Answer
\[0\]
Work Step by Step
\[\begin{gathered}
\mathop {\lim }\limits_{x \to \infty } {x^5}{e^{ - x/100}} \hfill \\
{\text{Evaluate }}f\left( x \right){\text{ for the given values and complete the table}}{\text{.}} \hfill \\
x = 1 \to f\left( 1 \right) = {\left( 1 \right)^5}{e^{ - \left( 1 \right)/100}} \approx 0.9900 \hfill \\
x = 10 \to f\left( {10} \right) = {\left( {10} \right)^5}{e^{ - \left( {10} \right)/100}} \approx 90483.7418 \hfill \\
x = {10^2} \to f\left( {{{10}^2}} \right) = {\left( {{{10}^2}} \right)^5}{e^{ - \left( {{{10}^2}} \right)/100}} \approx 3678794412 \hfill \\
x = {10^3} \to f\left( {{{10}^3}} \right) = {\left( {{{10}^3}} \right)^5}{e^{ - \left( {{{10}^3}} \right)/100}} \approx 4.539 \times {10^{10}} \hfill \\
x = {10^4} \to f\left( {{{10}^4}} \right) = {\left( {{{10}^4}} \right)^5}{e^{ - \left( {{{10}^4}} \right)/100}} \approx 3.7200 \times {10^{ - 24}} \hfill \\
x = {10^5} \to f\left( {{{10}^5}} \right) = {\left( {{{10}^5}} \right)^5}{e^{ - \left( {{{10}^5}} \right)/100}} \approx 0 \hfill \\
\boxed{\begin{array}{*{20}{c}}
x&{f\left( x \right)} \\
1&{0.9900} \\
{10}&{90483.7418} \\
{{{10}^2}}&{3678794412} \\
{{{10}^3}}&{4.539 \times {{10}^{10}}} \\
{{{10}^4}}&{3.7200 \times {{10}^{ - 24}}} \\
{{{10}^5}}&0
\end{array}} \hfill \\
{\text{Therefore,}} \hfill \\
\mathop {\lim }\limits_{x \to \infty } {x^5}{e^{ - x/100}} \approx 0 \hfill \\
{\text{Graph}} \hfill \\
\end{gathered} \]