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So I was able to show part (a) using the limit definition of the derivative, but I don't know how to approach part (b). I thought maybe assuming that there did exist such a sequence (yn) but couldn't find a way to produce a contradiction. Help!

  • $\begingroup$ Do you know Taylor's theorem? $\endgroup$ – PhoemueX Dec 7 '18 at 8:45
  • $\begingroup$ yeah the one that gives a statement about the remainder term? $\endgroup$ – Nick Dec 7 '18 at 12:21
  • $\begingroup$ Yes. Try to apply that to $f$, developing the power series at $0$. If there does not exist a sequence as in the claim, this would show that $f$ is represented by this power series. Why is this not true? $\endgroup$ – PhoemueX Dec 8 '18 at 8:27

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