Multivariable Calculus Final Exam Review

Solutions to a previous final exam for a multivariable calculus course.

[darshanshah]

1. Equation for a plane containing points 0:00
2. Find the angle between 2 vectors 5:09
3. Equation of plane containing 2 lines (with point on both given) 7:55
4.Sketch a cross sections 11:18
5.Take the partial derivative of a function 15:30
6. Derivative of a parametric function 17:31
7. Directional derivative and direction of fastest increase 22:43
8. Local maxima and minima 27:50
9. Set up a double integral 32:25
10. Change the order of integration for a double integral 35:00
11. Find the volume of a solid bounded by z = f(x, y) and z = g(x, y) 38:15
12. Volume of portion of a sphere 43:17
13. Setup a line integral of f.ds over c 48:50
14 and 15. I got lazy so there are a few line integrals of vector fields etc
16. Surface integrals start at 16 or 1:02:07

[OtisShantyOfficial]

watching this an hour before my final, godspeed!

[jamesmurphy]

I wish my professor would make problems this straight forward. She’s always adding tricky shit I have to deal with.

[whaledeity]

compared to my professor, this was a completely different and better way of explaining these problems, thank you so much.

[eithnemelee]

May everyone watching this just before the exam be granted good luck and passing grades!

[draynorofscythe]

thanks for this, you should have a lot more views, wayyyy more helpful than majority of the videos out there

[maverickschamps]

Was very helpful! Youre good at explaining this stuff, unlike my professor. Thank you very much.

[zaneparkerson]

Thank you! This review was excellent and has really helped me feel more confident going into my Calculus III Final. Great job!

[ficklegruber]

Thank you very much. My final is in 2 hours. I only need to get 50% to get a B. This video is really going to help me skim by

[vin]

wish my prof's exams were this straight forward and easy

[Whiteknight]

You will never know how greatful i am for this man THANK YOU SOOO MUCH FOR THIS VIDEO (YOUR A TRUE LIFE SAVER)

[Obkev]

My final is in an hour but I hate how my professor only gives us "general" problems, like no numbers just variables it honestly more harder

[joebashour]

This just saved my exam....
Thank you very much

[TwhiTEdits]

Thank you very much man, really needed these examples!

[GoldenPhoenix]

Final coming up, thanks for the help!

[joshlazor]

Anyone know how Patrick Brynes got pi/4 for phi at 45.00? I know that phi = cos^-1(z/p (row)), but I'm confused as to how to get z... We know that row is 4, so phi = cos^-1(z/4), but how do we know that it is pi/4...?

[XxPepperxX]

the z-r diagram on problem c-11 saved my life

[jneal]

For the first problem, what happened to the -9 you pulled from the normal vector? Can you always pull a constant out and plug in, or is it circumstantial?

[jrow]

Thanks man, appreciate the effort put into this video.

[lukeivanov]

Got an A in Calc 3, just here to sharpen my skills. Thanks for the vid :)