Use the graph of $g of x$

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.

$\lim_{x o2}g\left(x ight)$

Accepted Answer

Hello there today we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem, refer to the graph of the function F of X to find the given limit if exists, if the limit does not exist, write DNE limit as X approaches three of F of X. Awesome. So our limit that is given to us is the limit as X approaches three of F of X. And this problem also gives us a graph for us to refer to so quickly looking at our graph before we go and look at our multiple choice answers. You can see we have a standard line graph which starts at the origin 0.00 and then goes out to about like 36 where there's a hole and then going to look at our little which is in red. Our line graph is in red. And then we have a little point graph here in green which we have a closed interval of solid green dot at about 37 and it goes to a hole which is located at point about a little bit over 47. And then we have an inverted parabola in red, which is from about. So it was from four. So it's about 45. So 0.454 comma 52, I'm a little bit over six comma five. So it's an inverted parabola in red. And let's take a moment here. Now, the quickly note whether or not we're trying to figure out if the graph of the function F FX and we're trying to figure out using this function of F FX at this specific limit, the limit that's given to us exists or not. And if it doesn't exist, we have to put DNE which is short for do not or does not exist. That's what DNE stands for does not exist. OK? So with that in mind, now that we know that we're ultimately trying to figure out whether or not this limit exists, let's read off multiple choice answers to see what our final answer might be. So A is seven, B is five C is six and D is DNE. OK. So first off, in order to solve this problem, we need to determine the left side and the right side limit. So let us denote the left side limit. So the left side limit as LHL and let us also call the right side limit to be the RHL. So left hand limit, right hand limit. So let's solve for the right. S so let's solve for the left side first of the limit. So left hand limit and this is equal to the limit as X approaches or X approach is, and this is important to note. So this is as X approaches three from the left, that's what that negative sign in the power means that means it's approaching three from the left of F of X which is equal to six. So once again, quickly recap here. So this is the left side limit. So Lhl is equal to the limit as X approaches three from the left of F of X equals six. And from the right side limit, which is the right hand limit, it's going to be equal to the limit as X approaches three from the right, because we have a positive symbol in the power and this positive symbol indicates that it's approaching from three from the right and this is of F of X equals seven. And we pull these numbers from our graph itself. That's where the six and the seven are coming from just in case we're confused. So now it's important to note that sense. It's important to note that as we could see, the left hand limit cannot equal the right hand limit. Therefore, the given limit does not exist. So that is our final answer is, does not exist because LHL cannot equal RHL. So that is our final answer which let's make a little note here. Up above. So our final answer has to be D does not exist. So looking at our multiple choice answers, which as we should recall, maybe from the beginning, so D is, does not exist and that is our final answer. Hooray, we did it. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

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>

$\lim_{x\to2}g\left(x\right)$

Key Concepts

Limits

Continuity

Graphical Interpretation

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