MAC 2313 Midterm: MAC 2313 FIU Exam 215fk
15 Feb 2019
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Prof. s. hudson: [10 pts] evaluate the de nite integral r /2. 0 hcos(2t), sin(2t)i dt: [10 pts] find a unit vector u that is normal at p (1, 2) to the level curve of f (x, y) = Some may be easy, or similar to each other. You can do them in any order, but make your work / reasoning clear: ds/dt, the radius of curvature, b, n, [20 pts] answer t or f to each; you do not have to justify your answers. If d is an closed set in r2, then it contains all its boundary points. One level surface of f (x, y, z) = x2 + y2 z is a sphere. If fx and fy exist at p (3, 4), then f is continuous at p . r(t) = t2i + 3tj is a smooth parametrization of a curve c in r2.
