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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!

Learn how to calculate the limit of 1/x as x approaches infinity in calculus. Understand key concepts like rational functions and infinity, and explore the solution using the limit theorem. Suitable for students in Grades 11-12.

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