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.

d. $lim over x right arrow 1 of f of x$

Accepted Answer

Welcome back. Everyone refer to the graph of the function F FX to find a given limit if it exists. If the limit does not exist, write D and E, we're looking for the limit of F FX as X approaches two. For our answer choices A says the limit is three B four C five and D says it does not exist. Now, what are we trying to find here? Well, let's make a note. So we're looking for the limit as X approaches to FF FX. In other words, for this limit to exist, OK. We know that for the limit to exist, then the left hand limit, the limit from the left. OK. The limit as X approaches to from the left must be equal to the limit as X approaches to from the right of F FX. In other words, the left hand limit must be equal to the right hand limit. So if we can establish that, that means the limit exists and we can use our graph to figure out what that limit is. So let's go ahead and do that. First of all, when X equals two, then we know that this vertical line will represent the equation of the line that runs through X equals two. OK. Let me just clean this up a bit here. OK. So this dotted line is the line X equals two. Now, what do we notice from both the left and the right hand side, we notice that from the left hand side, OK. From the left hand side, as X approaches two, F FX approaches three, OK. And now if we look at it from the right hand side, OK. Again, as X approaches as X approaches two, then notice that F FX approaches three. OK. So since our limit from the left hand side equals three, and the limit from the right hand side also equals three, then the limit exists. And thus the limit as X approaches two of F FX is going to be equal to three. If we go to our answer choices. OK. That tells us then that A is the correct answer. Thanks for watching everyone. I hope this video helped.

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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>

d. $lim over x right arrow 1 of f of x$