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# Analysis help! watch

1. Hi, im a second year maths student and need a bit of help please!

Can you have a function t and h such that t and h are continuous at 1 but t+h is not continuous at 1? If so could I have an example please.

I believe its impossible, but im not sure as to how to explain it.

and my last question

Can you have a function t which is continuous at 1 and h which is not continuous at 1 thus having t+h continuous at 1? If so could i have an example please.

2. Neither are possible. You will be expected to prove why not.
3. Thanks, any tips on where to start? I have only been doing Analysis for 2 weeks, thus finding it hard :P
4. Use the definition of continuity in it's epsilon-delta glory. For the first one you basically need to show there exists a delta for any given epsilon>0 for t+h, given that you know t and h are continuous.

So you haven't done Analysis before and you're already tackling continuity?
5. Sure am dude, thanks for the help!

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Updated: October 14, 2009
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