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

question 56

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

• A) \(x - \frac { x ^ { 3 } } { 18 } + \frac { x ^ { 5 } } { 90 }\)
• B) \(x + \frac { x ^ { 3 } } { 18 } + \frac { x ^ { 5 } } { 600 }\)
• C) \(x + \frac { x ^ { 3 } } { 18 } + \frac { x ^ { 5 } } { 90 }\)
• D) \(x - \frac { x ^ { 3 } } { 18 } + \frac { x ^ { 5 } } { 600 }\)

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