Calculus 3, Spring 2020, Practice final exam solutions

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  1. Beard Meets Calculus
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No real way to thank you for making these but your videos are so well made and you explain the concepts stupid well. Thanks for the positivity in the videos and helping me with the exam, please don't stop making these! WE APPRECIATE YOU PROFESSOR BUTLER

_garycalgary
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Watching your videos always adds pieces of new knowledge.
THANK YOU so much professor, for sharing this and making it public.

eyalgvili
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final is tomorrow and your videos have been helpful. Thank you .

teeganfitzgerald
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Such an amazing class! Really helped me study for my finals. Thank you so much for the incredible video!

ourpraysejesus
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This impending final has been causing me to have panic attacks so your kind tone seems appropriate but my conclusion is that I have not lived a good life.

Commonfiend
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Are you perhaps a Mulligan wizard? Your work is clearly presented and well understood

Voyager
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Hello Dr. Butler, would you mind going over a certain problem that I am having trouble with? The problem is: Find the double integral of the vector field, F, * ds where S is the sphere x^2 + y^2 + z^2 = 4 with an outward normal vector and the vector field F(x, y, z) = <3x - sin(e^z), y - 2, z - x*y>

joshlazor
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I plan on getting into youtube soon-ish and want increase the number of this style of math video. How do you record the paper like this?

briendamathhatter
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for problem 5 about the directional derivative. is u always a unit vector (i.e. can i always just use one) or was that just the case for the specific problem?

heartandeyes