Question

For t ∈ $\R$, let [𝑡] denote the greatest integer less than or equal to t.
Let D = {(x, y) ∈ $\R^2$ ∶ x2 + y2 < 4}. Let f : D → $\R$ and g : D → $\R$ be defined by f(0, 0) = g(0, 0) = 0 and
$f(x,y)=[x^2+y^2]\frac{x^2y^2}{x^4+y^4},\ \ \ g(x,y)=[y^2]\frac{xy}{x^2+y^2}$
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 _________.

Answer 1

The correct answer is : 18.