Answer
$$0$$
Work Step by Step
$$\eqalign{
& f\left( x \right) = \frac{{x + 1}}{{x\sqrt x }} \cr
& {\text{Evaluate }}f\left( x \right){\text{ for the given values and complete the table}}{\text{.}} \cr
& x = {10^0} \to f\left( {{{10}^0}} \right) = \frac{{{{10}^0} + 1}}{{{{10}^0}\sqrt {{{10}^0}} }} = 2 \cr
& x = {10^1} \to f\left( {{{10}^1}} \right) = \frac{{{{10}^1} + 1}}{{{{10}^1}\sqrt {{{10}^1}} }} \approx 0.3478 \cr
& x = {10^2} \to f\left( {{{10}^2}} \right) = \frac{{{{10}^2} + 1}}{{{{10}^2}\sqrt {{{10}^2}} }} \approx 0.101 \cr
& x = {10^3} \to f\left( {{{10}^3}} \right) = \frac{{{{10}^3} + 1}}{{{{10}^3}\sqrt {{{10}^3}} }} \approx 0.0316 \cr
& x = {10^4} \to f\left( {{{10}^4}} \right) = \frac{{{{10}^4} + 1}}{{{{10}^4}\sqrt {{{10}^4}} }} \approx 0.0100 \cr
& x = {10^5} \to f\left( {{{10}^5}} \right) = \frac{{{{10}^5} + 1}}{{{{10}^5}\sqrt {{{10}^5}} }} \approx 0.00316 \cr
& x = {10^6} \to f\left( {{{10}^6}} \right) = \frac{{{{10}^6} + 1}}{{{{10}^6}\sqrt {{{10}^6}} }} \approx 0.00100 \cr} $$
\[\boxed{\begin{array}{*{20}{c}}
x&{f\left( x \right)} \\
{{{10}^0}}&{2.00000} \\
{{{10}^1}}&{0.34780} \\
{{{10}^2}}&{0.10100} \\
{{{10}^3}}&{0.03160} \\
{{{10}^4}}&{0.01000} \\
{{{10}^5}}&{0.00316} \\
{{{10}^6}}&{0.00100}
\end{array}}\]
$$\eqalign{
& \mathop {\lim }\limits_{x \to \infty } \frac{{x + 1}}{{x\sqrt x }} \cr
& = \mathop {\lim }\limits_{x \to \infty } \frac{{x + 1}}{{{x^{3/2}}}} \cr
& = \mathop {\lim }\limits_{x \to \infty } \frac{{\frac{x}{{{x^{3/2}}}} + \frac{1}{{{x^{3/2}}}}}}{{\frac{{x\sqrt x }}{{{x^{3/2}}}}}} \cr
& = \mathop {\lim }\limits_{x \to \infty } \frac{{\frac{1}{{{x^{1/2}}}} + \frac{1}{{{x^{3/2}}}}}}{1} \cr
& {\text{Evaluate the limit}} \cr
& {\text{ = }}\frac{1}{{{{\left( \infty \right)}^{1/2}}}} + \frac{1}{{{{\left( \infty \right)}^{3/2}}}} \cr
& = 0 \cr
& \cr
& {\text{Graph}} \cr} $$
