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.