An Elusive Limit Question 3: Using L'Hospital's Rule 7 Times in a Row (Using Wolfram Alpha)

In this video I go over the previous difficult trigonometric (and inverse trigonometric) function and this some apply L'Hospital's Rule to show that its limit as x approaches 0 is equal to 1. When plugging in x = 0 into the numerator and denominator of the function, we get the indeterminate form 0/0. This means we can apply L'Hospital's Rule and take the limit of the derivatives of the numerator and denominator. Since the question asked us to use a Computer Algebra System (CAS), I have calculated the derivatives using the amazing Wolfram Alpha online calculator: https://www.wolframalpha.com/

The first 6 derivatives or applications of L'Hospital's Rule all obtain the indeterminate form 0/0. But the 7th derivatives obtain the limits -168/(-168) = 1.

Time stamps:

- Question 3: Evaluate limit with l'Hospital's Rule: 0:00
- Solution: Limit is in an indeterminate form: 0:22
- Recap l'Hospital's rule: 2:16
- Using Wolfram Alpha, the first 6 derivatives are indeterminate but 7th is non-zero: 3:25
- The limit is equal to 1: 5:46

Full video below:

- Full video and playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0Gzt0ZAIWwnyZr91b7BGoGR
- Notes: https://peakd.com/hive-128780/@mes/laboratory-project-an-elusive-limit
- Infinite Sequences and Series: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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