CRN 12109: HW 7
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Problem 35. Let $f:\mathbb{R}\to\mathbb{R}$ be defined by \[f(x)=\begin{cases}x^2&\mbox{ if }x \mbox{ is rational}\\x^3 & \mbox{ if } x \mbox{ is irrational}\end{cases}\]
- For which values is $f$ continuous? Support your conjecture by a proof.
- For which values is $f$ differentiable? Support your conjecture by a proof.
Problem 31. Exercise 4.2.9
