An Elusive Limit Questions 1, 2: Limit Depends on Calculator Precision

mes (67)in DTube • 7 days ago

In this video I go over a very interesting trigonometric (and inverse trigonometric) function whose limit as x approaches 0 is unclear and gives different values depending on the calculator you use. I explore 3 different sets of calculations: the solution manual, Microsoft Excel, and Desmos online calculator. The solution manual has 10 digits of precision and makes it appear like the function is approaching 10/3. Microsoft Excel has 15 digits of precession and the functions appears to approach 0. Lastly, Demos gives an undefined result. Graphing out the function using Demos graphing calculator also gives an unclear answer as to what the limit should be: https://www.desmos.com/calculator/vhwpqsail1

Time stamps:

Rewriting the function notation: 0:00
Question 1: Evaluating the function for small values: 1:43
- Function approaches different values for different levels of calculator precision: 2:38
- sine and inverse sine are odd functions: 3:49
- tan and inverse tan are odd functions: 7:33
- The function is even: 10:58
- Microsoft Excel calculations shows limit is approaching 0: 15:35
- Desmos calculator gives undefined: 16:33
- Summary of results show limit is unclear: 17:26
Question 2: Graphing the function also shows the limit it unclear: 18:08
- Zooming into the graph using Desmos Graphing Calculator: 19:04