New Year's limit via Taylor series
In this video, you'll learn how to calculate a limit using Taylor series expansions of functions. In the limit, the uncertainty is 0/0, and L'Hôpital's rule can be applied to it, but this calculation only works after finding the fourth derivative of the numerator and denominator of the fraction. Therefore, it's easier to use series expansions here.
After watching to the end, you'll understand why the limit is called "New Year's" ;)
You can watch how to find the expansion for ln(1+x) here: • Разложения ln(1+x) и arctg(x) в ряд Тейлор...
You can watch the expansion for e^x and sin(x) (cos(x) is found similarly) here: • Разложения e^x и sin(x) в ряды Тейлора.
This video was made for 2020, the New Year's video for 2021: • Новогодняя фрактальная ёлочка из ковра Сер...