Problem 1
(a) For what Values of the Constant is the Vector Field Conservative?
(b). For the Values of a Determined in the First part of the Question Compute the Integral of over Defined as the Semicircle with Center , Radius and Oriented Counter-clockwise
Problem 2
Compute where and is the semicircle in the upper half-plane from to .
Consider the line from to and the region defined as the region enclosed by .
Problem 3
(a). Let Be a Vector Field and a Function. Fill in the Blanks to Make the Formula Correct
(b). Let and Be Two Vector Fields. what is
for any so the expression is also equal to 0.
Problem 4
Parametrize the part of the ellipsoid that lies inside the paraboloid .
Since must be greater than and will always be positive we can discard the negative part of the ellipsoid.
Problem 5
Find an equation for the tangent plane to the surface given by
at the point