The problem asks for the limit of $\frac{1}{x}$ as $x$ approaches $+\infty$:

$\lim_{x \to +\infty} \frac{1}{x}$

As $x$ increases without bound, $\frac{1}{x}$ gets smaller and smaller, approaching 0. Therefore, the correct answer is:

$\lim_{x \to +\infty} \frac{1}{x} = 0$

The correct response is "0".

Would you like more details or have any further questions?

Here are 5 related questions to consider:

1. What is the limit of $\frac{1}{x^2}$ as $x \to +\infty$?
2. How does $\lim_{x \to -\infty} \frac{1}{x}$ compare to $\lim_{x \to +\infty} \frac{1}{x}$?
3. What is the limit of $\frac{x}{x^2 + 1}$ as $x \to +\infty$?
4. What is the general behavior of rational functions as $x \to +\infty$?
5. How do limits at infinity differ from limits as $x$ approaches a finite value?

Tip: When dealing with limits involving infinity, always consider how the function behaves as the input becomes very large or very small!