I'm not even taking this class. I'm just stopping by with my favorite online professor that helped me get a 100 on my differential equation exam! Keep up what you are doing sir! I hope in seeing you making more videos for higher order differential equations!
Professor Leonard, I want to thank you for everything. Your videos have helped me immensely. I’m currently in an engineering program to become an electrical engineer/computer scientist and if it weren’t for your videos, I would not be where I’m at today. Someday I am going to return the favor. You are amazing!!
Professor Leonard, thank you for another beautiful video/lecture on How to determine the end behavior of rational functions that don't have Horizontal /Slant Asymptote.
Only a few textbooks (so far I found one), that really talks about this last cases, no horizontal asymptote, when the degree of numerator is larger than degree of denominator MORE THAN 1. It is called parabolic asymptote (for that example, y=x^2) , please refer to John W. Coburn, 2E, page 366.
I’ve been doing that but for some reason the last example with the cubic isn’t working out on desmos. It looks parabolic. But I agree with the professor that it should look cubic. 🤔 Anyone know why.
![1.7A - Rational Functions and End Behavior [AP Precalculus]](http://i.ytimg.com/vi/1Jlny_-XPyY/mqdefault.jpg)
Is it just me or is anyone else mesmerized by this man's bicep?
*Disclaimer, this video will make you insecure about your body and intelligence*
@4:55 thanks for making the decision to develop a new example instead of mixing up the first one. 💯
I'm not even taking this class. I'm just stopping by with my favorite online professor that helped me get a 100 on my differential equation exam! Keep up what you are doing sir! I hope in seeing you making more videos for higher order differential equations!
I click on the ads just to help my favorite professor of all time
Went through numerous videos to understand this and when I watched this video I couldn't believe how simple this concept was. Thanks!
Two lessons in one day? What a legend.
Professor Leonard, I want to thank you for everything. Your videos have helped me immensely. I’m currently in an engineering program to become an electrical engineer/computer scientist and if it weren’t for your videos, I would not be where I’m at today. Someday I am going to return the favor. You are amazing!!
return it yet?
Professor Leonard, thank you for another beautiful video/lecture on How to determine the end behavior of rational functions that don't have Horizontal /Slant Asymptote.
Only a few textbooks (so far I found one), that really talks about this last cases, no horizontal asymptote, when the degree of numerator is larger than degree of denominator MORE THAN 1. It is called parabolic asymptote (for that example, y=x^2) , please refer to John W. Coburn, 2E, page 366.
Thank you Mr.Leonard
If you guys didnt already know... put Leonard's polynomials into DESMOS to have a feel, (google desmos)
Thnx bro!
I’ve been doing that but for some reason the last example with the cubic isn’t working out on desmos. It looks parabolic. But I agree with the professor that it should look cubic. 🤔 Anyone know why.
Leonard's on a roll!
Brilliant, thank you so much. You explained this so well
Thank you very much professor!!
I do not care about petty rational functions just watch for Leonard
What about x raised to FRATION by difference in Numerator and denominator
What about something that is in factored form such as (x+3)^3/(x-3)^3
THANK YOU, THANK YOU FOR THIS. YOU ARE GOATED!!!!!!!!!!!!! (SUBED & LIKED)
thanks again
If the degree in the NUMERATOR is greater by 2 than the denominator then is it asymptotic to a Parabola?
Men I fucking love the video. Thank you so much!
THABK U SIR
Why there is no slant asymptotic behaviour when denominator degree is Greator than 1 like Numerator
because the asymptote goes from being linear (slant asymptote) to higher powers, like quadratic, cubic, quartic etc...
✍️
So cute