MA 227 Midterm: 3-12f-test2
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Show all of your work for full credit. Find the partial derivatives fxx, fxyy if f (x, y) = x cos(y) + xy. Find the following limit if it exists, or show it does not exist. Answer: . lim (x,y) (0,0) x2 2y2 x2 + y2. Let f (x, y, z) = xey sin(xz) + yz2 and x = s cos t, y = s sin t, z = s + t. find fs, ft (do not simplify). Use di erentials to estimate the amount of tin in a closed can with radius 5 in and height 10 in if the can is 0. 04 in thick. Use implicit di erentiation to nd zx, zy if xyz = ln(x + y + z) (do not sim- plify). Find maximum rate of change of the function f (x, y, z) = xey sin(xz) + yz2 at (0, 0, 1) and the direction in which it occurs.
