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

question 426

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 $10 ^ { - 3 }$ .
- $$F ( x ) = \int _ { 0 } ^ { x } \sin ^ { 3 } d t , [ 0,1 ]$$

• A) \(x ^ { 3 } - \frac { x ^ { 9 } } { 6 }\)
• B) \(x ^ { 3 } - \frac { x ^ { 7 } } { 6 }\)
• C) \(\frac { x ^ { 4 } } { 4 } - \frac { x ^ { 10 } } { 60 }\)
• D) \(\frac { x ^ { 4 } } { 4 } - \frac { x ^ { 8 } } { 48 }\)

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Definitions:

Cost Behavior

Refers to the way different types of production costs change when there is a change in the level of production.

Special Order

A one-time order not considered part of the company's normal ongoing operations, often requiring special pricing and production considerations.

Variable Costs

Expenses that fluctuate directly with changes in production volume, such as raw materials and direct labor.

Capacity

The maximum level of output that a company can sustain to make a product or provide a service under normal conditions.