Discuss the continuity of the function. $$f ( x , y , z ) = \frac { z } { x ^ { 2 } + y ^ { 2 } - 36 }$$
A) $f$ is continuous everywhere except at those points $( x , y , z )$ such that $x ^ { 2 } + y ^ { 2 } = 36$.
B) $f$ is continuous everywhere except at those points $( x , y , z )$ such that $x ^ { 2 } + y ^ { 2 } \leq 36$.
C) $f$ is continuous at those points $( x , y , z )$ such that $x ^ { 2 } + y ^ { 2 } \leq 36$.
D) $f$ is continuous only when $x ^ { 2 } + y ^ { 2 } = 36$.
E) $f$ is continuous everywhere in the $x y$-plane.

Question

Discuss the continuity of the function. $$f ( x , y , z ) = \frac { z } { x ^ { 2 } + y ^ { 2 } - 36 }$$
A) $f$ is continuous everywhere except at those points $( x , y , z )$ such that $x ^ { 2 } + y ^ { 2 } = 36$.
B) $f$ is continuous everywhere except at those points $( x , y , z )$ such that $x ^ { 2 } + y ^ { 2 } \leq 36$. 
C) $f$ is continuous at those points $( x , y , z )$ such that $x ^ { 2 } + y ^ { 2 } \leq 36$.
D) $f$ is continuous only when $x ^ { 2 } + y ^ { 2 } = 36$.
E) $f$ is continuous everywhere in the $x y$-plane.

Quizplus · Accepted Answer

The Answer of Discuss the continuity of the function. $$f ( x , y , z ) = \frac { z } { x ^ { 2 } + y ^ { 2 } - 36 }$$
A) $f$ is continuous everywhere except at those points $( x , y , z )$ such that $x ^ { 2 } + y ^ { 2 } = 36$.
B) $f$ is continuous everywhere except at those points $( x , y , z )$ such that $x ^ { 2 } + y ^ { 2 } \leq 36$. 
C) $f$ is continuous at those points $( x , y , z )$ such that $x ^ { 2 } + y ^ { 2 } \leq 36$.
D) $f$ is continuous only when $x ^ { 2 } + y ^ { 2 } = 36$.
E) $f$ is continuous everywhere in the $x y$-plane.

Discuss the Continuity of the Function f(x,y,z)=zx2+y2−36f ( x , y , z ) = \frac { z } { x ^ { 2 } + y ^ { 2 } - 36 }f(x,y,z)=x2+y2−36z​

Discuss the Continuity of the Function $f ( x , y , z ) = \frac { z } { x ^ { 2 } + y ^ { 2 } - 36 }$