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

Calculus

1. Limits and Continuity

Introduction to Limits

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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

Identify the point on the graph where x approaches 1. This is the point of interest for evaluating the limit.

Observe the behavior of the function f(x) as x approaches 1 from both the left and the right sides.

From the left side (x < 1), trace the graph towards x = 1 and note the y-value that the function approaches.

From the right side (x > 1), trace the graph towards x = 1 and note the y-value that the function approaches.

If the y-values from both sides are the same, that is the limit of f(x) as x approaches 1. If they differ, the limit does not exist.

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

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Find the limit using the graph of $f\left(x\right)$ shown.
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