Calculus 3, Session 19 -- Multi-variable Taylor polynomials

[@jaeen7665]

Professor Butler is legit the Bob Ross of math.

[@BeardMeetsCalculus]

Thank you.

[@Peter_1986]

First time I have seen a professor turn a question into a Hangman game, haha.

[@thatomothoagae7939]

The enthusiasm with which you explain these concepts makes mathematics to be as beautiful as it ought to...appreciated Prof

[@BeardMeetsCalculus]

Thank you. I do my best to convey that there is a lot of interesting things that happen, and not just a bunch of rules to memorize. Best of luck in your studies.

[@juanorellana8945]

Best explanation of this topic I've found in KZbin! You've been a life savior during this pandemic self-study of Calculus 3 (sadly, my local university doesn't provide online-quality material like this). Funny enough, the syllabus seem to match up almost perfectly. Greetings from Ecuador!

[@BeardMeetsCalculus]

I am glad that these videos are useful; that has always been my goal to be useful. That the videos line up is not too surprising as calculus is pretty much the same everywhere. Greetings from Iowa.

[@konstantinosbabalis1695]

This is exactly what I needed! Amazing lecture!

[@amatoallahouchen5894]

best explanation on youtube thanks a million!

[@BeardMeetsCalculus]

Woohoo. Glad it helped.

[@hassankhalid2753]

Great explanation. Thank you so much sir!!!!!!

[@BeardMeetsCalculus]

You are welcome. I am glad that you found it useful.

[@yasmeenkarachiwala9612]

Amazing! Thank you so much!

[@BeardMeetsCalculus]

You are welcome.

[@MrPabloguida]

So, is it right to say that 6.8 is the slope of the plane that is tangent to the surface at the point (3.1,1.1)?

[@BeardMeetsCalculus]

More to say that 6.8 is the "height" on the tangent plane over the point (3.1,1.1) and the tangent plane being a good approximation to the function means that f(3.1,1.1) is about 6.8. On a side note, planes don't have slopes (as the steepness in some sense can vary with which direction we look); instead planes have normal vectors.