Determine the continuity of the function $$f ( x , y ) = 11 \sin \frac { x } { y }$$
A) continuous except at $( 0,11 )$
B) continuous except at $( 2,0 )$
C) continuous for all $y \neq 0$
D) continuous for all $x \neq 0$
E) continuous everywhere

Question

Determine the continuity of the function $$f ( x , y ) = 11 \sin \frac { x } { y }$$ 
A) continuous except at $( 0,11 )$
B) continuous except at $( 2,0 )$
C) continuous for all $y \neq 0$
D) continuous for all $x \neq 0$
E) continuous everywhere

Quizplus · Accepted Answer

The function is not defined when $y=0$. However, for all $y
eq0$, the function is a composition of continuous functions and therefore continuous. Thus, the only point that is not in the domain of the function is $(0,11)$, so the function is continuous for all other points.

Determine the Continuity of the Function f(x,y)=11sin⁡xyf ( x , y ) = 11 \sin \frac { x } { y }f(x,y)=11sinyx​

Determine the Continuity of the Function $f ( x , y ) = 11 \sin \frac { x } { y }$