Find the Fourth Term of the Taylor Series for the Function

question 13

Multiple Choice

Find the fourth term of the Taylor series for the function $f(x) =\cos x$ about $x=\pi / 3$ .

• A) \(\frac{\left(x-\frac{\pi}{3}\right)^{3}}{12}\)
• B) \(-\frac{\left(x-\frac{\pi}{3}\right)^{3}}{12}\)
• C) \(\frac{\sqrt{3}\left(x-\frac{\pi}{3}\right)^{3}}{12}\)
• D) \(-\frac{\sqrt{3}\left(x-\frac{\pi}{3}\right)^{3}}{12}\)

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Definitions:

Borderline Personality Disorder

A mental health disorder characterized by unstable moods, behavior, and relationships, featuring impulsivity and a chronic sense of emptiness.

Amygdala

A region of the brain involved in experiencing emotions, particularly fear and pleasure, and plays a significant role in processing emotional reactions.

Borderline Personality Disorder

A mental health disorder that impacts the way a person thinks and feels about themselves and others, causing problems functioning in everyday life. It includes self-image issues, difficulty managing emotions and behavior, and a pattern of unstable relationships.

Transference-focused Therapy

A psychodynamic treatment that aims to help patients understand and change the emotional distortions rooted in the transference relationship with the therapist.