Find the Third-Degree Taylor Polynomial of the Function $f ( x ) = \int _ { 0 } ^ { x } \sin t ^ { 2 } d t \text { at } a = 0$

question 253

Essay

Find the third-degree Taylor polynomial of the function $f ( x ) = \int _ { 0 } ^ { x } \sin t ^ { 2 } d t \text { at } a = 0$ .

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Definitions:

Mild Depressive Symptoms

Less severe forms of depressive symptoms that may include sadness, irritability, or fatigue, but do not fully meet the criteria for major depression.

Rapid Cycling

a term in bipolar disorder indicating four or more mood episodes within a year.

Mild Mania

A less severe form of mania characterized by elevated or irritable mood, increased activity or energy, but without significant impairment in social or occupational functioning.

Major Depression

A mental disorder marked by persistent feelings of sadness or despair and a lack of interest in external stimuli, affecting one's ability to function daily.