https://file.aiquickdraw.com/mathbot/file/17264037963072denojvd.jpg

The question asks to evaluate the limit:

\[
\lim_{{x \to -\infty}} \frac{1}{x}
\]

### Solution:
As \( x \) approaches negative infinity, the denominator \( x \) becomes a very large negative number. Since the numerator remains \( 1 \), we can analyze the behavior of \( \frac{1}{x} \) as follows:

- As \( x \) becomes more negative, the fraction \( \frac{1}{x} \) approaches \( 0 \), but it remains **negative**.
- Thus, the value of \( \frac{1}{x} \) approaches \( 0 \) from the negative side.

Therefore, the correct answer is:

\[
\boxed{0}
\]

Would you like more details on limits at infinity or any other questions?

Here are 5 related questions:
1. What is the limit of \( \frac{1}{x} \) as \( x \to +\infty \)?
2. How does \( \frac{1}{x} \) behave as \( x \to 0 \) from the right and left?
3. What is the limit of \( \frac{1}{x^2} \) as \( x \to \infty \)?
4. How does the behavior of \( \frac{1}{x} \) change if \( x \) approaches a finite value?
5. What are some practical applications of limits at infinity?

**Tip:** When evaluating limits as \( x \to \infty \) or \( x \to -\infty \), consider how both the numerator and denominator behave as they approach extreme values.

This problem explores the limit of the function 1/x as x approaches negative infinity. Learn how to analyze the behavior of functions at infinity using key calculus concepts. Suitable for students in Grades 11-12.

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