Calculus 3, Spring 2020, Practice final exam solutions

Vimeo (ad-free) link to same video: https://vimeo.com/658573988 Note: This practice final was to help for a final exam administered online and so had a different format from traditional final exams. 0:00 Intro 2:51 Rewrite integral using Green's Theorem 6:34 Line integral (conservative) 9:54 Divergence Theorem application 14:39 Stokes' Theorem (Bring Your Own Surface) 20:21 Directional derivatives and angle between vectors 25:35 Changing regions when changing variables 30:49 Going from Cartesian to spherical coordinates 33:27 Classifying critical points 35:32 Lagrange multipliers 40:08 Tangent plant to implicit surface 47:40 Properties of the gradient (max increase) 49:53 Tangent plane to implicit surface 53:41 Finding position from acceleration 58:47 Identifying quadric surface 1:00:53 Implicit partial differentiation 1:04:53 Mass of polar region 1:11:06 Changing order of integration 1:14:38 Basic properties of integration 1:20:27 Properties of the cross product 1:22:49 Projection of one vector onto another 1:25:16 Second order Taylor polynomial approximation 1:34:39 Linear approximation to function 1:38:26 Mass of wire (1D) 1:40:25 Finding flux through a surface