# answers_12.1-12.4 - 12.1 4. c. The level curves are c = x 2...

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12.1 4. c. The level curves are 22 cx y =− . For c <0 these are hyperbolas on the y axis. For c > 0 these are hyperbolas on the x axis. For c = 0 these are intersecting lines y x = ± in the xy plane. 6. a. The domain is y real and x not equal to 0. The sketch of the domain would be the xy plane with the y axis as a dotted line (omitted). b. The range is the reals. 8. a. domain: 9 x y ≥+ b. Range 03 z The sketch of the domain is a circle and its interior of radius 3 and center (0,0). c. 222 9 cxy −=+ 10. a. Domain: all reals in xy plane b. Range 01 z <≤ 14. e 16. c 18. b 20. Sketch below. 22. A. is the top of a cone with z axis. B. the level curves are evenly spaced circles about the origin p.780 8. The domain is all the reals in 3D. The range is k < . 12.2 6. 1 14. 2 30b. continuous where 2 y x 36. limit dne (show by paths) 56. Use polar. Limit dne.

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## This note was uploaded on 02/11/2010 for the course MATH 2224 taught by Professor Mecothren during the Spring '03 term at Virginia Tech.

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answers_12.1-12.4 - 12.1 4. c. The level curves are c = x 2...

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