Provide an appropriate response.
-Let $f ( n ) = \sqrt { n ^ { 2 } + 4 } - \sqrt { n ^ { 2 } - 4 }$. What is $f ( n )$ approximately equal to as $n$ gets large? Hint: Compute various examples on your calculator.
A) $\frac { 4 } { n ^ { 2 } }$
B) $\frac { 4 } { \sqrt { n } }$
C) $\frac { 4 } { 2 n }$
D) $\frac { 4 } { n }$

Question

Quizplus · Accepted Answer

When we plug in larger and larger values of $n$, we see that the terms $\sqrt{n^2+4}$ and $\sqrt{n^2-4}$ both approach $n$, since the $n^2$ term will dominate as $n$ grows large. Therefore, $f(n)$ is approximately equal to $n-n=\boxed{\frac{4}{n}}$ as $n$ gets large.

Provide an Appropriate Response f(n)=n2+4−n2−4f ( n ) = \sqrt { n ^ { 2 } + 4 } - \sqrt { n ^ { 2 } - 4 }f(n)=n2+4​−n2−4​

Provide an Appropriate Response $f ( n ) = \sqrt { n ^ { 2 } + 4 } - \sqrt { n ^ { 2 } - 4 }$