quiz_01A - x 2 y 2 ≤ | y | Since lim x,y →(0 0 ±| y |...

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Math 213 — Quiz 1 Name Sample Solution 1. Find the limit, if it exists, or show that the limit doesn’t exist. lim ( x,y ) (0 , 0) xy p x 2 + y 2 First note that p x 2 + y 2 ≥ | x | and so | xy | p x 2 + y 2 ≤ | y | , or -| y | ≤ xy p
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Unformatted text preview: x 2 + y 2 ≤ | y | . Since lim ( x,y ) → (0 , 0) ±| y | = 0, it follows from the Squeeze Theorem that lim ( x,y ) → (0 , 0) xy p x 2 + y 2 = 0 ....
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