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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