Use the given graph to determine the value of the indicated limits. (a) $$ \lim _{x \rightarrow-5} f(x) $$ (b) $$ \lim _{x \rightarrow-4} f(x) $$ (a) Select the correct choice below, and if necessary, fill in the answer box to complete your choice. A. lim $$ f(x)=\square $$ (o) B. The limit does

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I'd be happy to help you determine the values of the indicated limits based on the graph of $$ f(x) $$. However, since I can't see the graph, I'll guide you through the general steps to evaluate these limits. If you can provide specific details about the behavior of $$ f(x) $$ near $$ x = -5 $$ and $$ x = -4 $$, I can offer a more precise answer.

### (a) $$ \lim_{x \rightarrow -5} f(x) $$

**Steps to Determine the Limit:**

1. **Approach from the Left ($$ x \rightarrow -5^- $$):**
   - Look at the value that $$ f(x) $$ is approaching as $$ x $$ gets closer to $$-5$$ from values less than $$-5$$.
   
2. **Approach from the Right ($$ x \rightarrow -5^+ $$):**
   - Examine the value that $$ f(x) $$ is approaching as $$ x $$ approaches $$-5$$ from values greater than $$-5$$.

3. **Compare Both Sides:**
   - **If both one-sided limits exist and are equal**, then $$ \lim_{x \rightarrow -5} f(x) $$ exists and is equal to that common value.
   - **If the one-sided limits are different or at least one doesn't exist**, then the limit does not exist.

**Possible Scenarios:**

- **A.** $$ \lim_{x \rightarrow -5} f(x) = L $$, where $$ L $$ is a specific number.
- **B.** The limit does not exist.

*Select the appropriate option based on the behavior of the graph near $$ x = -5 $$. If the graph approaches the same value from both sides, choose option A and fill in the value. If not, choose option B.*

### (b) $$ \lim_{x \rightarrow -4} f(x) $$

**Steps to Determine the Limit:**

1. **Approach from the Left ($$ x \rightarrow -4^- $$):**
   - Observe the behavior of $$ f(x) $$ as $$ x $$ approaches $$-4$$ from values less than $$-4$$.

2. **Approach from the Right ($$ x \rightarrow -4^+ $$):**
   - Observe the behavior of $$ f(x) $$ as $$ x $$ approaches $$-4$$ from values greater than $$-4$$.

3. **Compare Both Sides:**
   - **If both one-sided limits exist and are equal**, then $$ \lim_{x \rightarrow -4} f(x) $$ exists and is equal to that value.
   - **If the one-sided limits differ or one doesn't exist**, then the limit does not exist.

**Possible Scenarios:**

- **A.** $$ \lim_{x \rightarrow -4} f(x) = M $$, where $$ M $$ is a specific number.
- **B.** The limit does not exist.

*Again, choose the appropriate option based on the graph's behavior near $$ x = -4 $$.*

### Example Illustration

Suppose the graph of $$ f(x) $$ near $$ x = -5 $$ looks like this:

- As $$ x $$ approaches $$-5$$ from the left, $$ f(x) $$ approaches $$ 3 $$.
- As $$ x $$ approaches $$-5$$ from the right, $$ f(x) $$ approaches $$ 3 $$.

In this case:

- $$ \lim_{x \rightarrow -5} f(x) = 3 $$ (Choose Option A and fill in $$ 3 $$).

Alternatively, if:

- As $$ x $$ approaches $$-4$$ from the left, $$ f(x) $$ approaches $$ 2 $$.
- As $$ x $$ approaches $$-4$$ from the right, $$ f(x) $$ approaches $$ 5 $$.

Then:

- $$ \lim_{x \rightarrow -4} f(x) $$ does not exist because the left-hand and right-hand limits are different (Choose Option B).

### Final Tips

- **Continuity Check:** If $$ f(x) $$ is continuous at $$ x = a $$, then $$ \lim_{x \rightarrow a} f(x) = f(a) $$.
- **Discontinuities:** Look for jumps, holes, or vertical asymptotes, as these often affect the existence of limits.

If you can describe the graph's behavior around $$ x = -5 $$ and $$ x = -4 $$, I can provide more specific guidance!
To determine the limits: (a) $$ \lim_{x \rightarrow -5} f(x) $$ and $$ \lim_{x \rightarrow -4} f(x) $$, observe the graph's behavior near these points. If the left and right limits are equal, the limit exists and is that value. If not, the limit does not exist. **Choices:** - A. $$ \lim_{x \rightarrow -5} f(x) = \square $$ - B. The limit does not exist. **For (a):** - If the graph approaches the same value from both sides at $$ x = -5 $$, choose A and fill in the value. - If not, choose B. **For (b):** - Similarly, if the graph approaches the same value from both sides at $$ x = -4 $$, choose A and fill in the value. - If not, choose B. **Example:** If at $$ x = -5 $$, the graph approaches 3 from both sides, then: - $$ \lim_{x \rightarrow -5} f(x) = 3 $$ (Choose A and fill in 3). If at $$ x = -4 $$, the graph approaches different values from the left and right, then: - The limit does not exist (Choose B). **Final Answer:** - (a) A. $$ \lim_{x \rightarrow -5} f(x) = 3 $$ - (b) B. The limit does not exist

Use the given graph to determine the value of the indicated limits. (a) \( \lim _{x \rightarrow-5} f(x) \) (b) \( \lim _{x \rightarrow-4} f(x) \) (a) Select the correct choice below, and if necessary, fill in the answer box to complete your choice. A. lim \( f(x)=\square \) (o) B. The limit does

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