Q21Single correct2 Marks13 Apr 2025

For which of the following functions defined on $\mathbb{R}^2$ \ {(0,0)} does the limit of the function exist at (0,0)?

A

v_1(x,y) = $\sin$(1/(x^2 + y^2))

B

v_2(x,y) = (x^2 - y^2) $\sin$(1/(x^2 + y^2))

C

v_3(x,y) = $\sin$(x^2 + y^2)/(x^2 - y^2)

D

v_{4}(x,y) = $\sin$((x^2 - y^2)/(x^2 + y^2))