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is a video about \"Calculating the Area of a Regular Polygon Inscribed in a Circle Using Limits\" from the BUders university mathematics course Calculus-I. Prepared by: Kemal Duran...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/4334458/bf9e8eecc746be298fe790bfbd3f22d7/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/WsE-BwEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"2","reqid":"1774745232470864-3576560252209075132-balancer-l7leveler-kubr-yp-vla-14-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1774745232470864-3576560252209075132-balancer-l7leveler-kubr-yp-vla-14-BAL&text=videoid:9094824382926587795","teaser":[{"list":{"type":"unordered","items":["Bu video, matematik eğitimi formatında bir ders anlatımıdır. Eğitmen, limit konusunun matematiksel alanlardaki uygulamalarını göstermektedir.","Videoda, yarıçapı 4 cm olan bir çemberin içine en kenarlı bir düzgün çokgen çizerek, çokgenin alanını limit kullanarak hesaplama problemi çözülmektedir. Eğitmen önce geometrik çizimler yaparak problemi açıklar, ardından çokgenin alanını ifade eden formülü türetir ve limit hesaplamasını iki farklı yöntemle (lise kuralı ve Lopital kuralı) gösterir. Sonuç olarak, çemberin alanının 16π olduğu bulunur."]},"endTime":508,"title":"Bir Çemberin İçine Çizilebilecek Düzgün Çokgenin Alanını Limit ile Hesaplama","beginTime":0}],"fullResult":[{"index":0,"title":"Sorunun Tanıtımı","list":{"type":"unordered","items":["Videoda limit konusunun matematiksel uygulamalarından bir örneği ele alınacak.","Soruda yarıçapı 4 cm olan bir çemberin içine çizilebilecek en kenarlı düzgün çokgenin alanının limit kullanılarak bulunması isteniyor.","Çemberin içine çizilen çokgen, sonsuz kenarlı olduğunda çemberin alanıyla aynı olur."]},"beginTime":0,"endTime":94,"href":"/video/preview/9094824382926587795?parent-reqid=1774745232470864-3576560252209075132-balancer-l7leveler-kubr-yp-vla-14-BAL&text=Calculus+For+You&t=0&ask_summarization=1"},{"index":1,"title":"Çokgenin Alanının Hesaplanması","list":{"type":"unordered","items":["Çokgende her bir üçgen dilimini gören merkez açısı 360°/n veya 2π/n'dir.","Bir üçgen diliminin alanı 1/2 × 4 × 4 × sin(2π/n) = 8 × sin(2π/n) olarak hesaplanır.","Çokgende n tane üçgen dilim olduğundan, çokgenin alanı 8n × sin(2π/n) olarak ifade edilir."]},"beginTime":94,"endTime":179,"href":"/video/preview/9094824382926587795?parent-reqid=1774745232470864-3576560252209075132-balancer-l7leveler-kubr-yp-vla-14-BAL&text=Calculus+For+You&t=94&ask_summarization=1"},{"index":2,"title":"Limitin Uygulanması","list":{"type":"unordered","items":["Çokgenin alanının limiti, n sonsuza giderken 8n × sin(2π/n) şeklinde hesaplanır.","Bu limitte sonsuz × 0 belirsizliği oluşur, bu belirsizliği çözmek için iki yöntem vardır.","Birinci yöntem, lise yıllarında ezberletilen sinüs ve tanjant için özel bir kuraldır."]},"beginTime":179,"endTime":265,"href":"/video/preview/9094824382926587795?parent-reqid=1774745232470864-3576560252209075132-balancer-l7leveler-kubr-yp-vla-14-BAL&text=Calculus+For+You&t=179&ask_summarization=1"},{"index":3,"title":"Belirsizliğin Çözümü","list":{"type":"unordered","items":["İkinci yöntem olan L'Hôpital kuralı, belirsizliği çözmek için kullanılır.","Limit, sin(2π/n) / (1/8n) şeklinde yazılır ve n sonsuza giderken 16π olarak bulunur.","Bu sonuç, yarıçapı 4 cm olan çemberin alanı (πr² = π × 4² = 16π) ile aynıdır."]},"beginTime":265,"endTime":369,"href":"/video/preview/9094824382926587795?parent-reqid=1774745232470864-3576560252209075132-balancer-l7leveler-kubr-yp-vla-14-BAL&text=Calculus+For+You&t=265&ask_summarization=1"},{"index":4,"title":"L'Hôpital Kuralının Uygulanması","list":{"type":"unordered","items":["L'Hôpital kuralını uygulamak için önce sonsuz/sonsuz belirsizliğine getirilmesi gerekir.","Limit, sin(2π/n) / (1/8n) şeklinde yazılır ve n sonsuza giderken hesaplanır.","Pay ve paydanın ayrı ayrı türevi alınarak limit 16π olarak 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#calculusfordummies #introductiontocalculus This video is a basic introduction to calculus. If you are a beginner, then you can learn from this video. 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