$\text { Determine the values of } x \text { for which the function } f ( x ) = \sin x \text { can be replaced by the }$

question 93

Multiple Choice

$\text { Determine the values of } x \text { for which the function } f ( x ) = \sin x \text { can be replaced by the }$ Taylor polynomial $f ( x ) = \sin x \approx x - \frac { x ^ { 3 } } { 3 ! }$ if the error cannot exceed $0.008$ . Round your answer to four decimal places.

• A) \(- 0.9919 < x < 0.9919\)
• B) \(- 1.9838 < x < 1.9838\)
• C) \(- 0.2480 < x < 0.2480\)
• D) \(- 1.9919 < x < 1.9919\)
• E) \(- 0.4960 < x < 0.4960\)

---

Definitions:

Jurisdiction

The official power to make legal decisions and judgments, often within a defined area of responsibility or over certain types of legal cases.

Citizenry

The collective group of citizens or inhabitants of a particular jurisdiction, often referred to in context of their rights, duties, and participation in civic life.

Dormant Commerce Clause

A legal doctrine that prohibits states from enacting legislation that discriminates against or excessively burdens interstate commerce.

State Law

The body of law enacted by each state or territory in the United States, governing within its boundaries and apart from federal law.