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[ Math 206A Quiz 04 page 1 Monday 10/17/2010 Name_SV46,05 ftd folhs ° 1. Let F': U C R? + R? be defined by F((x,y)) = (a? —y, x + y +3) (where we've agreed to drop the “vector hats” except over the name of the function F'). 1B: Wwe ive fe slain Able : 1A. Sketch the domain of F. e Mies) cya Cove \ YOR zy & 4ex* x4) fh li-> L1,0) 0,0 te pont (x4) ical 2 ° . J J is (3 D) (52) (0,3) while means te Ayman 6 J io Be Feld apiurc: this duded reH0n, yy inc he cree yaw 4 It LH 1B. Note that F is a vector field. Draw this much of the field, starting at the following three vectors/points: (1,—3), (—1,0), and the origin. Put your sketch next to your answer to 1A, above. 2. In the space below, and on the same set of axes, sketch the level curves of f(x, y) = zy, for C = —2 and C = 1. Label which curve is which. xy= 2? y= x onl S903 al Yk Gt C= +] 3. Suppose the level curves for C = L —e, C = L, and C = L + for some function z = f(x,y) are as in the following figure. 3A. As (x,y) approaches (a, b), the limit of f(x, y) appears to be L. Estimate to a tenth of a centimeter the biggest possible 6 for which 0 < ||(x, y) — (a, 6)|| < 6 implies Ifa) — Ll
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