Use the graph of g(x) in the figure to find the following valu...

Question

Use the graph of g(x) in the figure to find the following values or state that they do not exist. If a limit does not exist, explain why.

$lim over x right arrow 4 of g of x$

Accepted Answer

Hi, everyone, let's take a look at this practice problem dealing with limits. This problem says refer to the graph of the function F of X, define the given limit if it exists. If the limit does not exist, write DNE. And here we're looking for the limit as X approaches 5 of F of X. So, the question we're given a graph of our function F of X. And it is a piecewise function, and it contains 3 pieces. The first piece goes from the 0 00. Up to the 0.36, and that is an open interval at that final point. The second piece goes from 3 0.37 to the 0.47. And that last point is actually an open interval as well. And then the final piece is a parabola that's opening up downwards, and it starts at the 0.45. It has a maximum at the 0.57 and it ends at the 0.65. We're given 4 possible choices as our answers. For choice A, we have 6, for choice B, we have 7, for choice C, we have 5, and for choice D, we have D and E. Now we're asked to find the limit as X approaches 5 for this function. And the first thing we need to do is determine whether this limit actually exists. So we call for a limit to exist. The limit has to be the same whether you're approaching from the left hand side of the function or the right hand side of the function. So we're going to look at both of those limits. So we're going to start off with the left hand limit. And for this, we're gonna be looking at the limit. As X approaches 5 from the left of F of X. And here we need to refer to our graph, and as we approach the point X equal to 5 from the left, That value, the Y value in this case, which is gonna be our value for the F of X, approaches the value of 7. So this limit is going to be equal to 7. That's one of the limits that we need to calculate. Now we do the same thing, but for the right hand limit. And here we're gonna take the limit. As x approaches 5 from the right of F of X. And so again, coming back to our graph, we're gonna approach the point X equal to 5 from the right hand side of the function. And again, this um function approaches the value of 7, as we approach X equal to 5 from the right. So this limit is going to be equal to 7. Now, since both of these limits approach the same value, then the limit does exist, and that limit has a value in this case of 7. So we can come down and look at our answer choices, and the correct answer choice corresponds to answer choice B. So I hope this explanation has been useful, and I'll see you in the next video.

Use the graph of g(x) in the figure to find the following values or state that they do not exist. If a limit does not exist, explain why. <IMAGE>
$lim over x right arrow 4 of g of x$

Key Concepts

Limits

Continuity

Existence of Limits

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