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→3^+ f(x)

Accepted Answer

Hi everyone, let's take a look at this practice problem dealing with limits. This problem says to use the graph below to evaluate the limit as X approaches to from the right of F of X. So below this question we're given a graph that shows F of X plotted on it, and it is a piecewise function, and it consists of three pieces. The first piece is a linear piece that starts from the point of -44 and goes to the point of -2.0. The next piece is parabolic, and it's opening upwards, and it begins at -2.0 and ends at 2.0. It also has a minimum at the point of 0.3, but that point is excluded from our function. We do have an individual point or the value of our function at X equal to 0, and that point is located at 0.1. Our final segment is a linear segment, and it begins at the point of 2.1 and ends at the point of 10. minus 5, and that initial point of 2.1 is excluded from our function. We're given 4 possible choices as our answers. For choice A, we have 1, for choice B, we have 0. for choice C, we have -1, and for choice D, we have minus 3. Now, the question asks us to find the limit as X approaches to from the right of this function. And so, we're going to use our graph to determine that limit. So, we need to approach the value of X equal to 2 from the right, following our function, and see what value that our function actually approaches. So, we're going to begin to values to the right of X equals 2. And we're going to follow our function towards the value of X equal to 2. And as we move to the left here, we see that our function is approaching a value of 1. That means that the limit. As X purchases to from the right of F of X. It's going to be equal to one, and that's actually the answer that we're looking for. And so we can come down here to our answer choices, and the correct answer choice corresponds to answer choice A. That should be noted that our function actually has a value of 0 when X is equal to 2. However, that value does not affect our limits. So recall that the limit is the value that the function approaches, and that may be different than the function's actual value, especially with a piece-wise function. So keep that in mind when you're working with limits in the future. 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→3^+ f(x)

Key Concepts

Limits

One-Sided Limits

Graphical Analysis

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