The Function F(x) = Sin $x ^ { 2 }$ Is Approximated by Its Second Taylor Polynomial

question 111

Multiple Choice

The function f(x) = sin $x ^ { 2 }$ is approximated by its second Taylor polynomial $\mathrm { P } 2$ (x) at x = 0. Which of the following statements is NOT true?

• A) f'(0) = 0
• B) \(\mathrm { P } 2\) (x) = \(\frac { 1 } { 3 }\) + \(x ^ { 2 }\)
• C) \(\mathrm { P } 2\) (x) = \(x ^ { 2 }\)
• D) f''(0) = 2
• E) none of these

---

Definitions:

Birthweight

The weight of a baby at birth, an important indicator of neonatal health and development.

Wechsler Adult Intelligence Scale

A standard psychological test for measuring adult intelligence in various cognitive domains.

Population Standard Deviation

A measure of the dispersion or variability within a full population data set.

Raw Scores

The original, unmodified scores obtained in any assessment without adjustments or transformations.