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2. Let D be an open, connected but not simply-connected subset of R2. Give an example of vector field F(x, y) = (P(x, y), Q(x, y)) satisfying each of the following cases. Explain your answer in detail. (a) Qx(x, y), and F is a gradient (conser- (b) V(x, y) = D, Py(x, y) vative) vector field. V(x, y) = D, Py(x, y) (conservative) vector field. = Qx(x, y), and F is not a gradient

2. Let D be an open, connected but not simply-connected subset of R2. Give an example of vector field F(x, y) = (P(x, y), Q(x, y)) satisfying each of the following cases. Explain your answer in detail. (a) Qx(x, y), and F is a gradient (conser- (b) V(x, y) = D, Py(x, y) vative) vector field. V(x, y) = D, Py(x, y) (conservative) vector field. = Qx(x, y), and F is not a gradient

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.4: Spanning Sets And Linear Independence
Problem 76E: Let f1(x)=3x and f2(x)=|x|. Graph both functions on the interval 2x2. Show that these functions are...
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2. Let D be an open, connected but not simply-connected subset of R2. Give an example of vector field F(x, y) = (P(x, y), Q(x, y)) satisfying each of the following cases. Explain your answer in detail. (a) (b) V(x, y) = D, Py(x, y) = Qx(x, y), and F is a gradient (conser- vative) vector field. V(x, y) = D, Py(x, y) = Q(x, y), and F is not a gradient (conservative) vector field.
Transcribed Image Text:2. Let D be an open, connected but not simply-connected subset of R2. Give an example of vector field F(x, y) = (P(x, y), Q(x, y)) satisfying each of the following cases. Explain your answer in detail. (a) (b) V(x, y) = D, Py(x, y) = Qx(x, y), and F is a gradient (conser- vative) vector field. V(x, y) = D, Py(x, y) = Q(x, y), and F is not a gradient (conservative) vector field.
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could you plz explain more about the b part? i didn't get it

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