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Math 53 Quiz 10 Name:
Problem 1 [5 pts]. Using Greens Theorem, evaluateC F dr where F =
(ex x2y, tan2 y + y2x) and C is the
circle of radius 1 centred at the origin.
Problem 2 [5 pts]. Find a parametrization for part of the plane z = x+3 that lies inside the cylinder x2+y2 = 1.Also explicitly state the parameter domain (i.e. if your variables names are u and v, give inequalities a u band c v d that define the region in the uv-plane where your parametric equations are defined).
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Problem 3. Consider the vector field A(x, y, z) =(0, 0, 12 ln(x
2 + y2)).
(a) [3 pts] Calculate the divergence and curl of A.(b) [2 pts] Is it possible for A to be the gradient of some function a(x, y, z), i.e. A = a? Why or why not?
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