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

question 105

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.

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