Where is the function continuous? $$f ( x , y ) = \frac { x y } { x ^ { 2 } + y ^ { 2 } }$$
A) $R ^ { 2 }$
B) $x \neq 0$
C) $y \neq 0$
D) $( x , y ) \neq ( 0,0 )$

Question

Quizplus · Accepted Answer

The function $f(x, y) = \frac{xy}{x^2 + y^2}$ is undefined when the denominator is zero, which only occurs when both $x = 0$ and $y = 0$ simultaneously. Therefore, the function is continuous everywhere except at the point $(0,0)$.

Where Is the Function Continuous f(x,y)=xyx2+y2f ( x , y ) = \frac { x y } { x ^ { 2 } + y ^ { 2 } }f(x,y)=x2+y2xy​

Where Is the Function Continuous $f ( x , y ) = \frac { x y } { x ^ { 2 } + y ^ { 2 } }$