Math 53 Quiz 10 Name: Problem 1 [5 pts]. Using Green’s Theorem, evaluate R C F · dr where F = ( e x - x 2 y, tan 2 y + y 2 x ) 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 x 2 + y 2 = 1. Also explicitly state the parameter domain (i.e. if your variables names are u and v, give inequalities a ≤ u ≤ b and c ≤ v ≤ d that define the region in the uv-plane where your parametric equations are defined). 1
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).
1
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?
