The image shows a mathematical notation that appears to be written on a grid or graph paper. The key mathematical expressions in the image are: 1. On the left side: \( \lim \) (possibly representing the limit of a function) with \( x \to \infty \) underneath it. 2. On the right side: The expression \( \frac{1}{x} \). This setup suggests that the problem is to evaluate the limit: \[ \lim_{x \to \infty} \frac{1}{x} \] ### Solution: As \( x \) approaches infinity, the value of \( \frac{1}{x} \) gets smaller and smaller, approaching zero. Therefore, the limit is: \[ \lim_{x \to \infty} \frac{1}{x} = 0 \] Would you like further details or explanations about this problem? Here are some related questions for further practice: 1. What is \( \lim_{x \to \infty} \frac{1}{x^2} \)? 2. What is \( \lim_{x \to 0} \frac{1}{x} \)? 3. How does \( \lim_{x \to \infty} \frac{1}{x} \) differ from \( \lim_{x \to -\infty} \frac{1}{x} \)? 4. What is the difference between limits as \( x \) approaches a finite value versus infinity? 5. Can the limit \( \lim_{x \to \infty} \frac{1}{x} \) be evaluated using L'Hôpital's Rule? If yes, how? 6. What happens if you replace \( \frac{1}{x} \) with \( \frac{1}{x+1} \)? How does the limit change? 7. What is the behavior of the function \( \frac{1}{x} \) as \( x \) approaches zero from the positive side? 8. How would you evaluate \( \lim_{x \to 0^+} \frac{1}{x} \)? **Tip:** Remember, when dealing with limits as \( x \) approaches infinity, consider how the function behaves as \( x \) becomes very large. This often simplifies the evaluation.