","B-a farkı 3 olarak 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hesaplanırken kök içindeki ifade u olarak alınarak u üzeri eksi bir bölü iki integrali alınıyor.","Sonuç olarak 2 karekök 4 eksi 2 karekök 1 hesaplanıyor ve sonuç 2 olarak bulunuyor."]},"beginTime":312,"endTime":355,"href":"/video/preview/1169669755244487116?parent-reqid=1769394139125214-15140574026912942731-balancer-l7leveler-kubr-yp-klg-155-BAL&text=Integral+Limited&t=312&ask_summarization=1"}],"linkTemplate":"/video/preview/1169669755244487116?parent-reqid=1769394139125214-15140574026912942731-balancer-l7leveler-kubr-yp-klg-155-BAL&text=Integral+Limited&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Limitlerin integral yardımı ile hesaplanması 3","related_orig_text":"Integral Limited","related_porno":false,"related_less_3m_off":true,"client":"d2d","no_cnt":1,"related_src":"serp","related":"{\"porno\":false,\"vfp\":1,\"orig_text\":\"Integral 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integralle hesaplanması, integralle limit...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/926314/8f4517afa89359371e6c9f89f2fc62ce/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/2kPMDAAAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"13","reqid":"1769394139125214-15140574026912942731-balancer-l7leveler-kubr-yp-klg-155-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769394139125214-15140574026912942731-balancer-l7leveler-kubr-yp-klg-155-BAL&text=videoid:14412685481863883236","teaser":[{"list":{"type":"unordered","items":["Bu video, bir matematik dersi formatında olup, bir eğitmen tarafından sonsuz toplamın limitinin nasıl hesaplanacağı anlatılmaktadır.","Videoda, n tane terimden oluşan bir sonsuz toplamın limitinin hesaplanması konusu ele alınmaktadır. Eğitmen önce belirsizlik durumunu açıklar, ardından integral kullanarak limitin nasıl hesaplanacağını adım adım gösterir. Özellikle toplam sembolü ve integral teoremi kullanılarak, limitin ln(2) olarak bulunması detaylı olarak anlatılmaktadır."]},"endTime":390,"title":"Sonsuz Toplamın Limiti Hesaplama Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Sonsuz Toplamın Limiti","list":{"type":"unordered","items":["Sonsuz toplamın limiti hesaplanmaya çalışılıyor, burada n tane terim var ancak n sonsuza gittiği için sonsuz toplam olarak adlandırılıyor.","Bir bölü sonsuzdan sıfır artı sıfır artı nokta nokta artı şeklinde bir toplam oluşur, ancak bu toplamın sonucu sıfır değildir.","Sıfır olmayan sonsuz tane sıfırın toplamı için \"çarpı sonsuz\" belirsizliği oluşur ve bu durumda direkt sonuç söyleyebileceğimiz bir durum yoktur."]},"beginTime":5,"endTime":80,"href":"/video/preview/14412685481863883236?parent-reqid=1769394139125214-15140574026912942731-balancer-l7leveler-kubr-yp-klg-155-BAL&text=Integral+Limited&t=5&ask_summarization=1"},{"index":1,"title":"İntegral Kullanarak Çözüm","list":{"type":"unordered","items":["İntegral kullanarak bu sorunun çözümü yapılabilir, limit n sonsuza giderken b eksi a bölü n toplam k eşittir a'dan b'ye f(x) dx formülüne başvurulur.","Toplam sembolü kullanılarak limit n sonsuza giderken bir bölü n toplam sembolü k eşittir bir bölü bir artı k bölü n şeklinde yazılır.","Paydayı n parantezine alarak b eksi a bölü n ifadesi oluşturulur ve bu ifade 1 olarak bulunur."]},"beginTime":80,"endTime":291,"href":"/video/preview/14412685481863883236?parent-reqid=1769394139125214-15140574026912942731-balancer-l7leveler-kubr-yp-klg-155-BAL&text=Integral+Limited&t=80&ask_summarization=1"},{"index":2,"title":"İntegral Hesaplama","list":{"type":"unordered","items":["a'yı 0, b'yi 1 alarak f(k/n) = 1 bölü (1+k/n) fonksiyonu elde edilir, bu da f(x) = 1 bölü (1+x) fonksiyonuna karşılık gelir.","İntegral a'dan b'ye f(x) dx şeklinde yazılır, a=0, b=1 olduğundan integral ln(1+x) sınırlar 0'dan 1'e hesaplanır.","İntegral hesaplandığında cevap ln(2) olarak bulunur."]},"beginTime":291,"endTime":390,"href":"/video/preview/14412685481863883236?parent-reqid=1769394139125214-15140574026912942731-balancer-l7leveler-kubr-yp-klg-155-BAL&text=Integral+Limited&t=291&ask_summarization=1"}],"linkTemplate":"/video/preview/14412685481863883236?parent-reqid=1769394139125214-15140574026912942731-balancer-l7leveler-kubr-yp-klg-155-BAL&text=Integral+Limited&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Limitlerin integral yardımı ile hesaplanması 2","related_orig_text":"Integral Limited","related_porno":false,"related_less_3m_off":true,"client":"d2d","no_cnt":1,"related_src":"serp","related":"{\"porno\":false,\"vfp\":1,\"orig_text\":\"Integral 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İntegral Yardimi İLE Hesaplanmasi...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/918314/de8e5f9ae44b20dfdbfa260b018b863a/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/RqdOmwAAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"14","reqid":"1769394139125214-15140574026912942731-balancer-l7leveler-kubr-yp-klg-155-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769394139125214-15140574026912942731-balancer-l7leveler-kubr-yp-klg-155-BAL&text=videoid:12925336680531343061","teaser":[{"list":{"type":"unordered","items":["Bu video, bir matematik eğitmeni tarafından sunulan bir ders anlatımıdır. Eğitmen, sonsuz toplam limit probleminin çözümünü adım adım göstermektedir.","Videoda, toplam sembolü içeren bir limit problemi ele alınmaktadır. Eğitmen önce toplam sembolünün önündeki yapıyı düzenleyerek, limitin integral yardımıyla çözülebileceğini göstermektedir. Ardından, limitin integraline dönüştürülmesi için gerekli dönüşümleri yaparak, son olarak da özel bir integral formülünü kullanarak çözümü tamamlamaktadır. Video, limit problemlerinin integral yardımıyla nasıl çözülebileceğini gösteren bir örnek sunmaktadır."]},"endTime":561,"title":"Sonsuz Toplam Limit Problemi Çözümü","beginTime":0}],"fullResult":[{"index":0,"title":"Sonsuz Terimli Limit Problemi","list":{"type":"unordered","items":["Video, toplam sembolü içeren ve sonsuz terim içeren bir limit probleminin çözümünü anlatıyor.","Toplamın limiti yerine bir f(x) fonksiyonunun integralini almak aynı şeydir.","Problemin çözümü için önce toplam sembolünün önüne b-a/n yapısını oluşturmak gerekiyor."]},"beginTime":19,"endTime":130,"href":"/video/preview/12925336680531343061?parent-reqid=1769394139125214-15140574026912942731-balancer-l7leveler-kubr-yp-klg-155-BAL&text=Integral+Limited&t=19&ask_summarization=1"},{"index":1,"title":"Limit İfadesinin Sadeleştirilmesi","list":{"type":"unordered","items":["Limit ifadesinde paydada n varken, yukarıda 3 olduğu için 3 sabit sayı gibi dışarı çıkarılabilir.","İfadeler sadeleştirilerek n sonsuza giderken 3/n toplam sembolü k=1'den n'ye kadar 1/(1+3k/n) çarpı e^(1+3k/n) şeklinde yazılır.","Formülde b-a/n yapısı 3/n'ye tekabül ediyor ve a=0, b=3 olarak seçiliyor."]},"beginTime":130,"endTime":394,"href":"/video/preview/12925336680531343061?parent-reqid=1769394139125214-15140574026912942731-balancer-l7leveler-kubr-yp-klg-155-BAL&text=Integral+Limited&t=130&ask_summarization=1"},{"index":2,"title":"Fonksiyonun Bulunması ve İntegral Hesaplanması","list":{"type":"unordered","items":["f(x) fonksiyonu 1/(1+x) çarpı e^(√(1+x)) olarak bulunuyor.","İntegral hesaplaması için e^(√(1+x)) bölü 1/(√(1+x)) dx integrali 0'dan 3'e kadar hesaplanıyor.","Dönüşüm yaparak √(1+x)=u alınarak integral 2e^(u) dx şeklinde yazılır ve sonucu e olarak bulunur."]},"beginTime":394,"endTime":554,"href":"/video/preview/12925336680531343061?parent-reqid=1769394139125214-15140574026912942731-balancer-l7leveler-kubr-yp-klg-155-BAL&text=Integral+Limited&t=394&ask_summarization=1"}],"linkTemplate":"/video/preview/12925336680531343061?parent-reqid=1769394139125214-15140574026912942731-balancer-l7leveler-kubr-yp-klg-155-BAL&text=Integral+Limited&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Limitlerin integral yardımı ile hesaplanması 5","related_orig_text":"Integral Limited","related_porno":false,"related_less_3m_off":true,"client":"d2d","no_cnt":1,"related_src":"serp","related":"{\"porno\":false,\"vfp\":1,\"orig_text\":\"Integral 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