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Bir eğitmen tarafından trigonometrik ifadelerin Tyler polinomunun nasıl bulunacağı anlatılmaktadır.","Videoda, beşinci dereceden Tyler polinomunun hesaplanması ve x=2 noktasındaki yaklaşık değerinin bulunması adım adım gösterilmektedir. Eğitmen önce Tyler polinomunun formülünü açıklar, ardından sinüs fonksiyonunun türevlerini hesaplayarak polinomu bulur. Son olarak, x=2 noktasındaki hata payını hesaplamak için gerçek değer ve hesaplanan değer arasındaki farkı hesaplar ve hata polinomunu bulma yöntemini kısaca anlatır. Video, sınavlara yönelik bir soru çözümü niteliğindedir."]},"endTime":720,"title":"Tyler Polinomu Soru Çözümü","beginTime":0}],"fullResult":[{"index":0,"title":"Tyler Polinomu Tanıtımı","list":{"type":"unordered","items":["Soru çözüm eğitim ve yazılım kanalında Tyler serisi polinomuna kaldığı yerden devam ediliyor.","Önceki videolarda sayısal analizle ilgili iki adet soru çözümü ve konu anlatımı yapılmıştı.","Bu videoda trigonometrik ifadelerin Tyler polinomunun nasıl bulunabileceği incelenecek."]},"beginTime":0,"endTime":37,"href":"/video/preview/2903274716612106923?parent-reqid=1769373659712389-18017472934028798691-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Sinx1967&t=0&ask_summarization=1"},{"index":1,"title":"Tyler Polinomu Formülü","list":{"type":"unordered","items":["Tyler polinomu formülü yazılmalı, kafanın ezbere gitmemeli.","Beşinci dereceden Tyler polinomu formülü: P₅(x) = f(x) + f'(x)x + f''(x)x²/2! + f'''(x)x³/3! + f''''(x)x⁴/4! + f'''''(x)x⁵/120! şeklinde yazılır.","Formülde türev ifadeleri sağ tarafa yazılmalı ki sonradan kolaylık olsun."]},"beginTime":37,"endTime":155,"href":"/video/preview/2903274716612106923?parent-reqid=1769373659712389-18017472934028798691-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Sinx1967&t=37&ask_summarization=1"},{"index":2,"title":"Trigonometrik Fonksiyonun Türevleri","list":{"type":"unordered","items":["f(x) = sin(x) fonksiyonunun türevleri: f'(x) = cos(x), f''(x) = -sin(x), f'''(x) = -cos(x), f''''(x) = sin(x), f'''''(x) = cos(x).","x = 0'da sin(0) = 0, cos(0) = 1 değerleri kullanılır.","Tyler polinomu formülü adım adım hesaplanır."]},"beginTime":155,"endTime":373,"href":"/video/preview/2903274716612106923?parent-reqid=1769373659712389-18017472934028798691-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Sinx1967&t=155&ask_summarization=1"},{"index":3,"title":"Tyler Polinomunun Hesaplanması","list":{"type":"unordered","items":["Tyler polinomu P₅(x) = 0, x - x³/6, x⁵/120 şeklinde bulunur.","x = 2 için Tyler polinomunun değeri hesaplanır: P₅(2) = 0, 2 - 8/6, 2⁵/120 = 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videoda sıkıştırma (sandviç) teoremini öğreneceğiz ve limit x sıfıra giderken sinx/x in sonucunun 1 olduğunu ispatlayacağız. Kafanıza takılan varsa yorum bırakabilirsiniz. Destek olmak için...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3919775/7067426065c5a0675487121e6155a401/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/8LEBJgEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"6","reqid":"1769373659712389-18017472934028798691-balancer-l7leveler-kubr-yp-vla-227-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769373659712389-18017472934028798691-balancer-l7leveler-kubr-yp-vla-227-BAL&text=videoid:9367011482521495410","teaser":[{"list":{"type":"unordered","items":["Bu video, bir matematik dersi formatında olup, bir eğitmen tarafından limit konusunun devamı olarak sıkıştırma teoremi (sandviç teoremi) anlatılmaktadır.","Videoda öncelikle sıkıştırma teoremi grafik üzerinden açıklanmakta ve teorik olarak anlatılmaktadır. Ardından, sinüs x bölü x limitinin sıkıştırma teoremi kullanılarak nasıl ispatlanacağı adım adım gösterilmektedir. Eğitmen, birim çember kullanarak sinüs, kosinüs ve tanjant fonksiyonlarının alanlarını karşılaştırarak, sinüs x bölü x'in limitinin 1 olduğunu ispatlamaktadır. Video, bu limitin grafiksel gösterimiyle sonlanmaktadır."]},"endTime":663,"title":"Sıkıştırma Teoremi ve Sinüs/X Limitinin İspatı","beginTime":0}],"fullResult":[{"index":0,"title":"Sıkıştırma Teoremi Nedir?","list":{"type":"unordered","items":["Limit konusunda temel limitlerin hesaplanabilmesi için çarpanlarına ayırma veya eşlilikle çarpma gibi cebirsel işlemler kullanılır.","Sıkıştırma (sandviç) teoremi, limit hesaplamalarında önemli bir yere sahiptir.","Sıkıştırma teoremi, bir fonksiyonun diğer iki fonksiyon arasında kalması durumunda limitin de bu iki fonksiyonun limitine eşit olduğunu belirtir."]},"beginTime":2,"endTime":90,"href":"/video/preview/9367011482521495410?parent-reqid=1769373659712389-18017472934028798691-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Sinx1967&t=2&ask_summarization=1"},{"index":1,"title":"Sıkıştırma Teoreminin Matematiksel İfadesi","list":{"type":"unordered","items":["Eğer a civarında f(x) ≥ g(x) ve g(x) ≥ h(x) ise, limit x→a'da f(x) = h(x) ise, limit 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Öğretmen, öğrencilere hitap ederek konuyu adım adım açıklamaktadır.","Video, türe üç'te bileşke fonksiyonların türevini konu almaktadır. İlk bölümde bileşke fonksiyonların türev formülü (f bileşke g'nin türevi = f'in türevi çarpı g'nin türevi) açıklanmakta ve iki farklı örnek üzerinden çözüm yapılmaktadır. İkinci bölümde ise iç içe fonksiyonların türevi, trigonometrik fonksiyonların (sinüs, kosinüs, tanjant, kotanjant) türevleri ve çarpımın türevi gibi temel kavramlar örneklerle pekiştirilmektedir.","Video, türev konusunun temel kavramlarını öğrenmek isteyenler için faydalı bir kaynaktır ve her kural detaylı olarak açıklanmaktadır."]},"endTime":912,"title":"Türev Dersi: Bileşke Fonksiyonların Türevi ve Temel Kurallar","beginTime":0}],"fullResult":[{"index":0,"title":"Bileşke Fonksiyonun Türevi","list":{"type":"unordered","items":["Bileşke fonksiyonun türevi, birincinin türevi çarpı ikincinin türevi şeklinde hesaplanır.","Türev alırken, birincinin içerisine türevini aldıktan sonra ikinci fonksiyonun aynısını yazmak gerekir.","Bileşke fonksiyonun türevini önce bileşkeyi alıp sonra türevini almak da mümkündür ve bu yöntem daha kolaydır."]},"beginTime":4,"endTime":44,"href":"/video/preview/6840201290057509962?parent-reqid=1769373659712389-18017472934028798691-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Sinx1967&t=4&ask_summarization=1"},{"index":1,"title":"Örnek 1","list":{"type":"unordered","items":["f(x) = x² + 1 ve g(x) = 3x - 1 fonksiyonları için f bileşke g'nin türevi hesaplanır.","f bileşke g(x) = (3x - 1)² + 1 şeklinde bulunur.","Türev alındığında (2(3x - 1))(3x - 1) + 2 = 18x - 12 sonucu elde edilir."]},"beginTime":44,"endTime":129,"href":"/video/preview/6840201290057509962?parent-reqid=1769373659712389-18017472934028798691-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Sinx1967&t=44&ask_summarization=1"},{"index":2,"title":"Örnek 2","list":{"type":"unordered","items":["f(x) = 2x⁵ - 3 ve g(x) = x + 1 fonksiyonları için f bileşke g'nin türevi hesaplanır.","f bileşke g(x) = 2(x + 1)⁴ - 3 şeklinde bulunur.","Türev alındığında 10x(x + 1)³ + 0, sonucu elde edilir."]},"beginTime":129,"endTime":182,"href":"/video/preview/6840201290057509962?parent-reqid=1769373659712389-18017472934028798691-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Sinx1967&t=129&ask_summarization=1"},{"index":3,"title":"Türev Alma Kuralları","list":{"type":"unordered","items":["Türev alma konusunda, f(x) = 3x² + x + 1 gibi temiz orijinal fonksiyonların türevi f'(x) = 6x + 1 olarak hesaplanır.","Bozuk fonksiyonların türevi alırken, f(x)'in türevi çarpı içerdeki fonksiyonun türevi alınır.","Türev alma sırasında x'in türevi her zaman 1 olarak alınır ve çarpmada etkisiz olduğu için belirtilmez."]},"beginTime":184,"endTime":330,"href":"/video/preview/6840201290057509962?parent-reqid=1769373659712389-18017472934028798691-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Sinx1967&t=184&ask_summarization=1"},{"index":4,"title":"Trigonometrik Fonksiyonların Türevi","list":{"type":"unordered","items":["Sinüs fonksiyonunun türevi: f(x) = sin(x) ise f'(x) = cos(x) olur.","Kosinüs 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