20e_04s_1e

20e_04s_1e - Math 20E First Midterm 48 points April 21,...

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Math 20E First Midterm 48 points April 21, 2004 Print Name, ID number and Section on your blue book. BOOKS and CALCULATORS are NOT allowed. One side of one page of NOTES is allowed. You must show your work to receive credit. Hint: In some cases, short cuts can reduce computation. 1. (24 points) Let F = ( x 2 + y 2 ) i + z j + z k , and f = xyz . In each case, either compute the requested item or brie±y explain why it makes no sense. (a) the curl of f (b) the divergence of f (c) ( F × ∇ f ) · F (d) f × F (e) the divergence of F (f) ( F × F ) × F 2. (9 points) For each of the following regions, answer the following questions: (i) Is it open? (ii) Is it connected? (iii) Is it simply connected? You do not need to explain your answers. (a) The set of points ( x, y, z ) with x 2 + y 2 + z 2 < 2 and
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