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Another continuity question watch

1. Can someone check my working is correct here please? I just want to make sure I understand things correctly here.
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2. Yep, you got the correct bounds. This time you've shown that your delta will work (like what james22 said in the last thread) albeit in a rather hasty way at the bottom, but in a formal proof you'd have to be more explicit.

But yes, you've got it.
3. (Original post by 0x2a)
Yep, you got the correct bounds. This time you've shown that your delta will work (like what james22 said in the last thread) albeit in a rather hasty way at the bottom, but in a formal proof you'd have to be more explicit.

But yes, you've got it.
Could you make an suggestions for the improvement of my answer please? as understand it, I just proved that the function is continuous at 0, because i was able to find a delta, right?

Thanks a lot for the help
4. (Original post by pineapplechemist)
Could you make an suggestions for the improvement of my answer please? as understand it, I just proved that the function is continuous at 0, because i was able to find a delta, right?

Thanks a lot for the help
You haven't necessarily proved that it is continuous, because for a function to be continuous at a point there must exist a for all , such that when then , but the thing is, once you have a concrete example like in your case, in most circumstances it is quite easy to extend this to any general .

Other than that, the thing I was nitpicking at was to write a formal proof at the bottom.

i.e. Choose any , let , and let .

Then , thus , whenever .
5. (Original post by 0x2a)
You haven't necessarily proved that it is continuous, because for a function to be continuous at a point there must exist a for all , such that when then , but the thing is, once you have a concrete example like in your case, in most circumstances it is quite easy to extend this to any general .

Other than that, the thing I was nitpicking at was to write a formal proof at the bottom.

i.e. Choose any , let , and let .

Then , thus , whenever .
Thanks so much!

So because we can choose epsilon=delta the function is continuous at 0?
6. (Original post by pineapplechemist)
Thanks so much!

So because we can choose epsilon=delta the function is continuous at 0?
Yes, in this case the delta we need is easy because we can just set it to epsilon.

Np

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