Provide an Appropriate Response $f ( n ) = \sqrt { n ^ { 2 } + 9 } - \sqrt { n ^ { 2 } - 9 }$

question 132

Multiple Choice

Provide an appropriate response.
-Let $f ( n ) = \sqrt { n ^ { 2 } + 9 } - \sqrt { n ^ { 2 } - 9 }$ . What is $f ( n )$ approximately equal to as $n$ gets large? Hint: Compute various examples on your calculator.

• A) \(\frac { 9 } { n ^ { 2 } }\)
• B) \(\frac { 9 } { 2 n }\)
• C) \(\frac { 9 } { \sqrt { n } }\)
• D) \(\frac { 9 } { \mathrm { n } }\)

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Definitions:

False Dichotomy

A logical fallacy consisting of a situation in which only two alternatives are considered, when in fact there are additional options.

Reasoning Fallacy

A flaw or error in reasoning that undermines the logical validity of an argument.

Alternative Explanations

Different reasons or theories provided to account for a phenomenon or observation.

Critical Thinking

The objective analysis and evaluation of an issue in order to form a judgment, often requiring skepticism and the questioning of assumptions.