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What is the value of lim(x→0, y→0) xy / (x² + y²) ?

1. 1
2. -1
3. 0
4. Limit does not exist

Correct answer: Limit does not exist

Solution

The limit does not exist because the value of the expression xy / (x² + y²) approaches different values depending on the path taken towards (0,0). For example, approaching along the line y = x gives a different limit than approaching along the line y = -x.

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