Find the Equation for the Level Surface of the Function $$f ( x , y , z ) = e ^ { \left( x ^ { 2 } + y ^ { 2 } - z \right) } , ( 3,5,9 )$$

question 170

Multiple Choice

Find the equation for the level surface of the function through the given point.
- $$f ( x , y , z ) = e ^ { \left( x ^ { 2 } + y ^ { 2 } - z \right) } , ( 3,5,9 )$$

• A) \(\ln \left( x ^ { 2 } + y ^ { 2 } - z \right) = 25\)
• B) \(e ^ { \left( x ^ { 2 } + y ^ { 2 } - z \right) } = \ln ( 25 )\)
• C) \(x ^ { 2 } + y ^ { 2 } - z = \ln ( 25 )\)
• D) \(x ^ { 2 } + y ^ { 2 } - z = e ^ { 25 }\)

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