If $f ( x ) = \frac { x } { \sin x }$

question 242

Multiple Choice

If $f ( x ) = \frac { x } { \sin x }$ , find $f ^ { \prime } \left( \frac { \pi } { 4 } \right)$ .

• A) \(1 + \frac { \pi } { 4 }\)
• B) \(1 + \frac { \pi } { 2 }\)
• C) \(\sqrt { 2 } \left( 1 + \frac { \pi } { 2 } \right)\)
• D) \(1 - \frac { \pi } { 2 }\)
• E) \(1 - \frac { \pi } { 4 }\)
• F) \(\sqrt { 2 } \left( 1 + \frac { \pi } { 4 } \right)\)
• G) \(\sqrt { 2 } \left( 1 - \frac { \pi } { 2 } \right)\)
• H) \(\sqrt { 2 } \left( 1 - \frac { \pi } { 4 } \right)\)

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Definitions:

Avoidant Personality Disorder

A mental health condition characterized by a long-standing pattern of extreme shyness, feelings of inadequacy, and sensitivity to rejection.

Shame

A painful feeling of humiliation or distress caused by the consciousness of wrong or foolish behavior.

Group Therapy

A type of psychotherapy where one or more therapists conduct sessions with multiple individuals simultaneously.

Avoidant Personality Disorder

A psychological disorder defined by a persistent state of intense timidity, a sense of insufficiency, and a high sensitivity to being rejected.