Determine the continuity of the function $$f ( x , y , z ) = \frac { 5 z } { x ^ { 2 } + y ^ { 2 } - 3 }$$
A) continuous except at $( 0,0 )$
B) continuous for $x ^ { 2 } + y ^ { 2 } = 3$
C) continuous except at $( 5,0 )$
D) continuous except at $( 0,3 )$
E) continuous for $x ^ { 2 } + y ^ { 2 } \neq 3$

Question

Determine the continuity of the function $$f ( x , y , z ) = \frac { 5 z } { x ^ { 2 } + y ^ { 2 } - 3 }$$ 
A) continuous except at $( 0,0 )$
B) continuous for $x ^ { 2 } + y ^ { 2 } = 3$
C) continuous except at $( 5,0 )$
D) continuous except at $( 0,3 )$
E) continuous for $x ^ { 2 } + y ^ { 2 } \neq 3$

Quizplus · Accepted Answer

The function $f(x, y, z) = \frac{5z}{x^2 + y^2 - 3}$ is undefined when the denominator is zero, which occurs when $x^2 + y^2 = 3$. Therefore, it is continuous for all other values, meaning $x^2 + y^2 \neq 3$.

Determine the Continuity of the Function f(x,y,z)=5zx2+y2−3f ( x , y , z ) = \frac { 5 z } { x ^ { 2 } + y ^ { 2 } - 3 }f(x,y,z)=x2+y2−35z​

Determine the Continuity of the Function $f ( x , y , z ) = \frac { 5 z } { x ^ { 2 } + y ^ { 2 } - 3 }$