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

question 307

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

• A) \(x - \frac { x ^ { 3 } } { 3 } + \frac { x ^ { 5 } } { 5 } - \frac { x ^ { 7 } } { 7 }\)
• B) \(x - \frac { x ^ { 3 } } { 3 } + \frac { x ^ { 5 } } { 5 } - \frac { x ^ { 7 } } { 7 } + \frac { x ^ { 9 } } { 9 }\)
• C) \(x - \frac { x ^ { 3 } } { 3 } + \frac { x ^ { 5 } } { 10 } - \frac { x ^ { 7 } } { 42 }\)
• D) \(x - \frac { x ^ { 3 } } { 3 } + \frac { x ^ { 5 } } { 10 } - \frac { x ^ { 7 } } { 42 } + \frac { x ^ { 9 } } { 216 }\)

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Definitions:

Survivor Bias

The analytical error of focusing on the surviving subjects of a study or process and overlooking those that did not survive due to lack of visibility.

Broad Sample

A wide-ranging or extensive group of people or items selected from a population, used for research or statistical analysis.

Survivor Bias

A logical error that involves focusing on the people or things that survived some process and inadvertently overlooking those that did not because of their lack of visibility.

Financially Successful

A state or condition of having significant income, profit, or assets, exceeding financial liabilities and obligations.