Level Curves and Traces of Multivariable Functions

[@Circaman8]

In 20 minutes you taught me more than my professors did.

[@mohdashraf4438]

Please continue your teaching it's not what others able to teach. Exceptional especiallly the saftware explanations thanks a lot

[@andrewbulawa3273]

Glad you found it helpful!

[@malefetsanekoalane4549]

Your explanations leave nothing out. You answer questions before they get asked. Thanks 👍

[@Nejim-t6r]

So much in only 20 minutes , thank you !

[@fourKay-chingChong]

Wow , you explain so good, can see that you have put lot of efforts in making these videos . Kudos , thanksss

[@steafansteinocher462]

this explanation is peak. Yes pun intended because I actually learned something.

[@victorlarsson7309]

This is insanely cool

[@AhmedAbdullah-m9v]

wow sersly awesome what my prof cant teach me in 1 hours you did it in just 6 mins

[@mehreenhossain9927]

thank you so much, this is an excellent explanation

[@RealEverythingComputers]

Awesome video thank you!

[@prashantgupta3360]

brother you saved you from this nightmare

[@seamusmoran4776]

This is so helpful thank you very much!!!!

[@chukwumautomi8153]

Mann i wish you showed the algebra for the equations

[@aaronashleytiangco1178]

thank you for this! very educational 🙌

[@MabrokAllafi]

ما شاء الله 🎉

[@jjeditor8423]

sir please continue and upload more tutorial

[@roopajaunpuriya3955]

Very good

[@badrmoubile9219]

Thanks, super helpfull.

[@MelikaSalari]

Thanks a lot

[@_mahershehab1574]

❤

[@muzikaaly]

thanks man you are guru

[@baharali2058]

should you take these piont for every qustion?

[@andrewbulawa3273]

If you mean the values of c we chose here, there's no restriction on what those might be in general But, for specific problems, some values will be more appropriate than others. You will need to rely on your intuition and experience to choose the best values of c. Sometimes it's just trial and error.

[@priyanshu-y9k]

Please show us how to draw a level surface for ln(16 - 4x^2 - y^2 - 4x^2)

[@andrewbulawa3273]

I suppose you mean to have a third variable, z, in that expression? If so then you should be able to follow the same reasoning starting at 17:15 in the video. The surface won't be a sphere, but something similar. I recommend looking at how it intersects the coordinate planes (xy-plane, yz-plane, and xz-plane). You can do that by setting one variable equal to zero and looking at the curve defined by the remaining two variables.

[@getasewadamu5353]

Thanks

[@EsraAbay200]

Hello, can I contact you? If you have a telegram or any communication site.

[@andrewbulawa3273]

Best to just leave a comment here. If I have time I will try to respond.