Multivariable Calculus | ArcLength

[@MrCentrax]

I'm really amazed by all your content. Whenever I doubt about something I search your channel

[@georgettebeulah4427]

This video make so much meaning and I can understand a lot from it very well done thank you.

[@ChaineYTXF]

Always nice. I comment to improve your visibility.

[@byronwatkins2565]

If you cut the cylinder vertically, you get a square with side 2pi and the helix is the diagonal.

[@rafael7696]

Very nice

[@programstix3837]

thank you

[@user-ic7ii8fs2j]

how formal would you say this playlist(Multivariable Calculus) is ? How rigorous are the proofs compared to textbook such as e.g. Shifrin's Multivariable Mathematics

[@dewookus]

Your video does a great job of explaining the intuition behind the formula for arclength. The only part I'm confused about is the use of the MVT (6 minute mark). The single variable calulus MVT gives us a t* for each component of the vector valued function r, but would not seem to imply that we have a single t* that works for every component of r. That is, we might have n different t*, one for r1, another for r2, etc. Can you help with this? Thanks for all the work you put into these great videos.

[@thesecondderivative8967]

If this is late, ignore me. But I believe it doesn't because he wrote t_i * not t*. So, that implies that there are n different t* like you stated.