Two examples on working with Taylor series

array(10) { [0]=> object(stdClass)#4626 (5) { ["video_id"]=> int(9999999) ["related_video_id"]=> string(11) "CezrT7JUQzU" ["related_video_title"]=> string(51) "Using power series to solve a differential equation" ["posted_time"]=> string(21) "4 года назад" ["channelName"]=> string(13) "Meredith Burr" } [1]=> object(stdClass)#4599 (5) { ["video_id"]=> int(9999999) ["related_video_id"]=> string(11) "fGxYRTqFhs0" ["related_video_title"]=> string(49) "Introduction to Taylor Polynomials (11.1, part 2)" ["posted_time"]=> string(21) "4 года назад" ["channelName"]=> string(13) "Meredith Burr" } [2]=> object(stdClass)#4624 (5) { ["video_id"]=> int(9999999) ["related_video_id"]=> string(11) "EZVh-ZClVM4" ["related_video_title"]=> string(22) "Combining power series" ["posted_time"]=> string(21) "4 года назад" ["channelName"]=> string(13) "Meredith Burr" } [3]=> object(stdClass)#4631 (5) { ["video_id"]=> int(9999999) ["related_video_id"]=> string(11) "lPZQYslq-jQ" ["related_video_title"]=> string(45) "Introduction to computing limits of sequences" ["posted_time"]=> string(21) "4 года назад" ["channelName"]=> string(13) "Meredith Burr" } [4]=> object(stdClass)#4610 (5) { ["video_id"]=> int(9999999) ["related_video_id"]=> string(11) "CanPPyybfYI" ["related_video_title"]=> string(73) "Получится ли обобщить интеграл Френеля?" ["posted_time"]=> string(22) "10 дней назад" ["channelName"]=> string(5) "Hmath" } [5]=> object(stdClass)#4628 (5) { ["video_id"]=> int(9999999) ["related_video_id"]=> string(11) "CUb-JOteeyo" ["related_video_title"]=> string(54) "Another example on finding the area between two curves" ["posted_time"]=> string(21) "4 года назад" ["channelName"]=> string(13) "Meredith Burr" } [6]=> object(stdClass)#4623 (5) { ["video_id"]=> int(9999999) ["related_video_id"]=> string(11) "WZN3cLhnWh8" ["related_video_title"]=> string(42) "О Зеленского вытерли ***" ["posted_time"]=> string(24) "13 часов назад" ["channelName"]=> string(27) "Анатолий Шарий" } [7]=> object(stdClass)#4633 (5) { ["video_id"]=> int(9999999) ["related_video_id"]=> string(11) "M-9NV2hdQwQ" ["related_video_title"]=> string(60) "11 Летний Оро Жертвует Слона Непо!" ["posted_time"]=> string(24) "14 часов назад" ["channelName"]=> string(11) "ChessMaster" } [8]=> object(stdClass)#4609 (5) { ["video_id"]=> int(9999999) ["related_video_id"]=> string(11) "wBZ86epOMI0" ["related_video_title"]=> string(146) "ИЗРАИЛЬ vs. ИРАН: ТРЕТЬЯ МИРОВАЯ? Прогноз от Павла Щелина, политического философа" ["posted_time"]=> string(24) "15 часов назад" ["channelName"]=> string(7) "SOBOLEV" } [9]=> object(stdClass)#4627 (5) { ["video_id"]=> int(9999999) ["related_video_id"]=> string(11) "ezvdTMT8X5U" ["related_video_title"]=> string(104) "Ященко ПОЯСНИЛ за ЕГЭ 2025?! Разбор ответа составителей ЕГЭ" ["posted_time"]=> string(21) "8 дней назад" ["channelName"]=> string(79) "Профиматика | Профильная математика | ЕГЭ2025" } }