Exercise 1: Taylor Derivatives Equal the Function's Derivatives at x = a
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In this video I prove that the derivatives of a Taylor Polynomial are equal to the derivatives of the corresponding function used in the approximation when x = a. This is because any derivative at x = a of any Taylor polynomial cancels out all the terms (since a - a = 0) except the first term, which is just the corresponding derivative of f at x = a.
Timestamps:
- Exercise 1: Taylor Derivatives are the same as the function used in the Taylor Polynomial: 0:00
- Solution: Taylor derivatives cancel out all the terms except the first: 0:30
- n-th Taylor derivative is equal to the n-th derivative of f: 8:09
Full video, notes, and playlists:
- Full video and playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0F76sIU8xm09oqBTq1mlry3
- HIVE notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-applications-of-taylor-polynomials
- Infinite Sequences and Series: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .
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