Question 1 Worth 10 points Given vectors  and

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

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 .

Question 11 Worth 8 points Find the area of the surface S, where S is the part of the surface 

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 planes 

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

Question 1 Worth 10 points a.   Change the point

Question 10 Worth 8 points Use polar coordinates to find the volume of the solid below the plane  and above the disk

Question 4 Worth 8 points Find the equation of the normal line to the surface    at the point .