MATH 317 Midterm: MATH 317 2008 Winter Test 1

• School: UBC
• Department: Mathematics
• Course: MATH 317
• Professor: all

Document Summary

The duration of this exam is 150 minutes. There are 10 problems, each worth an equal number of points. This problem is about the logarithmic spiral in the plane. Find the point in the rst quadrant where the graph of the function y = 1 maximal curvature. Find ~f at the point (1, 1, 1). (length is measured in m along the three coordinate axes. ) The curve c is the helix which winds around the cylinder x2 + y2 = 1 (counterclock- wise, as viewed from the positive z-axis, looking down on the xy-plane). It starts at the point (1, 0, 0), winds around the cylinder once, and ends at the point (1, 0, 1). Compute the line integral of the vector eld. ~f (x, y, z) = h y, x, z2i along c. ~f d~r, where ~f is the conservative vector eld.