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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Видео Plugging a Sequence into a Function and Examples канала Math Easy Solutions
math, science, calculus, algebra, sequences, series, cymantics, introduction, mathematics, education, STEM, fibonacci sequence, recursive, notation, set of all real numbers, general formula for n-th term, nth term, limit of a sequence, infinite limits, rational number, limits, infinity, limits at infinity, power rule, limits for sequences, converges, absolute values, stewart calculus, solutions, examples, limits of sequences, theorem 3, squeeze theorem, factorials, l'hospital's rule