Complete the table and numerically estimate the limit as $x$ approaches infinity for $f ( x ) = x - \sqrt { x ^ { 2 } + 4 }$.
$\begin{array}{|c|c|c|c|c|c|c|c|}
\hline x & 10^{0} & 10^{1} & 10^{2} & 10^{3} & 10^{4} & 10^{5} & 10^{6} \
\hline f(x) & & & & & & & \
\hline
\end{array}$

A) 0
B) 4
C) $- 4$
D) $\infty$
E) limit does not exist

Question

Complete the table and numerically estimate the limit as $x$ approaches infinity for $f ( x ) = x - \sqrt { x ^ { 2 } + 4 }$.
$\begin{array}{|c|c|c|c|c|c|c|c|}
\hline x & 10^{0} & 10^{1} & 10^{2} & 10^{3} & 10^{4} & 10^{5} & 10^{6} \
\hline f(x) & & & & & & & \
\hline
\end{array}$

A) 0
B) 4
C) $- 4$
D) $\infty$
E) limit does not exist

Quizplus · Accepted Answer

The limit of $f(x) = x - \sqrt{x^2 + 4}$ as $x$ approaches infinity is 0. This is because both $x$ and $\sqrt{x^2 + 4}$ grow indefinitely, but their difference approaches 0, as the term under the square root is dominated by $x^2$ at very large values of $x$, making the square root essentially equal to $x$ for large values, thus their difference approaches 0.

Complete the Table and Numerically Estimate the Limit As xxx Approaches Infinity For

Complete the Table and Numerically Estimate the Limit As $x$ Approaches Infinity For