Find the limit using the graph of f ( x ) f\left(x\right) f ( x ) shown. lim x → 1 f ( x ) \lim_{x\rarr1}f\left(x\right) lim x → 1 f ( x )

Here we're asked to find the limit using the graph of f of x, our function that is shown below. And the limit that we're asked to find here based on our graph is the limit of f of x as x approaches 1. Now looking at our graph here, this is our function f of x and we specifically are looking at our function as x approaches 1, meaning that we wanna look at values that are getting a really, really close to 1 from either side and kind of observe what our function is doing at that point. Now as we're getting really, really close to 1 coming in from this left side, I see that my function is getting close to a value of 2. Then coming in from that right side, I see the same thing that my function is getting really close to a value of 2. Now that tells us that our limit of f of x as x approaches 1 here is simply equal to 2, and we're all done here. Let me know if you have any questions, 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.
$\lim_{x\rarr1}f\left(x\right)$

$2$

$1$

$0$

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 1 using the graph provided. This involves analyzing the behavior of the function f(x) near x = 1.

Step 2: Locate x = 1 on the graph. Identify the vertical line corresponding to x = 1 and observe the values of f(x) as x approaches 1 from both the left-hand side (x → 1⁻) and the right-hand side (x → 1⁺).

Step 3: Examine the graph near x = 1. Look at the y-values of the function as the curve approaches x = 1 from both directions. If the y-values converge to a single value, that is the limit.

Step 4: Verify continuity or any jumps. Check if the graph has a break, jump, or discontinuity at x = 1. If the graph is continuous at x = 1, the limit will equal the function value at x = 1.

Step 5: Conclude the limit. Based on the graph, determine the y-value that the function approaches as x gets arbitrarily close to 1 from both sides. This is the limit of f(x) as x → 1.