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009A Sample Midterm 2 - Revision history
2026-04-22T10:53:54Z
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MathAdmin: /* Problem 4 */
2017-11-11T19:07:35Z
<p><span dir="auto"><span class="autocomment"> Problem 4 </span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 19:07, 11 November 2017</td>
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<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>== [[009A_Sample Midterm 2,_Problem_4|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 4&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>== [[009A_Sample Midterm 2,_Problem_4|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 4&nbsp;</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"> <del class="diffchange diffchange-inline">Find </del>the <del class="diffchange diffchange-inline">derivatives of the following functions. Do not simplify.</del></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"> <ins class="diffchange diffchange-inline">To determine drug dosages, doctors estimate a person's body surface area (BSA) (in meters squared) using </ins>the <ins class="diffchange diffchange-inline">formula:</ins></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="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"><del class="diffchange diffchange-inline">(a) &nbsp; </del><math <del class="diffchange diffchange-inline">style="vertical-align: -5px"</del>><del class="diffchange diffchange-inline">f(x)</del>=<del class="diffchange diffchange-inline">x^3(x^</del>{\<del class="diffchange diffchange-inline">frac</del>{<del class="diffchange diffchange-inline">4</del>}{<del class="diffchange diffchange-inline">3}</del>}<del class="diffchange diffchange-inline">-1)</del></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><ins class="diffchange diffchange-inline">::</ins><span class="exam"><math><ins class="diffchange diffchange-inline">\text{BSA}</ins>=<ins class="diffchange diffchange-inline">\frac</ins>{\<ins class="diffchange diffchange-inline">sqrt</ins>{<ins class="diffchange diffchange-inline">hm}</ins>}{<ins class="diffchange diffchange-inline">60</ins>}</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="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"><del class="diffchange diffchange-inline">(b) </del>&nbsp; <math style="vertical-align: -<del class="diffchange diffchange-inline">14px</del>"><del class="diffchange diffchange-inline">g(x)</del>=<del class="diffchange diffchange-inline">\frac{x^3+x^{</del>-<del class="diffchange diffchange-inline">3}}{1+6x}</del></math>&nbsp; <del class="diffchange diffchange-inline">where </del>&nbsp;<math style="vertical-align: <del class="diffchange diffchange-inline">0px</del>"><del class="diffchange diffchange-inline">x</del>><del class="diffchange diffchange-inline">0</del></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"><ins class="diffchange diffchange-inline">where </ins>&nbsp;<math style="vertical-align: <ins class="diffchange diffchange-inline">0px">h</math>&nbsp; is the height in centimeters and &nbsp;<math style="vertical</ins>-<ins class="diffchange diffchange-inline">align: 0px</ins>"><ins class="diffchange diffchange-inline">m</math>&nbsp; is the mass in kilograms. Calculate the rate of change of BSA with respect to height for a person of a constant mass of &nbsp;<math style</ins>=<ins class="diffchange diffchange-inline">"vertical</ins>-<ins class="diffchange diffchange-inline">align: 0px">m=85.</ins></math>&nbsp; <ins class="diffchange diffchange-inline">What is the rate at </ins>&nbsp;<math style="vertical-align: <ins class="diffchange diffchange-inline">-1px</ins>"><ins class="diffchange diffchange-inline">h=170</math>&nbsp; and &nbsp;<math style="vertical-align: -1px"</ins>><ins class="diffchange diffchange-inline">h=190?</ins></math><ins class="diffchange diffchange-inline">&nbsp; Express your results in the correct units. Does the BSA increase more rapidly with respect to height at lower or higher heights?</ins></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>== [[009A_Sample Midterm 2,_Problem_5|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 5&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>== [[009A_Sample Midterm 2,_Problem_5|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 5&nbsp;</span>]] ==</div></td></tr>
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MathAdmin
https://wiki.math.ucr.edu/index.php?title=009A_Sample_Midterm_2&diff=1612&oldid=prev
MathAdmin at 14:56, 20 April 2017
2017-04-20T14:56:31Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 14:56, 20 April 2017</td>
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<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">(c) &nbsp; <math style="vertical-align: -18px">h(x)=\frac{(5x^2+7x)^3}{\ln(x^2+1)} </math></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">(c) &nbsp; <math style="vertical-align: -18px">h(x)=\frac{(5x^2+7x)^3}{\ln(x^2+1)} </math></div></td></tr>
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<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|Kayla Murray]]'''</ins></div></td></tr>
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MathAdmin
https://wiki.math.ucr.edu/index.php?title=009A_Sample_Midterm_2&diff=1477&oldid=prev
MathAdmin: Created page with "'''This is a sample, and is meant to represent the material usually covered in Math 9A for the midterm. An actual test may or may not be similar.''' '''Click on the''' '''<s..."
2017-04-09T18:50:22Z
<p>Created page with "'''This is a sample, and is meant to represent the material usually covered in Math 9A for the midterm. An actual test may or may not be similar.''' '''Click on the''' '''<s..."</p>
<p><b>New page</b></p><div>'''This is a sample, and is meant to represent the material usually covered in Math 9A for the midterm. An actual test may or may not be similar.''' <br />
<br />
'''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 />
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== [[009A_Sample Midterm 2,_Problem_1|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 1&nbsp;</span></span>]] ==<br />
<span class="exam"> Evaluate the following limits.<br />
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<span class="exam">(a) Find &nbsp;<math style="vertical-align: -14px">\lim _{x\rightarrow 2} \frac{\sqrt{x^2+12}-4}{x-2}</math><br />
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<span class="exam">(b) Find &nbsp;<math style="vertical-align: -19px">\lim _{x\rightarrow 0} \frac{\sin(3x)}{\sin(7x)} </math><br />
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<span class="exam">(c) Evaluate &nbsp;<math style="vertical-align: -20px">\lim _{x\rightarrow (\frac{\pi}{2})^-} \tan(x) </math><br />
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== [[009A_Sample Midterm 2,_Problem_2|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 2&nbsp;</span>]] ==<br />
<span class="exam">The function &nbsp;<math style="vertical-align: -5px">f(x)=3x^7-8x+2</math>&nbsp; is a polynomial and therefore continuous everywhere.<br />
<br />
<span class="exam">(a) State the Intermediate Value Theorem.<br />
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<span class="exam">(b) Use the Intermediate Value Theorem to show that &nbsp;<math style="vertical-align: -5px">f(x)</math>&nbsp; has a zero in the interval &nbsp;<math style="vertical-align: -5px">[0,1].</math><br />
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== [[009A_Sample Midterm 2,_Problem_3|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 3&nbsp;</span>]] ==<br />
<span class="exam"> Use the definition of the derivative to find &nbsp; <math>\frac{dy}{dx}</math> &nbsp; for the function &nbsp;<math style="vertical-align: -12px">y=\frac{1+x}{3x}.</math><br />
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== [[009A_Sample Midterm 2,_Problem_4|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 4&nbsp;</span>]] ==<br />
<span class="exam"> Find the derivatives of the following functions. Do not simplify.<br />
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<span class="exam">(a) &nbsp; <math style="vertical-align: -5px">f(x)=x^3(x^{\frac{4}{3}}-1)</math><br />
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<span class="exam">(b) &nbsp; <math style="vertical-align: -14px">g(x)=\frac{x^3+x^{-3}}{1+6x}</math>&nbsp; where &nbsp;<math style="vertical-align: 0px">x>0</math><br />
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== [[009A_Sample Midterm 2,_Problem_5|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 5&nbsp;</span>]] ==<br />
<span class="exam"> Find the derivatives of the following functions. Do not simplify. <br />
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<span class="exam">(a) &nbsp; <math style="vertical-align: -5px">f(x)=\tan^3(7x^2+5) </math><br />
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<span class="exam">(b) &nbsp; <math style="vertical-align: -5px">g(x)=\sin(\cos(e^x)) </math><br />
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<span class="exam">(c) &nbsp; <math style="vertical-align: -18px">h(x)=\frac{(5x^2+7x)^3}{\ln(x^2+1)} </math></div>
MathAdmin