Question:

For t ∈ R\R, let [𝑡] denote the greatest integer less than or equal to t.
Let D = {(x, y) ∈ R2\R^2 ∶ x2 + y2 < 4}. Let f : D → R\R and g : D → R\R be defined by f(0, 0) = g(0, 0) = 0 and
f(x,y)=[x2+y2]x2y2x4+y4,   g(x,y)=[y2]xyx2+y2f(x,y)=[x^2+y^2]\frac{x^2y^2}{x^4+y^4},\ \ \ g(x,y)=[y^2]\frac{xy}{x^2+y^2}
for (x, y) ≠ (0, 0). Let E be the set of points of D at which both f and g are discontinuous. The number of elements in the set E is _________.

Updated On: Oct 1, 2024
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Correct Answer: 18

Solution and Explanation

The correct answer is : 18.
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