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The answer to part (e), \(\lim_{x \to 0} f(x) = 0\), can be explained by analyzing the graph of the function \( f(x) \).

When evaluating the limit \(\lim_{x \to 0} f(x)\), we need to check the behavior of the function as \(x\) approaches 0 from both sides (left and right). In the graph:

- As \(x\) approaches 0 from the left (\(x \to 0^-\)), the function values seem to approach 0.
- As \(x\) approaches 0 from the right (\(x \to 0^+\)), the function also appears to approach 0.

Since the function approaches the same value (0) from both directions, the two-sided limit \(\lim_{x \to 0} f(x) = 0\).

Therefore, the correct answer for part (e) is indeed 0 because both the left-hand and right-hand limits at \(x = 0\) converge to 0.

Would you like more details on limit evaluation, or any clarification on other parts of the question?

Here are five related questions to expand your understanding:
1. What is the difference between a two-sided limit and a one-sided limit?
2. How does a function's discontinuity affect the limit?
3. What is the significance of a limit approaching infinity?
4. How can limits help identify asymptotes in a graph?
5. What happens if the left-hand limit and right-hand limit are not equal?

**Tip:** When evaluating limits from a graph, always check the behavior of the function from both the left and right sides of the point.

Explore why the limit of f(x) as x approaches 0 equals 0 by analyzing the graph of a function. This explanation covers graphical analysis of limits from both the left and right, ensuring a clear understanding of continuity and two-sided limits.

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