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 limits. This problem says to evaluate the limit as X approaches 4 of F of X using the following graph. Below the question we're given a graph that has the curve F of X on it, and it is a piecewise function consisting of a parabolic piece that starts from approximately -5.5.4 and goes to the point of -2.2, and that last end point is excluded. We then have another piece that is linear, that starts at -2.1, and goes to the point of 0.3. We then have another linear piece that begins at 0.3 and goes to the point of 4.1. However, there are two points that are excluded on this line. The first point is 2.2, and the second point is the endpoint of 4.1. We then have a singular point located at X equal to 2, and it is located at the point of 2.1. And then finally, we have the last um segment, which is a parabolic curve that begins at 4.4 and goes down to approximately 6.5.1. We are also given 4 possible choices as our answers. For choice A, we have 1, for choice B, we have 3, for choice C, we have 4, and for choice D, we have the limit does not exist. So we're asked to find the limit as X approaches 4 of F of X. So recall that for a limit to exist, the limit must be the same whether I approached the value for X either from the left-hand side or the right hand side. So we're actually going to calculate the limit from both sides. So we're going to start off with the left hand limit. And so here we're going to be looking at the limit. As x approaches 4 from the left of F of X. And so we'll come over here to our graph, and we'll locate the point of X equal to 4. And as we approach that that value of X from the left hand side, our function is approaching the value of 1. So this limit is going to be equal to 1. We're gonna do something similar for the right hand limit. So here we're going to be looking at the limit as X approaches 4 from the right of F of X. So here we'll need to look at X equal to 4, and we're gonna approach that from the right side. And if we look at approaching X equal to 4 from the right hand side for our function, our function is actually approaching a value of 4. So this limit is going to be equal to 4. Now, these two limits are not equal to each other, so therefore, the limit does not exist. And that is going to be the answer that we're actually looking for. And if we come down to our answer choices, this actually 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

Graphical Analysis

Continuity

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