$$\mathop {\lim }\limits_{{\text{x}} \to \infty } {{\text{x}}^{\frac{1}{{\text{x}}}}}$$ is A. $$\infty $$ B. 0 C. 1 D. Not defined

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

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