Find the limit using the graph of f ( x ) f\left(x\right) f ( x ) shown. lim x → − 2 f ( x ) \lim_{x\rarr-2}f\left(x\right) lim x → − 2 f ( x )

Here, we're asked to find the limit using the graph of f of x shown below. Now here, the limit that we're asked to find is the limit of f of x, our function, as x approaches negative 2. So let's go ahead and take a look at our graph here. And we wanna look at what our graph is doing when x is getting really, really close to negative 2 from either side. So first coming in from that left side getting really, really close to negative 2, I see that my function seems to be approaching a value of negative 3. Then coming in from that right side, I see the same thing happening. As we're getting really, really close to that x value of negative 2 here, we seem to be approaching negative 3 on our function. So here, the limit of f of x as x approaches negative 2 is equal to negative 3. Now something that might be a bit confusing here is that if we look at the actual value of our function at negative 2, it seems to be equal to 4 because there's a hole on our graph and it sort of jumps up there like a piecewise function might. Now that doesn't matter here because remember that a limit is looking at our values, getting really, really close as x is approaching our value of negative 2, not when x is negative 2. So it doesn't matter that the actual value of our function here is 4. Our limit is still negative 3. Let me know if you have any questions there, and I'll see you in the next one.

1. Limits and Continuity

Introduction to Limits

Business Calculus

1. Limits and Continuity

Introduction to Limits

Struggling with Business Calculus?

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Multiple Choice

Find the limit using the graph of $f\left(x\right)$ shown.
$\lim_{x\rarr-2}f\left(x\right)$

$4$

$-2$

$-3$

Unable to determine

Verified step by step guidance

Step 1: Understand the problem. The goal is to find the limit of f(x) as x approaches -2 using the graph provided. A limit describes the value that f(x) approaches as x gets closer to a specific point.

Step 2: Analyze the graph near x = -2. Observe the behavior of the function f(x) as x approaches -2 from both the left-hand side (x → -2⁻) and the right-hand side (x → -2⁺).

Step 3: From the graph, note that as x approaches -2 from the left, the function f(x) approaches -3. Similarly, as x approaches -2 from the right, the function f(x) also approaches -3.

Step 4: Confirm that the left-hand limit and right-hand limit are equal. Since both limits are -3, the overall limit exists and is equal to -3.

Step 5: Conclude that lim_{x→-2}f(x) = -3 based on the graph's behavior near x = -2.

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Struggling with Business Calculus?

Find the limit using the graph of f(x)f\left(x\right)f(x)shown.limx→−2f(x)\lim_{x\rarr-2}f\left(x\right)limx→−2f(x)

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Introduction to Limits practice set

Find the limit using the graph of $f\left(x\right)$ shown.
$\lim_{x\rarr-2}f\left(x\right)$