Attachment 27985any help with this question would be muchly appreciated

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- Apr 17th 2013, 12:44 AMcalmo11Limits and continuity
Attachment 27985any help with this question would be muchly appreciated

- Apr 17th 2013, 02:31 AMGusbobRe: Limits and continuity
How rigorous does this need to be? For instance, are you suppose to use the epsilon-delta definitions? It is very easy to apply in this case:

For all , choose so that . So the limit is .

You can easily generalise this to arbitrary instead of . And by generalise I mean replace every instance of with and you'll get a valid proof.

The limit for b) is also two. You need minor modification to the proof above. For example, take to be the distance for (or ) to the nearest integer.

In light of parts a) and b), it should be obvious if and where the function is continuous. - Apr 17th 2013, 06:11 AMHallsofIvyRe: Limits and continuity
For x any number "close" to 3, but not equal to 3, x is NOT an integer so f(x)= 2. Therefore

For x any number "close" to , but not equal to , x is NOT an integer so f(x)= 2. Therefore