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 .

------------------------------------------------------

Become a MES Super Fan! https://www.youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

MES Links: https://mes.fm/links

MES Truth: https://mes.fm/truth
Official Website: https://MES.fm
Hive: https://peakd.com/@mes

Email me: [email protected]

Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps