Provide an Appropriate Response $x$ Can $\sin x$ Be Replaced By $x - \frac { x ^ { 3 } } { 6 }$

question 199

Multiple Choice

Provide an appropriate response.
-For approximately what values of $x$ can $\sin x$ be replaced by $x - \frac { x ^ { 3 } } { 6 }$ with an error of magnitude no greater than $5 \times 10 ^ { - 8 } ?$

• A) \(| x | < 0.09029\)
• B) \(| x | < 0.04949\)
• C) \(| x | < 0.03310\)
• D) \(| x | < 0.06544\)

---

Definitions:

Security Market Line

A line that represents the relationship between the risk of an investment and its expected return, used in capital asset pricing model (CAPM) to determine risk-adjusted returns.

Unsystematic Risk

The risk associated with a specific company or industry, also known as "diversifiable risk" or "idiosyncratic risk."

Expected Risk Premium

The additional return over the risk-free rate that investors demand to compensate for the risk of holding a risky asset.

Systematic Risk Principle

The concept that an investor can reduce the overall risk of an investment portfolio through diversification, except for inherent market risks that cannot be diversified away.