**Unformatted text preview: **3 . 7. (8 points) Sketch the graph (which is a 2-dimensional surface in R 3 ) of the function f ( x,y ) = x-y + 2. 4 8. (10 points) Sketch the vector ﬁeld in the plane given by f ( x,y ) = h x,-2 y i . [ Hint: Your answer should be a set of axes with a bunch of arrows exhibiting the ﬂow of the vector ﬁeld.] 5 9. Which of the following sets is open and which is closed? Which is nei-ther? Give brief reasons for your answers. (a) (3 points) S = { ( x,y ) ∈ R 2 : x 2 + y 2 < 1 } (b) (3 points) T = { ( x,y ) ∈ R 2 : 1 ≤ x < 2 } (c) (3 points) U = { ( x,y,z ) ∈ R 3 :-1 ≤ x ≤ 1 ,-1 ≤ y ≤ 1 ,-1 ≤ z ≤ 1 } (d) (3 points) V = { ( x,y,z ) ∈ R 3 : 1 ≤ x 2 + y 2 + z 2 < 2 } 6 10. (10 points) Explain why this function f has no limit at the origin: f ( x,y ) = xy x 2 + y 2 . 7...

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- Spring '14
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- Linear Algebra