Math 230 Summer 2023 Mastery Assignment 4
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Math 230 — Summer 2023
Mastery Assignment 3
Due August 10, 2023 11:59 PM
Instructions:
. Upload the answers to Gradescope using a separate sheet of paper.
. Points will be deducted for incomplete reasoning and disorganized work (even if your answers are correct).
. If you have any difficulties/questions,you are encouraged to discuss these problems with me.
. Late assignments must go into the Late Assignment Dropbox on Canvas.
1. (10 points) Use spherical coordinates to compute the surface area of a sphere of radius R (i.e. set up and evaluate a surface integral which represents the area of a sphere of radius R).
2. (10 points) Compute the work done by F = ⟨3y,−2x,3y⟩ over the circle x2 + y2 = 9, z = 2 (oriented counterclockwise) by using Stoke’s theorem.Find and classify (using the second derivative test) the critical points of the function
f(x,y) = x3 + 2xy − 2y2 − 10.
3. (10 points) Compute the flux of F = ⟨zx,yx3 , x2 z⟩ out of the surface which bounds the solid region with boundary given by y = 4 − x2 − z2 , y = 0.
2023-08-09