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

question 236

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 $10 ^ { - 3 }$ .
- $$F ( x ) = \int _ { 0 } ^ { x } \left( \tan ^ { - 1 } t \right) ^ { 2 } d t , [ 0,0.5 ]$$

• A) \(\frac { x ^ { 3 } } { 3 } - \frac { 2 x ^ { 9 } } { 27 }\)
• B) \(\frac { x ^ { 3 } } { 3 } - \frac { 2 x ^ { 15 } } { 15 }\)
• C) \(\frac { x ^ { 3 } } { 3 } - \frac { 2 x ^ { 9 } } { 9 }\)
• D) \(\frac { x ^ { 3 } } { 3 } - \frac { x ^ { 15 } } { 15 }\)

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Definitions:

Prices

The plural form referring to the various amounts of money that goods or services are bought and sold for in a market.

Price Discrimination

The strategy of selling the same product or service at different prices to different customers, based on their willingness or ability to pay.

Consumer Surplus

The discrepancy between the total sum consumers are prepared and capable of spending for a product or service, and the total sum they end up paying.

Single-price Monopoly

a market structure where a monopolist sells a product or service at a single price to all consumers, with no price discrimination.