Taylor polynomials are incredibly powerful for approximations and analysis. Help fund future projects: An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: #thanks Home page: Full series: Series like this one are funded largely by the community, through Patreon, where supporters get early access as the series is being produced. Timestamps 0:00 - Approximating cos(x) 8:24 - Generalizing 13:34 - e^x 14:25 - Geometric meaning of the second term 17:13 - Convergence issues Correction: At 14:38, the last term should include a factor of 1/2 Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld Vietnamese: ngvutuan2811 ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: Various social media stuffs: Website: Twitter: Patreon: Facebook: Reddit: