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

question 458

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 $10 ^ { - 3 }$ .
- $$F ( x ) = \int _ { 0 } ^ { x } \frac { \ln \left( 1 + t ^ { 2 } \right) } { t } d t , [ 0,0.6 ]$$

• A) \(\frac { x ^ { 2 } } { 2 } - \frac { x ^ { 4 } } { 4 } + \frac { x ^ { 6 } } { 6 }\)
• B) \(\frac { x ^ { 2 } } { 2 } - \frac { x ^ { 4 } } { 16 } + \frac { x ^ { 6 } } { 128 }\)
• C) \(\frac { x ^ { 2 } } { 2 } - \frac { x ^ { 4 } } { 8 } + \frac { x ^ { 6 } } { 32 }\)
• D) \(\frac { x ^ { 2 } } { 2 } - \frac { x ^ { 4 } } { 8 } + \frac { x ^ { 6 } } { 18 }\)

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Definitions:

Flexible Budget Sales

Projected sales figures that can adjust based on changes in production levels or market conditions.

Actual Sales

Revenue generated from goods sold or services provided in a particular period, factually recorded.

Sales Variance

Sales variance is the difference between actual sales and budgeted or planned sales, used to assess performance.

Variable Costs

Costs that vary directly with the level of production or business activity.