In Fuji systems, an s# of 200 represents approximately 1 mR of exposure, if an S# of 400 is indicated the image receptor has been (overexposed or underexposed). Choose one

Use the Divergence theorem to calculate the flux integral

(12 points) Partial credit problem. You must upload a scan of your solution at the end of the exam. Please show all of your workings for full points. Let be the parallelogram in the -plane with vertices ,

Find the directional derivative of the function at the point

Which integral gives the surface area of the surface parametrized by

Let be the solid upper-half of the unit sphere in

(12 points) Partial credit problem. You must upload a scan of your solution at the end of the exam. Please show all of your workings for full points. A particle has the position function and is moving under an acceleration of

(12 points) Partial credit problem. You must upload a scan of your solution at the end of the exam. Please show all of your workings for full points. Let be the loop given by the intersection of the surface and the cylinder , with counter-clockwise orientation. Let

Which of the following is the tangent plane to the graph of the function

(12 points) Partial credit problem. You must upload a scan of your solution at the end of the exam. Please show all of your workings for full points. Let S be the surface given by the portion of the graph of  that lies above the 1/8th of the unit disk in the -plane which is illustrated below. Compute