https://file.aiquickdraw.com/mathbot/file/1724092273404x4gp0e7v.jpg

Use the graph of  y=f(x)
to find the limits:

Step 3 of 4 :  Find  limx→1−f(x)
.

To find the limit \(\lim_{x \to 1^-} f(x)\) from the given graph, we need to analyze the behavior of the function \(f(x)\) as \(x\) approaches \(1\) from the left side (i.e., from values less than 1).

Looking at the graph:

- As \(x\) approaches 1 from the left (\(x \to 1^-\)), the value of \(f(x)\) is moving towards a specific point on the graph.
- We need to locate the point just before \(x = 1\) and see the corresponding \(y\)-value on the graph.

On the graph:

- When \(x\) is slightly less than 1 (coming from the left), the graph shows that \(f(x)\) is approaching the \(y\)-value of 2.

Therefore, the limit is:
\[
\lim_{x \to 1^-} f(x) = 2
\]

Would you like further details or have any questions? Here are five related questions that expand on this topic:

1. How do you determine \(\lim_{x \to 1^+} f(x)\) from the graph?
2. What is the importance of one-sided limits in calculus?
3. How can we determine if a function is continuous at a point using limits?
4. What is the difference between \(\lim_{x \to 1^-} f(x)\) and \(\lim_{x \to 1^+} f(x)\)?
5. How do you find the overall limit \(\lim_{x \to 1} f(x)\) if both one-sided limits are equal?

**Tip:** When analyzing limits from a graph, always carefully observe the function's behavior as it approaches the specified point from the left and the right separately.

Learn how to find the limit lim(x → 1^-) f(x) using the graph of y=f(x). Analyze the function's behavior as x approaches 1 from the left side, illustrating the concept with examples. Suitable for advanced high school students and calculus enthusiasts.

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