https://file.aiquickdraw.com/mathbot/file/17259375634904gnac20b.jpg

Let's examine the graph and determine if the limit \(\lim_{x \to 0} f(x)\) exists, and if so, find its value.

### Observations from the Graph:

1. As \(x\) approaches 0 from the left (\(x \to 0^-\)):
   - The function \(f(x)\) appears to approach the value 1.

2. As \(x\) approaches 0 from the right (\(x \to 0^+\)):
   - The function \(f(x)\) also appears to approach the value 1.

### Conclusion:
Since both the left-hand limit and right-hand limit as \(x\) approaches 0 are equal and approach the same value (1), the two-sided limit exists and is equal to 1.

Thus, \[
\lim_{x \to 0} f(x) = 1.
\]

Let me know if you'd like more details, or have any other questions!

Here are 5 related questions for further exploration:

1. What does it mean for a limit to not exist?
2. How do you evaluate limits algebraically versus graphically?
3. What is the formal definition of a limit (using epsilon-delta)?
4. How do limits relate to continuity at a point?
5. What happens when the left-hand and right-hand limits are not equal?

**Tip:** When both the left-hand and right-hand limits match at a point, the two-sided limit exists at that point.

Decide whether the limit exists. If it exists, find its value. The limit is lim(x → 0) f(x), where the graph of f(x) is given.

This problem involves determining the existence of a limit as x approaches 0 for the function f(x) using its graph. The solution explains how to evaluate the left-hand and right-hand limits to conclude that the two-sided limit exists and is equal to 1. Suitable for Calculus I students.

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