MATH 32A Study Guide - Midterm Guide: Level Set, Tangent Space, Directional Derivative

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23 Nov 2018
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You will receive little or no credit for a correct answer to a problem which is not accompanied by su cient explanations. If you have a question about any particular problem, please raise your hand and one of the proctors will come and talk to you. At the completion of the exam, please hand the exam booklet to your ta. If you have any questions about the grading of the exam, please see the instructor within 15 calendar days of the examination. I certify that the work appearing on this exam is completely my own: Suppose you are walking on the surface z = 4x2 + y2 2 directly above the curve. Find the values of t for which you are walking uphill. ~r(t) = hcos t, sin ti, t [0, 2 ]. Evaluate the following limit, or show that the limit does not exist. Let f (x, y) = (cid:26) 3xy2 x2+y4.