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The red hydrogens depicted in the figure below are: Q3.png 

Question 2 (10 points) Evaluate

Question 12 (10 points) Find the dimensions of a closed rectangular box of volume which has the least surface area. 

Question 8 (10 points) Given 

Question 1 (10 points) Set-up the triple integral to determine the volume of the described region, but do not evaluate it.  Use cylindrical coordinates. A solid that lies within the cylinder  and above the -plane and below the cone  

Question 9 (10 points) Use Stokes’ Theorem to evaluate

Question 5 (10 points) Evaluate the line integral 

Question 4 (10 points) Consider the surface with equation . a. Find the equation of the tangent plane to this surface at the point .  b. What is the linearization ? c. Use to approximate the value of

Question 1 (10 points)  Determine the limit or show it does not exist.    a.

Question 6 (10 points) Near a buoy, the depth of a lake at the point with coordinates is