Find the limit
lim𝑥→−7^− 12/𝑥+7

To find the limit of the expression as \(x \to -7^-\), we need to evaluate the behavior of the function 

\[
\frac{12}{x + 7}
\]

as \(x\) approaches \(-7\) from the left (indicated by the \(-\) sign).

### Step-by-step Solution:

1. **Expression Setup:**
   \[
   f(x) = \frac{12}{x + 7}
   \]

2. **Approaching \(x = -7\) from the Left:**

   As \(x\) approaches \(-7\) from the left (\(x \to -7^-\)), the denominator \(x + 7\) approaches \(0\). Specifically, since \(x\) is slightly less than \(-7\), \(x + 7\) will be a small negative number.

3. **Behavior of the Function:**
   
   The expression \(\frac{12}{x + 7}\) will become very large in magnitude but negative, as dividing by a small negative number results in a large negative value.

4. **Conclusion:**
   
   As \(x \to -7^-\), \(\frac{12}{x + 7} \to -\infty\).

### Limit Result:

\[
\lim_{x \to -7^-} \frac{12}{x + 7} = -\infty
\]

The limit of \(\frac{12}{x + 7}\) as \(x\) approaches \(-7\) from the left is \(-\infty\).

---

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:
1. What happens to \(\lim_{x \to -7^+} \frac{12}{x + 7}\)?
2. How would the limit change if the numerator were negative?
3. How do you determine the limits of rational functions at vertical asymptotes?
4. What is the difference between one-sided limits and two-sided limits?
5. Can you explain what happens to \(\frac{12}{x+7}\) when \(x\) approaches a number other than \(-7\)?

**Tip:** Always consider the direction from which \(x\) is approaching when calculating one-sided limits.

Learn how to find the limit of the function 12/(x + 7) as x approaches -7 from the left. Understand the behavior of rational functions near vertical asymptotes and how limits are evaluated in calculus. Suitable for advanced high school students and calculus learners.

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