Q1Single correct5 Marks10 May 2026

Consider the function $f: \mathbb{R}^2 \to \mathbb{R}$ defined as follows: $$f(x, y) = \begin{cases} \frac{\sin(x^2 - y^2)}{\sqrt{x^2 + y^2}} & \text{if } (x, y) \neq (0, 0) \\ 0 & \text{else} \end{cases}$$ Choose the correct option.

A

lim_{(x,y)->(0, $\pi$/2)} f(x,y) = 0

B

lim_{(x,y)->(a, $\pi$/2)} f(x,y) is not defined for any non-zero a in R.

C

lim_{(x,y)->(1, 0)} f(x,y) = 1

D

lim_{(x,y)->(0,0)} f(x,y) = 0