Which of the Following Sets of Functions Are Linearly Independent $( 0 , \infty )$

question 36

Multiple Choice

Which of the following sets of functions are linearly independent on $( 0 , \infty )$ ? Select all that apply.

• A) \(\left\{ 1 , \sin ^ { 2 } x , \cos ^ { 2 } x \right\}\)
• B) \(\{ 1 , x + 3,2 x \}\)
• C) \(\left\{ \sqrt { x } , x , x ^ { 2 } \right\}\)
• D) \(\left\{ 1 , \tan ^ { 2 } x , \sec ^ { 2 } x \right\}\)
• E) \(\{ 1 / x , x , \ln x \}\)

---

Definitions:

Social Issues

Subjects of concern or controversy that directly impact society and its constituents, including matters like poverty, education, healthcare, and equality.

Political Socialization

The process by which individuals learn and frequently internalize a political lens framing their perceptions of how power is arranged and how the world around them is (and should be) organized; those perceptions, in turn, shape and define individuals’ definitions of who they are and how they should behave in the political and economic institutions in which they live.

Significant Events

Noteworthy or important occurrences that have a substantial impact on societies or environments.

Generational Effect

The influence that significant events have on the attitudes and values of the generation that experiences them firsthand.