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I have been trying to figure this question out for a while now, it's in a past paper I'm studying for my Calculus exam tomorrow. But we don't get given the memo's. I have done simpler versions of this question where it was a straight line, but this really confused me. Please can you guys help me out, or if you don't like giving answers straight out, can you please push me in the right direction?

Determine at which values f(x) is continuous:
f(x) = 2x if x <= 0
f(x) = sinx if 0 < x <= pi
f(x) = (x-pi)^2 if x > pi

Any help would be appreciated. Thanks in advance.

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If I draw the graph, I cannot find a value for x that the graph wouldn't be continuous. But I'm not sure how to write that in math. – nickcorin Oct 30 '12 at 20:12
up vote 2 down vote accepted

All the individual pieces are continuous, so you only have to worry about the joints. At $x=0$ does $f(x)$ approach the same value from the left and right? At $x=\pi$ note that $f(\pi )$ is undefined, so it can't be continuous there. Can you see how to define it so that it is?

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Oh I'm sorry, I had a typo in my question. It is <= to pi in the middle equation. Sorry about that! :/ – nickcorin Oct 30 '12 at 19:56
In that case you do the same there. Does $f(x)$ approach the same value from each side? – Ross Millikan Oct 30 '12 at 20:22

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