Find the Polynomial of Lowest Degree That Will Approximate $F ( x )$

question 176

Multiple Choice

Find the polynomial of lowest degree that will approximate $F ( x )$ throughout the given interval with an error of magnitude less than than $10 ^ { - 3 }$ .
- $$\mathrm { F } ( \mathrm { x } ) = \int _ { 0 } ^ { \mathrm { x } } \frac { \tan ^ { - 1 } \mathrm { t } } { \mathrm { t } } \mathrm { dt } , [ 0,0.5 ]$$

• A) \(x - \frac { x ^ { 3 } } { 9 } + \frac { x ^ { 5 } } { 25 }\)
• B) \(x - \frac { x ^ { 3 } } { 6 } + \frac { x ^ { 5 } } { 120 }\)
• C) \(x - \frac { x ^ { 3 } } { 3 } + \frac { x ^ { 5 } } { 60 }\)
• D) \(x - \frac { x ^ { 3 } } { 3 } + \frac { x ^ { 5 } } { 5 }\)

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Definitions:

Central Traits

Central traits are the key characteristics that define an individual's personality and are thought to be relatively stable and consistent across different situations.

Object-relations School

A psychoanalytic theory focusing on relationships and the impact of early family interactions on the development of the self.

Extroversion Versus Introversion

A personality dimension describing the extent to which an individual is outgoing and energized by social interaction (extroversion) or prefers solitude and minimizes social engagement (introversion).

Central Traits

Personality attributes that are considered particularly characteristic of an individual and which form a basic foundation of personality.