Use the graph of f in the figure to find the following values ...

Question

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

h. $lim over x right arrow 3 of f of x$

Accepted Answer

Welcome back, everyone refer to the graph of the function F FX to find the given limit if exists. If the limit does not exist. Write DNE the limit of F FX as X approaches five. Here we have a diagram of our function or a graph rather of our function. And for answer choices, A says the limit is four B three C five and D says it does not exist. Now, how are we going to figure out the limit here? OK. The limit uh F FX, let me write that properly here as X approaches five. OK? Or are we going to figure that out? Well, we know that this limit exists. OK. The limit exists if the limit from the left hand side, that is the limit of F FX as X approaches five from the left. So that should be a minus sign here is equal to the limit of FX as X approaches five from the right. So if we're going to figure out the limit first, we need to see what the left hand limit is. And the right hand limit is. And if they are equal, the limit exists and we will be able to find the value. So first, let's figure out if they are equal. Now, if we go to X equals five on our graph, I'm going to use this dotted line to represent X equals five. OK. Here. And that's the point on which X is five and the X axis. OK. Then we can look at what is happening to our function as it approaches from the left and from the right, let's start with it approaching from the left. What do you notice? Well, as X approaches five from the left, notice that F FX approaches six. Therefore, the limit of F FX as X approaches five from the left. Let me you know what, let me just write that properly here. So our limit as X approaches five from the left of F FX is equal to six. Now what happens as it approaches from the right? Well, no notice that as X approaches P from the right F of X approaches three. OK. In other words here, the limit as X approaches five from the right of F of X equals three. What do we notice here? Well, now we can tell that our left hand limit is not equal to our right hand limit. Thus, that means the limit. OK, does not exist. Therefore, a limit does not exist if we go back to our answer choices, that means DDNE does not exist is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

Use the graph of f in the figure to find the following values or state that they do not exist. If a limit does not exist, explain why. <IMAGE>

h. $lim over x right arrow 3 of f of x$

Key Concepts

Limits

Continuity

Existence of Limits

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