Use the graph of f in the figure to evaluate the function or a...

Question

Use the graph of f in the figure to evaluate the function or analyze the limit.

lim x→1 f(x)

Accepted Answer

Hi, everyone, let's take a look at this practice problem dealing with the limits. This problem says to use the graph below to determine the limit as X opposed to 0 of F of X. Below the question we're given a graph that has the curve F of X on it, and it is a piecewise function, with the first piece being a linear piece that is going from the point of -6-2, to the point of -2.2, and that excludes that final endpoint. The next segment is a parabolic curve that begins at Minus 2.1 and goes to the point of 0.3. We then have a linear line segment for our next um piece, and that is going from 0.3 to the point of 4.1. However, there are two points that are excluded on this line. The point of 2.2 is excluded, as well as the 0.4.1. We also have an individual point located at The point of 2.1. And finally, for our last segment, it is a parabolic curve that begins at 4.4 and goes to the point of 6.2. We're also given 4 possible choices as our answers. For choice A, we have 0, for choice B, we have 1, for choice C, we have 2, and for choice D, we have 3. Now we need to find the limit as X approaches 0 of this function. Now, we call that for a limit to exist. The limit must be the same whether I approach the point from the left hand side or the right hand side of that point. So we're going to be looking at two different limits, the left hand limit and the right hand limit. So we're going to start off with the left hand limit. And so this is gonna be the limit. As X approaches 0 from the left of F of X. So, to determine this limit, we'll come over to our graph, and we're actually going to approach the point X equal to 0 from the left, and we do that, we'll follow our curve, and it is approaching a value of 3. So that means that this limit is going to be equal to 3. We'll do the same thing for the right hand limit. So here we're going to have the limit. As X approaches 0 from the right of F of X. So, we'll do something similar, except we're going to be used in our graph, and looking at The value of our function as it approaches 0 from the right. So, as we approach X equal to 0, our function here is approaching a value of 3 again. So that means that this limit is going to be equal to 3. Now, in both cases, my limits are equal to 3. So, since I'm approaching the same value, the limit does exist and its value is equal to 3. So I can come down to my answer choices, and the correct answer choice corresponds to answer choice D. So I hope that this explanation has been useful, and I'll see you in the next video.

Use the graph of f in the figure to evaluate the function or analyze the limit. <IMAGE>
lim x→1 f(x)

Key Concepts

Limits

Continuity

Graphical Analysis

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