The correct answer is $\boxed{\text{D}}$.
The limit $\lim_{x\to\infty}x^{1/x}$ is not defined. This is because as $x$ approaches infinity, the value of $x^{1/x}$ approaches both 0 and infinity.
For example, when $x=1$, $x^{1/x}=1$. When $x=10$, $x^{1/x}=10^{1/10}\approx 1.054$. When $x=100$, $x^{1/x}=100^{1/100}\approx 1.0546$. As you can see, the value of $x^{1/x}$ is getting closer and closer to 1 as $x$ gets larger.
However, when $x=1/10$, $x^{1/x}=10^{-1/10}\approx 0.954$. When $x=1/100$, $x^{1/x}=10^{-1/100}\approx 0.9546$. As you can see, the value of $x^{1/x}$ is getting closer and closer to 0 as $x$ gets smaller.
Therefore, the limit $\lim_{x\to\infty}x^{1/x}$ does not exist.