https://wiki.math.ucr.edu/index.php?action=history&feed=atom&title=022_Exam_2_Sample_A
022 Exam 2 Sample A - Revision history
2026-04-22T20:33:12Z
Revision history for this page on the wiki
MediaWiki 1.35.0
https://wiki.math.ucr.edu/index.php?title=022_Exam_2_Sample_A&diff=1000&oldid=prev
MathAdmin at 18:39, 28 July 2015
2015-07-28T18:39:51Z
<p></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 18:39, 28 July 2015</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l34" >Line 34:</td>
<td colspan="2" class="diff-lineno">Line 34:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><span class="exam"></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><span class="exam"></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Use calculus to set up and solve the word problem:''' Find the length and width of a rectangle that has a perimeter of 48 meters and maximum area.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Use calculus to set up and solve the word problem:''' Find the length and width of a rectangle that has a perimeter of 48 meters and maximum area.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">'''Contributions to this page were made by [[Contributors|John Simanyi]]'''</ins></div></td></tr>
</table>
MathAdmin
https://wiki.math.ucr.edu/index.php?title=022_Exam_2_Sample_A&diff=757&oldid=prev
MathAdmin: /* Problem 1 */
2015-05-30T18:27:40Z
<p><span dir="auto"><span class="autocomment"> Problem 1 </span></span></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 18:27, 30 May 2015</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l3" >Line 3:</td>
<td colspan="2" class="diff-lineno">Line 3:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== [[022_Exam_2_Sample_A,_Problem_1|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 1&nbsp;</span></span>]] ==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== [[022_Exam_2_Sample_A,_Problem_1|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 1&nbsp;</span></span>]] ==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><span class="exam">Find the derivative of &thinsp;<math style="vertical-align: -<del class="diffchange diffchange-inline">42%</del>">y\,=\,\ln \frac{(x+5)(x-1)}{x}.</math></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><span class="exam">Find the derivative of &thinsp;<math style="vertical-align: -<ins class="diffchange diffchange-inline">13px</ins>">y\,=\,\ln \frac{(x+5)(x-1)}{x}.</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== [[022_Exam_2_Sample_A,_Problem_2|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 2&nbsp;</span>]] ==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== [[022_Exam_2_Sample_A,_Problem_2|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 2&nbsp;</span>]] ==</div></td></tr>
</table>
MathAdmin
https://wiki.math.ucr.edu/index.php?title=022_Exam_2_Sample_A&diff=553&oldid=prev
MathAdmin: /* Problem 8 */
2015-05-16T02:52:46Z
<p><span dir="auto"><span class="autocomment"> Problem 8 </span></span></p>
<table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 02:52, 16 May 2015</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l25" >Line 25:</td>
<td colspan="2" class="diff-lineno">Line 25:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== [[022_Exam_2_Sample_A,_Problem_8|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 8&nbsp;</span>]] ==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== [[022_Exam_2_Sample_A,_Problem_8|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 8&nbsp;</span>]] ==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><span class="exam"></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><span class="exam"></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Use differentials to approximate the change in profit given <math style="vertical-align: -5%">x = 10</math> units and <math style="vertical-align: 0%">dx = 0.2</math> units, where profit is given by <math style="vertical-align: -<del class="diffchange diffchange-inline">15</del>%">P(x) = -4x^2 + 90x - 128</math>.</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Use differentials to approximate the change in profit given <math style="vertical-align: -5%">x = 10</math><ins class="diffchange diffchange-inline">&thinsp; </ins>units and <math style="vertical-align: 0%">dx = 0.2</math><ins class="diffchange diffchange-inline">&thinsp; </ins>units, where profit is given by <math style="vertical-align: -<ins class="diffchange diffchange-inline">22</ins>%">P(x) = -4x^2 + 90x - 128</math>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== [[022_Exam_2_Sample_A,_Problem_9|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 9&nbsp;</span>]] ==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== [[022_Exam_2_Sample_A,_Problem_9|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 9&nbsp;</span>]] ==</div></td></tr>
</table>
MathAdmin
https://wiki.math.ucr.edu/index.php?title=022_Exam_2_Sample_A&diff=482&oldid=prev
MathAdmin: Created page with "'''This is a sample, and is meant to represent the material usually covered in Math 22 for the second exam. An actual test may or may not be similar. Click on the <span class=..."
2015-05-14T22:06:03Z
<p>Created page with "'''This is a sample, and is meant to represent the material usually covered in Math 22 for the second exam. An actual test may or may not be similar. Click on the <span class=..."</p>
<p><b>New page</b></p><div>'''This is a sample, and is meant to represent the material usually covered in Math 22 for the second exam. An actual test may or may not be similar. Click on the <span class="biglink" style="color:darkblue;">&nbsp;boxed problem numbers&nbsp;</span> to go to a solution.'''<br />
<div class="noautonum">__TOC__</div><br />
<br />
== [[022_Exam_2_Sample_A,_Problem_1|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 1&nbsp;</span></span>]] ==<br />
<span class="exam">Find the derivative of &thinsp;<math style="vertical-align: -42%">y\,=\,\ln \frac{(x+5)(x-1)}{x}.</math><br />
<br />
== [[022_Exam_2_Sample_A,_Problem_2|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 2&nbsp;</span>]] ==<br />
<span class="exam"> Find the antiderivative of&thinsp; <math style="vertical-align: -10%">y\,=\,3x^2-12x+8.</math><br />
== [[022_Exam_2_Sample_A,_Problem_3|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 3&nbsp;</span>]] ==<br />
<span class="exam"> Find the antiderivative of <math style="vertical-align: -50%">\int \frac{1}{3x+2}\,dx.</math><br />
== [[022_Exam_2_Sample_A,_Problem_4|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 4&nbsp;</span>]] ==<br />
<span class="exam"> Find the antiderivative of <math style="vertical-align: -45%">\int (3x+2)^4\,dx.</math><br />
== [[022_Exam_2_Sample_A,_Problem_5|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 5&nbsp;</span>]] ==<br />
<span class="exam"> '''Set up the equation to solve. You only need to plug in the numbers - not solve for particular values!'''<br />
<br />
<span class="exam">How much money would I have after 6 years if I invested $3000 in a bank account that paid 4.5% interest, <br />
::<span class="exam">(a) compounded monthly?<br />
::<span class="exam">(b) compounded continuously?<br />
== [[022_Exam_2_Sample_A,_Problem_6|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 6&nbsp;</span>]] ==<br />
<span class="exam">Find the area under the curve of&thinsp; <math style="vertical-align: -60%">y\,=\,\frac{8}{\sqrt{x}}</math>&thinsp; between <math style="vertical-align: -5%">x=1</math> and <math style="vertical-align: -5%">x=4</math>.<br />
<br />
== [[022_Exam_2_Sample_A,_Problem_7|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 7&nbsp;</span>]] ==<br />
<span class="exam">Find the quantity that produces maximum profit, given the demand function <math style="vertical-align: -15%">p\,=\,90-3x</math> and cost function <math style="vertical-align: -5%">C\,=\,200-30x+x^2</math>.<br />
<br />
== [[022_Exam_2_Sample_A,_Problem_8|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 8&nbsp;</span>]] ==<br />
<span class="exam"><br />
Use differentials to approximate the change in profit given <math style="vertical-align: -5%">x = 10</math> units and <math style="vertical-align: 0%">dx = 0.2</math> units, where profit is given by <math style="vertical-align: -15%">P(x) = -4x^2 + 90x - 128</math>.<br />
<br />
== [[022_Exam_2_Sample_A,_Problem_9|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 9&nbsp;</span>]] ==<br />
<span class="exam"><br />
Find all relative extrema and points of inflection for the function <math style="vertical-align: -45%">g(x) = \frac{2}{3}x^3 + x^2 - 12x</math>. Be sure to give coordinate pairs for each point. You do not need to draw the graph.<br />
<br />
== [[022_Exam_2_Sample_A,_Problem_10|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 10&nbsp;</span>]] ==<br />
<span class="exam"><br />
'''Use calculus to set up and solve the word problem:''' Find the length and width of a rectangle that has a perimeter of 48 meters and maximum area.</div>
MathAdmin