Find the Equation for the Level Surface of the Function $$f ( x , y , z ) = \sum _ { n = 0 } ^ { \infty } \frac { ( z y + x ) ^ { n } } { 2 ^ { n } n _ { x } ^ { n } } , ( 6,4,4 )$$

question 298

Multiple Choice

Find the equation for the level surface of the function through the given point.
- $$f ( x , y , z ) = \sum _ { n = 0 } ^ { \infty } \frac { ( z y + x ) ^ { n } } { 2 ^ { n } n _ { x } ^ { n } } , ( 6,4,4 )$$

• A) \(\frac { z y + x } { 2 x } = \frac { 11 } { 6 }\)
• B) \(\frac { ( z y + x ) ^ { n } } { 2 n _ { x ^ { n } } } = \frac { 11 } { 6 }\)
• C) The level surfaces cannot be determined.
• D) \(\sum _ { n = 0 } ^ { \infty } \frac { ( z y + x ) ^ { n } } { 2 ^ { n } x ^ { n } } = \frac { 11 } { 6 }\)

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