The question presents multiple independent statements (typically labeled ㄱ, ㄴ, ㄷ or similar) about limits, continuity, or function behavior and asks the student to determine which combination of statements is correct.
A function $f$ defined on the set of real numbers satisfies the inequalities $$1 \leq f ( x ) \leq 2$$ for every $x$. Accordingly,\ I. $\lim _ { x \rightarrow 1 } \frac { 1 } { f ( x ) }$ exists.\ II. $\lim _ { x \rightarrow 1 } \frac { f ( x ) } { x }$ exists.\ III. $\lim _ { x \rightarrow 1 } ( | f ( x ) | - f ( x ) )$ exists. Which of the following statements are always true?\ A) Only I\ B) Only II\ C) Only III\ D) I and II\ E) II and III