Plugging a Sequence into a Function and Examples

In this video I go over Theorem 3, which states that if a sequence has a limit, then plugging it into a continuous function at that limit is the same as plugging in the limit. I will prove this Theorem in a later video. I also go over 2 examples, one on applying Theorem 3, and another on using the Squeeze Theorem to find the limit of a sequence.

#math #limits #sequences #calculus #education

Timestamps:

- Theorem 3: Plugging a convergent sequence into a continuous function is the same as plugging in its limit: 0:00
- Example 8: Limit of sin(pi/n): 1:00
- Example 9: Convergence of n! / n: 2:10
- The terms are decreasing and approaching 0: 5:14
- Applying squeeze theorem: 7:13

Notes and playlists:

- Summary: https://inleo.io/threads/view/mes/re-leothreads-kv8bpszt
- Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0HUgfK34Voi6BvrNqt4X4BV
- Notes: https://peakd.com/mathematics/@mes/infinite-sequences-limits-squeeze-theorem-fibonacci-sequence-and-golden-ratio-more
- Infinite Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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