#2**+13 **

If a function is continuous at "a," then, these three conditions have to be met......

Notice that the second and third are met, but not the first one.....as geno has said, this function does not exist at x = 2, so it isn't continuous.......(note that we can see this just from the way the function is defined in the problem itself !!! x < 2 and x > 2 means that we don't know what happens* at* 2....)

N

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CPhill
Oct 21, 2014

#1**+13 **

The question is: Why is it not continuous at x = 2?

You gave the answer to that when you said that it is not defined at that location.

The limit, approaching from both the left and the right is 4; thus, it has a limit at x = 2, even though it is not defined at that location; even though it is not defined at that location. Indeed, there is a 'hole' in the graph at that location, which makes is discontinuous, even though it has a limit at that point.

geno3141
Oct 21, 2014

#2**+13 **

Best Answer

If a function is continuous at "a," then, these three conditions have to be met......

Notice that the second and third are met, but not the first one.....as geno has said, this function does not exist at x = 2, so it isn't continuous.......(note that we can see this just from the way the function is defined in the problem itself !!! x < 2 and x > 2 means that we don't know what happens* at* 2....)

N

NN

CPhill
Oct 21, 2014