Q14Multiple correct3 Marks31 Aug 2025Consider the function f:R2→Rf: \mathbb{R}^2 \to \mathbb{R}f:R2→R defined by f(x,y)={y2−x2x4+(y−sin(x2))2if (x,y)≠(0,0)0if (x,y)=(0,0)f(x, y) = \begin{cases} \frac{y^2 - x^2}{x^4 + (y - \sin(x^2))^2} & \text{if } (x, y) \neq (0, 0) \\ 0 & \text{if } (x, y) = (0, 0) \end{cases}f(x,y)={x4+(y−sin(x2))2y2−x20if (x,y)=(0,0)if (x,y)=(0,0) Choose all curves along which the limit of fff exists at (0,0)(0, 0)(0,0).Ay = 0Bx = 0Cy = x^2Dy = xEy = sin(x^2)
