Calculus 6.08g - An Intuitive Proof of l`Hopital`s Rule

An intuitive, graphical proof of l'Hopital's Rule, and some pertinent comments.

[Miguel_anitez]

Learned about this rule in my Ap Calc AB class a few months ago. I asked the teacher where it came from and why it works and she said to just use it and she didn’t fully know. Thanks for teaching me! I find calculus very fascinating to learn and it’s people like you who make the world a better place. Consider becoming a teacher, you are very skilled!

[mousaalsaeed]

most intuitive explaining I've ever seen 😲

[willpugh-calotte]

What a great explanation! Sometimes a graphical demonstration like this, although not a rigorous proof to the academic standard, is sufficient for the student to "see" why some rule works. I had a similar problem when shown Descartes' Rule of Signs, but with no proof offered. When I tried to find a proof of Descartes' Rule, the offerings were too advanced for me. Eventually, I reasoned out a graphical justification for Descartes' Rule myself, and that was sufficient to put me "at peace" with the rule and move on.

[alkankondo]

This was an excellent intuitive proof! It was carefully explained and easy to understand. So worth the time to watch! Also, your handwriting is very clean and neat!

[johnholme]

Beautiful! Thanks for taking the time to produce this video, everything is now Chrystal clear!

[minhokim]

Wonderful, but could you please provide me with more explanation for the case of infinite/infinite? It sounds like limit f(x)/g(x) = limit (1/g(x))/(1/f(x))=d(1/g(x))/d(1/f(x)), which is not equal to df(x)/dg(x)

[pianowhiz]

I loved this! Certainly one of the better YouTubers I’ve seen in terms of ability to explain and not leave holes for the student

[thomasni]

Wonderful proof dereck. you may want to use Desmos to do your graphing in the future though, it looks a lot neater than the emulated calculator :D

[IanPryor]

I really like how you graphed each function independently! That is super helpful and offers a new ways to use L'Hopital's Rule

[bp]

You know when you know why something is the case, but you can't really explain it, and then someone does it for you so elegantly that your own understanding improves? That's this video. Thanks.

[loopz_attack]

i am starting to understand what df/dx means in my calc 1 class. It really helps visualize what i am solving for instead of just plugging in numbers and getting the answer. I feel closer to math every time i see a good explanation of a concept.

[Ed-ykyh]

This was an unbelievably helpful and clearly explained video, thank you Derek!

[TheEpicGod]

Fantastic graph and method of explanation. This should be put into all textbooks

[DavidPauwelynTravelingbyfoot]

Fantastic. I am sharing this with all my students from now on. Thanks.

[APaleDot]

Beautiful. Exactly the kind of proof I was looking for.

[gustavotaucei]

Congratulations for the video. Great work!

[KarlBonner]

I figured this proof out on my own - and I didn't even remember that it was actually L'Hopital's rule!

[tonksonk]

Hey, I finally understand Lhopital's rule! This tutorial rocks

[mrtale]

omg this is the only tutorial that showed why assumption of f(a) = 0 is a valid assumption, thank you!

[MrCigarro]

What a fantastic explanation. Thank you very, very, much.