In this video I go over further into determining the slope of tangent lines to parametric curves and this time show the general condition in which we can do this. In my earlier video I derived the equation for the slope but simply assumed that for some parametric equations we can remove the parameter to form an equation of the form y = F(x). In this video I show that the general condition in which we can eliminate the parameter is if, for the parametric equations x = f(t) and y = g(t), we have f’ being a continuous function that is never equal to 0 for a given interval. This condition makes it possible to find the inverse of the function thus we can use that the fact to plug into g(t). I explain how to do this in the video so make sure to watch it!
Watch on VidMe: https://vid.me/vKEEh
Watch on BitChute: https://www.bitchute.com/video/eW28wYxWnlEB/
Download PDF Notes: https://1drv.ms/b/s!As32ynv0LoaIhuMbzM5UzIft5JqRqg
View Video Notes Below!
Download These Notes: Link is in Video Description.
View These Notes as an Article: https://steemit.com/@mes
Subscribe via Email: http://mes.fm/subscribe
Donate! :) https://mes.fm/donate
Reuse of My Videos:
- Feel free to make use of / re-upload / monetize my videos as long as you provide a link to the original video.
Fight Back Against Censorship:
- Bookmark sites/channels/accounts and check periodically
- Remember to always archive website pages in case they get deleted/changed.
Check out my Reddit and Voat Math Forums:
Buy "Where Did The Towers Go?" by Dr. Judy Wood: https://mes.fm/judywoodbook
Follow My #FreeEnergy Video Series: https://mes.fm/freeenergy-playlist
USEFUL TIP: If I'm going too fast or too slow, play this video at a different speed.
- TOP SECRET LIFE HACK: Your brain gets used to faster speed (#Try2xSpeed)
- #Try4xSpeed by Replacing youtube.com with hooktube.com in the video URL ;)
General Condition for Determining Tangents
In my earlier video, https://youtu.be/deQwD2o0Sas, I assumed we could re-write the parametric equations, x = f(t) and y = g(t), in the form y = F(x).
In this video I will look at the General Condition for which this is possible, through the following exercise:
Exercise: If f' is continuous and f'(t) ≠ 0 for a ≤ t ≤ b, show that the parametric curve x = f(t), y = g(t), for a ≤ t ≤ b, can be put in the form y = F(x).
HINT: Show that f-1 exists.
