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    I've been stuck on this question on my homework for a while.
    I know that for part (a) you need to use lim(f(x))=f(a) as x->a and for part (b) the limit definition of a derivative but I have no idea what to plug into either of the formulae.

    For (a), f(x)=e^(-1/x) when x is not 0 and f(x)=p when x=0 so shouldn't the only value of p for which it is continuous be 0?

    Show first that the limit \lim_{x \to 0} f(x) exists by showing that \lim_{x\to 0^-} f(x) = \lim_{x \to 0^+} f(x) and use that to deduce p (your value is correct btw, you should just understand where it comes from)

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