MAT-2130 Midterm: MATH 2130 App State summer2014 Test1 answer key
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Name: x = cos( ) sin( ) y = sin( ) sin( ) z = 2 (1 + cos(2 ): (12 points) the following are plots of several vector elds. Please note that all of the vectors have been scaled down so they do not overlap each other. Write a, b, and c next to the appropriate vector eld"s formula. Put an x next to the formula whose vector eld is not shown. Yes / no: (9 points) let f(x, y, z) = (cid:10)x + y2z3, y + x5z, sin(y) + z(cid:11). Compute the divergence and curl of f. determine if the vector eld is conservative. Is / is not conservative: (9 points) use a double riemann sum to approximate zz. Use midpoint rule and a 2 2 grid of rectangles (2 across and 2 up) to partition r. R x: (12 points) evaluate z 6. Include a sketch of the associated region of integration.
