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

Multiple Choice

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.