Solve the Problem $f ( x , y , z ) = \int _ { z } ^ { y } e ^ { \theta } d \theta - \int _ { x } ^ { \sqrt { 2 } } t d t$

question 174

Multiple Choice

Solve the problem.
-Find an equation for the level surface of the function $f ( x , y , z ) = \int _ { z } ^ { y } e ^ { \theta } d \theta - \int _ { x } ^ { \sqrt { 2 } } t d t$ that passes through the point $( 0 , \ln 2 , \ln 4 )$ .

• A) \(e ^ { y } + e ^ { z } - \frac { x ^ { 2 } } { 2 } = - 2\)
• B) \(e ^ { y } - e ^ { z } + \frac { x ^ { 2 } } { 2 } = 2\)
• C) \(e ^ { y } - e ^ { z } + \frac { x ^ { 2 } } { 2 } = - 2\)
• D) \(e ^ { y } + e ^ { z } - \frac { x ^ { 2 } } { 2 } = 2\)

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Definitions:

Maladaptive Responses

Actions or behaviors that may provide a temporary solution to a stressor but ultimately are ineffective or harmful in the long-term.

Self-help Group

A voluntary association of individuals who share a common desire to overcome personal issues or improve their life circumstances, often providing mutual support and resources.

Psychoanalytic Therapy

A therapeutic approach developed by Sigmund Freud that seeks to explore and resolve unconscious conflicts and emotional issues through techniques like dream analysis and free association.

Structured Behavior Therapy

A systematic approach to modifying behavior through a set of clearly defined protocols and techniques, commonly used to address specific psychological disorders.