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# Continuity watch

1. Please, please please help me with this questions. Really struggling as i have been off uni ill for over a week now and missed alot of classes to make it worse this assesment is due in asap!!

Many thanks, Hanna. x
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2. For the first one

So you can conclude the first function is continuous at 1. The way to view the above, is you're interested in knowing if the two functions 'meet' at . So when we're looking at the values of tending to 1, but from the left (so using the function for when ) and then doing it for the values to the right but obviously using the function for when
3. (Original post by K80dol)
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Since you've missed a few lectures I'd just like to add something to what Noble has said: continuity at a does not only rely on both sides of the curve meeting at a, the function also needs to be defined at a and if so, its value there needs to agree with both limits. Here is an added example:

yet is discontinuous at 1 because of the obvious issue with

If we defined , like what is done in the third exercise of yours, then continuity will rely on what value we choose:

On the other hand:

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Updated: March 15, 2013
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