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20cMidterm1 - Math 20C Test 1B 100 points Directions Show...

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Unformatted text preview: Math 20C Test 1B 100 points October 22, 2008--------------------------------------------------------------------------------------------------- Directions: Show all work and justify all answers.---------------------------------------------------------------------------------------------------- (1) Show that as (x, y) approaches (0, 0), (A) the function yx 3 / (x 4 + y 4 ) has no limit ; (B) the function yx 4 / (x 4 + y 4 ) DOES have a limit. (If you claim some function is bounded, be sure to explain how you know.) (16 pts)---------------------------------------------------------------------------------------------------------- (2) An ant is crawling on the top of the surface S given by the formula z = ( x 2 + y 2 ) 1/4 . The ant is climbing in a direction heading away from the z-axis. True or False : The ant’s climb is getting steeper and steeper. (Explain your answer in words, using level curves.) (13 pts)-----------------------------------------------------------------------------------------------------------...
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