http://helmut.knaust.info/mediawiki/index.php?action=history&feed=atom&title=CRN_12109%3A_HW_7 2026-05-15T17:16:57Z Revision history for this page on the wiki MediaWiki 1.19.1 http://helmut.knaust.info/mediawiki/index.php?title=CRN_12109:_HW_7&diff=915&oldid=prev 2013-11-13T04:47:26Z

<p></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr valign='top'> <td colspan='2' style="background-color: white; color:black;">← Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 04:47, 13 November 2013</td> </tr><tr><td colspan="2" class="diff-lineno">Line 3:</td> <td colspan="2" class="diff-lineno">Line 3:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>'''Problem 32.''' Exercise 4.4.7</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>'''Problem 32.''' Exercise 4.4.7</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>'''Problem 33.''' Exercise 4.4.9. Hint for (b): Consider $\sqrt{x}$ on $[0,1]$. &#160;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>'''Problem 33.''' Exercise 4.4.9. Hint for (b): Consider $<ins class="diffchange diffchange-inline">f(x)=</ins>\sqrt{x}$ on $[0,1]$. &#160;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>'''Problem 34.''' Exercise 4.5.7</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>'''Problem 34.''' Exercise 4.5.7</div></td></tr> </table>

HelmutKnaust http://helmut.knaust.info/mediawiki/index.php?title=CRN_12109:_HW_7&diff=914&oldid=prev 2013-11-13T04:47:04Z

<p></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr valign='top'> <td colspan='2' style="background-color: white; color:black;">← Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 04:47, 13 November 2013</td> </tr><tr><td colspan="2" class="diff-lineno">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">'''Problem 31.''' Exercise 4.3.1</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">'''Problem 32.''' Exercise 4.4.7</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">'''Problem 33.''' Exercise 4.4.9. Hint for (b): Consider $\sqrt{x}$ on $[0,1]$. </ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">'''Problem 34.''' Exercise 4.5.7</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>'''Problem 35.''' Let $f:\mathbb{R}\to\mathbb{R}$ be defined by</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>'''Problem 35.''' Let $f:\mathbb{R}\to\mathbb{R}$ be defined by</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>\[f(x)=\begin{cases}x^2&amp;\mbox{ if }x \mbox{ is rational}\\x^3 &amp; \mbox{ if } x \mbox{ is irrational}\end{cases}\] &#160;</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>\[f(x)=\begin{cases}x^2&amp;\mbox{ if }x \mbox{ is rational}\\x^3 &amp; \mbox{ if } x \mbox{ is irrational}\end{cases}\] &#160;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div># For which values is $f$ continuous? Support your conjecture by a proof.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div># For which values <ins class="diffchange diffchange-inline">of $x$ </ins>is $f$ continuous? Support your conjecture by a proof.</div></td></tr> <tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div># For which values is $f$ differentiable? Support your conjecture by a proof.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div># For which values <ins class="diffchange diffchange-inline">of $x$ </ins>is $f$ differentiable? Support your conjecture by a proof.</div></td></tr> <tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&#160;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr> <tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">'''Problem 31.''' Exercise 4.2.9</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr> </table>

HelmutKnaust http://helmut.knaust.info/mediawiki/index.php?title=CRN_12109:_HW_7&diff=913&oldid=prev 2013-11-13T04:38:35Z

<p>Created page with &quot;&#039;&#039;&#039;Problem 35.&#039;&#039;&#039; Let $f:\mathbb{R}\to\mathbb{R}$ be defined by \[f(x)=\begin{cases}x^2&amp;\mbox{ if }x \mbox{ is rational}\\x^3 &amp; \mbox{ if } x \mbox{ is irrational}\end{cases}\...&quot;</p> <p><b>New page</b></p><div>'''Problem 35.''' Let $f:\mathbb{R}\to\mathbb{R}$ be defined by<br /> \[f(x)=\begin{cases}x^2&amp;\mbox{ if }x \mbox{ is rational}\\x^3 &amp; \mbox{ if } x \mbox{ is irrational}\end{cases}\] <br /> # For which values is $f$ continuous? Support your conjecture by a proof.<br /> # For which values is $f$ differentiable? Support your conjecture by a proof.<br /> <br /> '''Problem 31.''' Exercise 4.2.9</div>

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