Stock options give the owner the right to purchase common stock at a fixed price over a specified period of time. As the stock’s price increases above the fixed option price, the value of the option increases.

Question 10 Worth 8 points Use polar coordinates to find the volume of the solid bounded by the paraboloid

Question 12 Worth 8 points Given that and is the triangular region with vertices , set up two different integrals which evaluate the volume between the region and the surface in two different ways. Do not evaluate these two integrals.

Question 2 Worth 8 points Find the unit vectors that are parallel to the tangent line to the curve at the point .

Question 10 Worth 8 points Use polar coordinates to find the volume of the solid under the paraboloid

Question 4 Worth 8 points Find the exact mass of a thin wire in the shape of a helix   , where

Question 4 Worth 8 points Find an equation of the tangent plane to the surface

Question 10 Worth 8 points Find the length of the curve where  , and  

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.    Describe in words the surface with equation