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 Evaluate

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

Question 5 Worth 8 points Given Find

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

Question 5 Worth 8 points Find the distance between the point and the plane.

Question 12 Worth 10 points Evaluate the line integral by applying Green’s Theorem to

Question 3 Worth 8 points Set up the following triple integral, but do not calculate it: a solid bounded by the graphs of the equations   and   

Question 5 Worth 8 points Use Green’s Theorem to find the work done by the force in moving a particle from the origin along the -axis  to then along the line segment to and then back to the origin along the -axis.

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 scalar tangential component of acceleration of a particle with position vector .