Question 10 Worth 8 points Use the indicated change of variables to evaluate the following double integral.

Question 1 Worth 10 points a.    Change the point

Question 2 Worth 8 points Convert this integral from rectangular coordinates to spherical coordinates (Do not evaluate the integral)

Question 7 Worth 8 points Determine whether or not the vector field is conservative. If it is conservative, find a function  such that

Question 9 Worth 8 points Evaluate 

Question 7 Worth 8 points Determine whether or not the vector field is conservative. If it is conservative, find a function  such that

Question 1 Worth 10 points a.   Change the point

Question 10 Worth 8 points Use polar coordinates to find the volume of the solid inside the sphere   and outside the cylinder  .

Question 9 Worth 8 points Use Lagrange multipliers to find the maximum value of the function  subject to the constraint  .  

Question 12 Worth 10 points a.    Sketch the plane curve and the vectors and when  .    (Do NOT attempt to find  and  when making this sketch, and note that this a 2-dimensional sketch).   b.    Find the unit tangent vector when for the curve defined by .