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want to thank all of you for your help.. My email is : wass11121996@gmail.com ! TheMain causes of this error are : ! 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Eğitmen önce denklemin bu aralıkta bir kökünün olduğunu çarpanlara ayırma yöntemiyle göstermekte, ardından g(x) sabit nokta fonksiyonunu belirlemek için iki farklı yöntem sunmaktadır. Daha sonra P(n) ve G(n) fonksiyonlarını kullanarak iterasyonları gerçekleştirmekte ve her adımda hata değerini hesaplamaktadır.","Videoda 10^-2 hassaslıkta iterasyonlar başlatılarak kök yaklaşık değeri bulunmakta ve beşinci iterasyon sonucunda virgülden sonra dört basamak alınarak sonuç verilmektedir."]},"endTime":1091,"title":"Tekrarlama Metodu ile Kök Bulma Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Tekrarlama Metodu Örnek Sorusu","list":{"type":"unordered","items":["Video, tekrarlama metodu (sabit nokta metodu) konusuna örnek bir sorunun çözümünü sunuyor.","Soruda x² - 2x - 3 denkleminin [2,4] kapalı aralığındaki çözümü bulunacak.","Denklemin bu aralıkta bir kökü olduğunu çarpanlara ayırarak (x-3)(x+1) olarak gösteriyoruz ve kökün 3 olduğu, aralığın içinde bulunduğu belirtiliyor."]},"beginTime":0,"endTime":131,"href":"/video/preview/6151304663751752070?parent-reqid=1769681431662881-14747480565370533227-balancer-l7leveler-kubr-yp-klg-194-BAL&text=Fixer+Analysis&t=0&ask_summarization=1"},{"index":1,"title":"Sabit Nokta Fonksiyonu Belirleme","list":{"type":"unordered","items":["Tekrarlama metodu için x = g(x) şeklinde bir sabit nokta fonksiyonu belirlenmesi gerekiyor.","İki farklı g(x) fonksiyonu bulunuyor: g(x) = (x²-3)/2 ve g(x) = √(2x+3).","g'(x) \u003c 1 şartını sağlayan g(x) fonksiyonu seçilmesi gerekiyor, bu şekilde aralıktan seçilen her x değeri köke yaklaşıyor."]},"beginTime":131,"endTime":334,"href":"/video/preview/6151304663751752070?parent-reqid=1769681431662881-14747480565370533227-balancer-l7leveler-kubr-yp-klg-194-BAL&text=Fixer+Analysis&t=131&ask_summarization=1"},{"index":2,"title":"Sabit Nokta Fonksiyonu Seçimi","list":{"type":"unordered","items":["g(x) = (x²-3)/2 için g'(2) = 2 ve g'(4) = 4, bu değerler 1'den büyük olduğu için bu fonksiyon kullanılamaz.","g(x) = √(2x+3) için g'(2) = 1/√7 ve g'(4) = 1/√11, bu değerler 1'den küçük olduğu için bu fonksiyon kullanılabilir.","Piyasada yaygın kullanılan yöntem, g'(x) \u003c 1 olma şartını doğrudan kontrol etmek yerine, g'(x) ≤ 1/√7 (her x ∈ [2,4] için) şeklinde ifade etmek."]},"beginTime":334,"endTime":602,"href":"/video/preview/6151304663751752070?parent-reqid=1769681431662881-14747480565370533227-balancer-l7leveler-kubr-yp-klg-194-BAL&text=Fixer+Analysis&t=334&ask_summarization=1"},{"index":3,"title":"Iterasyonlar ve Hassaslık","list":{"type":"unordered","items":["p₀ = 4 ile başlayarak iterasyonlar gerçekleştirilecek ve 10⁻² hassaslıkla köke yaklaşılacak.","İlk iterasyonda p₁ = g(p₀) = g(4) = √(2·4+3) ≈ 3,3166 bulunuyor.","Hassaslık kontrolü için |3 - 3,3166| = 0,3166 > 10⁻² olduğu için iterasyonlar devam etmelidir."]},"beginTime":602,"endTime":766,"href":"/video/preview/6151304663751752070?parent-reqid=1769681431662881-14747480565370533227-balancer-l7leveler-kubr-yp-klg-194-BAL&text=Fixer+Analysis&t=602&ask_summarization=1"},{"index":4,"title":"İterasyon Yöntemiyle Kök Bulma","list":{"type":"unordered","items":["İkinci iterasyonda p₂ = g(p₁) formülü kullanılarak hesaplama yapılıyor.","Hesaplamada g fonksiyonu kullanılarak kök değeri bulunuyor ve hassasiyet 10⁻² (virgülden sonra 2 basamak) olarak belirleniyor.","Gerçek kök değeri 3,37 ve yaklaşık kök değeri 3,3316 bulunuyor, hata değeri 0,0384 olarak hesaplanıyor."]},"beginTime":769,"endTime":864,"href":"/video/preview/6151304663751752070?parent-reqid=1769681431662881-14747480565370533227-balancer-l7leveler-kubr-yp-klg-194-BAL&text=Fixer+Analysis&t=769&ask_summarization=1"},{"index":5,"title":"İterasyonların Devamı","list":{"type":"unordered","items":["Üçüncü iterasyonda p₃ = g(p₂) formülü kullanılarak hesaplama yapılıyor ve yaklaşık kök değeri 3,44 olarak bulunuyor.","Dördüncü iterasyonda p₄ = g(p₃) formülü kullanılarak hesaplama yapılıyor ve yaklaşık kök değeri 3,1114 olarak bulunuyor.","Beşinci iterasyonda p₅ = g(p₄) formülü kullanılarak hesaplama yapılıyor ve yaklaşık kök değeri 3,38 olarak bulunuyor."]},"beginTime":864,"endTime":1034,"href":"/video/preview/6151304663751752070?parent-reqid=1769681431662881-14747480565370533227-balancer-l7leveler-kubr-yp-klg-194-BAL&text=Fixer+Analysis&t=864&ask_summarization=1"},{"index":6,"title":"Sonuç ve Hassasiyet","list":{"type":"unordered","items":["Beşinci iterasyonda hata değeri 0,0112 olarak hesaplanıyor ve bu 10⁻² hassasiyet değerinden küçük olduğu için iterasyonlar sonlandırılıyor.","Yaklaşık kök değeri 3,38 olarak bulunuyor ve virgülden sonra 4 basamak alınarak hesaplama yapılıyor.","Sorunun hassasiyet değeri belirtilmediği durumda 10⁻² hassasiyet değeri kullanılarak çözüm 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