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# Continuity Question watch

1. Hi,

Would anyone be able to explain how to do this question?

There is a solution posted which claims that f is continuous at a value a if and only if a is not an integer, however I don't understand how to reach that conclusion or how to justify it.

It would be really helpful if someone could also explain how to approach this type of question in general (i.e. working with functions that have continuous and discontinuous regions).

Thanks,
Dan
2. (Original post by DanKeitley)
Hi,

Would anyone be able to explain how to do this question?

There is a solution posted which claims that f is continuous at a value a if and only if a is not an integer, however I don't understand how to reach that conclusion or how to justify it.
Let

Then e.g.

So there seems to be a bit of a jump in the graph near 2. It's useful to draw the graph of the function so you can see the discontinuities.

Now to formalise this, I guess you want to investigate what happens with, say:

as , or something along those lines, with some arbitrary replacing 2.
3. (Original post by atsruser)
Let

Then e.g.

So there seems to be a bit of a jump in the graph near 2. It's useful to draw the graph of the function so you can see the discontinuities.

Now to formalise this, I guess you want to investigate what happens with, say:

as , or something along those lines, with some arbitrary replacing 2.
You're right, I should have drawn the graph! The solution given takes a sequence with and chooses an where k<x<k+1 for some integer k. It then shows .

I'm having difficulties with this problem as well which I think is fairly similar. .

I have the solution (see below) but I don't really understand why they've done what they have.

Thanks a lot for your help.

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Updated: December 28, 2014
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