Find the Equation for the Level Surface of the Function

question 202

Multiple Choice

Find the equation for the level surface of the function through the given point.
- $$f ( x , y , z ) = \int _ { y } ^ { z } ( \ln \theta + 1 ) d \theta + \int _ { 0 } ^ { x } t e ^ { t } d t , \left( 4 , e ^ { 3 } , e ^ { - 5 } \right)$$

• A) \(- 5 e ^ { - 5 } - 3 e ^ { 3 } + 3 e ^ { 4 } + 1 = \ln \theta + 1 + t e ^ { t }\)
• B) \(- 6 e ^ { - 5 } - 2 e ^ { 3 } + 3 e ^ { 4 } + 1 = \int _ { y } ^ { z } ( \ln \theta + 1 ) d \theta + \int _ { 0 } ^ { x } t e ^ { t } d t\)
• C) \(- 5 e ^ { - 5 } - 3 e ^ { 3 } + 3 e ^ { 4 } - 7 = \int _ { y } ^ { z } ( \ln \theta + 1 ) d \theta + \int _ { 0 } ^ { x } t e ^ { t } d t\)
• D) \(- 5 e ^ { - 5 } - 3 e ^ { 3 } + 3 e ^ { 4 } + 1 = \int _ { y } ^ { z } ( \ln \theta + 1 ) d \theta + \int _ { 0 } ^ { x } t e ^ { t } d t\)

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