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

question 176

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 $10 ^ { - 3 }$ .
- $$\mathrm { F } ( \mathrm { x } ) = \int _ { 0 } ^ { \mathrm { x } } \frac { \tan ^ { - 1 } \mathrm { t } } { \mathrm { t } } \mathrm { dt } , [ 0,0.5 ]$$

• A) \(x - \frac { x ^ { 3 } } { 9 } + \frac { x ^ { 5 } } { 25 }\)
• B) \(x - \frac { x ^ { 3 } } { 6 } + \frac { x ^ { 5 } } { 120 }\)
• C) \(x - \frac { x ^ { 3 } } { 3 } + \frac { x ^ { 5 } } { 60 }\)
• D) \(x - \frac { x ^ { 3 } } { 3 } + \frac { x ^ { 5 } } { 5 }\)

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Definitions:

Menses

The monthly shedding of the uterine lining in females, which is a part of the menstrual cycle.

Placenta

An organ that develops in the uterus during pregnancy, facilitating nutrient uptake, waste elimination, and gas exchange between the mother's and the fetus's blood.

Progesterone

A steroid hormone released by the corpus luteum in the ovary, essential for maintaining pregnancy and regulating the menstrual cycle.

Reproductive Tract

The series of organs and ducts through which gametes travel and where fertilization, gestation, and childbirth occur, differing in structure between males and females.