View the step-by-step solution to:

# Math 232 Midterm II Name_______________________________ (Please Print) Last, First Answer each question as accurately as possible. Please explain...

Need help on questions 2 - 9. thank you =]

Math 232 Midterm II Name_______________________________ (Please Print) Last, First 4. (10 pts) Evaluate the line integral, 2 2 C x z ds + , where C is the circle ( ) 0, cos , sin t a t a t = r , 0 2 t π ≤ ≤ . You may assume that 0 a > . 5. (10 pts) Evaluate ( ) ( ) 2,2,2 2 2 1,1,1 1 1 x y dx dy dz y z y z + - - . Justify your answer. 6. Let K be an arbitrary smooth simple closed curve in the plane that does not pass through the origin ( ) 0,0 . Let ( ) ( ) 2 2 , ln f x y x y = + . a. (10 pts) Evaluate K f ds ∇ ⋅ n i given that ( ) 0,0 lies outside K. b. (10 pts) Evaluate K f ds ∇ ⋅ n i given that ( ) 0,0 lies inside K . 7. (10 pts) A thin spherical shell of radius 5 centered at the origin has a hole of radius 5 3 2 removed from the top. Find the center of mass of this shell assuming that the density is proportional to the square of the distance from the z -axis. 8. (10 pts) Find an equation of the tangent plane to the given parametric surface, 2 x u = , 2 y v = , z uv = , at the point where 1 u = and 1 v = . 9. (10 pts) Evaluate the surface integral S d ∫∫ F S , where ( ) 4 , , , , x y z x y z = F and S is the part of the cone 2 2 z x y = + beneath the plane 1 z = with downward orientation.

### Why Join Course Hero?

Course Hero has all the homework and study help you need to succeed! We’ve got course-specific notes, study guides, and practice tests along with expert tutors.

### -

Educational Resources
• ### -

Study Documents

Find the best study resources around, tagged to your specific courses. Share your own to gain free Course Hero access.

Browse Documents