Answer
\[0\]
Work Step by Step
\[\begin{gathered}
f\left( x \right) = \frac{{10}}{{\sqrt {2{x^2} - 1} }} \hfill \\
{\text{Evaluate }}f\left( x \right){\text{ for the given values and complete the table}}{\text{.}} \hfill \\
x = {10^0} \to f\left( {{{10}^0}} \right) = \frac{{10}}{{\sqrt {2{{\left( {{{10}^0}} \right)}^2} - 1} }} = 10 \hfill \\
x = {10^1} \to f\left( {{{10}^1}} \right) = \frac{{10}}{{\sqrt {2{{\left( {{{10}^1}} \right)}^2} - 1} }} \approx 0.70888 \hfill \\
x = {10^2} \to f\left( {{{10}^2}} \right) = \frac{{10}}{{\sqrt {2{{\left( {{{10}^2}} \right)}^2} - 1} }} \approx 0.070712 \hfill \\
x = {10^3} \to f\left( {{{10}^3}} \right) = \frac{{10}}{{\sqrt {2{{\left( {{{10}^3}} \right)}^2} - 1} }} \approx 0.00707 \hfill \\
x = {10^4} \to f\left( {{{10}^4}} \right) = \frac{{10}}{{\sqrt {2{{\left( {{{10}^4}} \right)}^2} - 1} }} \approx 0.0007071 \hfill \\
x = {10^5} \to f\left( {{{10}^5}} \right) = \frac{{10}}{{\sqrt {2{{\left( {{{10}^5}} \right)}^2} - 1} }} \approx 0.00007071 \hfill \\
x = {10^6} \to f\left( {{{10}^6}} \right) = \frac{{10}}{{\sqrt {2{{\left( {{{10}^6}} \right)}^2} - 1} }} \approx 0 \hfill \\
\boxed{\begin{array}{*{20}{c}}
x&{f\left( x \right)} \\
{{{10}^0}}&{10} \\
{{{10}^1}}&{0.70888} \\
{{{10}^2}}&{0.070712} \\
{{{10}^3}}&{0.00707} \\
{{{10}^4}}&{0.0007071} \\
{{{10}^5}}&{0.00007071} \\
{{{10}^6}}&0
\end{array}} \hfill \\
{\text{Therefore,}} \hfill \\
\mathop {\lim }\limits_{x \to \infty } f\left( x \right) = \mathop {\lim }\limits_{x \to \infty } \left( {\frac{{10}}{{\sqrt {2{x^2} - 1} }}} \right) = 0 \hfill \\
{\text{Graph}} \hfill \\
\end{gathered} \]
