CRN 12109: HW 7
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| + | '''Problem 31.''' Exercise 4.3.1 | ||
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| + | '''Problem 32.''' Exercise 4.4.7 | ||
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| + | '''Problem 33.''' Exercise 4.4.9. Hint for (b): Consider $f(x)=\sqrt{x}$ on $[0,1]$. | ||
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| + | '''Problem 34.''' Exercise 4.5.7 | ||
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'''Problem 35.''' Let $f:\mathbb{R}\to\mathbb{R}$ be defined by | '''Problem 35.''' Let $f:\mathbb{R}\to\mathbb{R}$ be defined by | ||
\[f(x)=\begin{cases}x^2&\mbox{ if }x \mbox{ is rational}\\x^3 & \mbox{ if } x \mbox{ is irrational}\end{cases}\] | \[f(x)=\begin{cases}x^2&\mbox{ if }x \mbox{ is rational}\\x^3 & \mbox{ if } x \mbox{ is irrational}\end{cases}\] | ||
| − | # For which values is $f$ continuous? Support your conjecture by a proof. | + | # For which values of $x$ is $f$ continuous? Support your conjecture by a proof. |
| − | # For which values is $f$ differentiable? Support your conjecture by a proof. | + | # For which values of $x$ is $f$ differentiable? Support your conjecture by a proof. |
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Latest revision as of 23:47, 12 November 2013
Problem 31. Exercise 4.3.1
Problem 32. Exercise 4.4.7
Problem 33. Exercise 4.4.9. Hint for (b): Consider $f(x)=\sqrt{x}$ on $[0,1]$.
Problem 34. Exercise 4.5.7
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 of $x$ is $f$ continuous? Support your conjecture by a proof.
- For which values of $x$ is $f$ differentiable? Support your conjecture by a proof.
