Q53Multiple correct3 Marks11 Dec 2022

Consider a function g(x, y) such that g(x, y) = { u(x, y) if x = y, v(x, y) if x != y } where u(x, y) = x^3 + e^y and v(x, y) = y^3 + y e^x. Which of the following options is/are true?

A

g(x, y) is continuous at the origin.

B

f_{xy}(1, 2) = e.

C

f_{xy}(x, y) is not continuous at $(1, 2)$.

D

f_y(1, 1) = 2 + e.