022 Sample Final A - Revision history

https://wiki.math.ucr.edu/index.php?action=history&feed=atom&title=022_Sample_Final_A 022 Sample Final A - Revision history 2026-04-22T10:53:39Z Revision history for this page on the wiki MediaWiki 1.35.0 https://wiki.math.ucr.edu/index.php?title=022_Sample_Final_A&diff=908&oldid=prev MathAdmin: /*  Problem 14  */ 2015-06-06T20:51:39Z

<p><span dir="auto"><span class="autocomment"> Problem 14 </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 20:51, 6 June 2015</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l55" >Line 55:</td> <td colspan="2" class="diff-lineno">Line 55:</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_Sample_Final_A,_Problem_14|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 14&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_Sample_Final_A,_Problem_14|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 14&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"> Find the following limit: <math style="vertical-align: -15px">\qquad \lim_{x \rightarrow \,-3}\frac{x^2 + 7x + 12}{x^2 - 2x - <del class="diffchange diffchange-inline">14</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"> Find the following limit: <math style="vertical-align: -15px">\qquad \lim_{x \rightarrow \,-3}\frac{x^2 + 7x + 12}{x^2 - 2x - <ins class="diffchange diffchange-inline">15</ins>}</math>.</div></td></tr> </table>

MathAdmin https://wiki.math.ucr.edu/index.php?title=022_Sample_Final_A&diff=895&oldid=prev MathAdmin: /*  Problem 6  */ 2015-06-05T23:40:22Z

<p><span dir="auto"><span class="autocomment"> Problem 6 </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 23:40, 5 June 2015</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l18" >Line 18:</td> <td colspan="2" class="diff-lineno">Line 18:</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_Sample_Final_A,_Problem_6|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 6&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_Sample_Final_A,_Problem_6|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 6&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"> Sketch the curve, including all relative <del class="diffchange diffchange-inline">exterma </del>and points of inflection: <math style="vertical-align: -4px">y = 3x^4 - 4x^3</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"> Sketch the curve, including all relative <ins class="diffchange diffchange-inline">extrema </ins>and points of inflection: <math style="vertical-align: -4px">y = 3x^4 - 4x^3</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_Sample_Final_A,_Problem_7|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 7&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_Sample_Final_A,_Problem_7|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 7&nbsp;</span>]] ==</div></td></tr> </table>

MathAdmin https://wiki.math.ucr.edu/index.php?title=022_Sample_Final_A&diff=891&oldid=prev MathAdmin at 23:01, 5 June 2015 2015-06-05T23:01:57Z

<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 23:01, 5 June 2015</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l44" >Line 44:</td> <td colspan="2" class="diff-lineno">Line 44:</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_Sample_Final_A,_Problem_11|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 11&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_Sample_Final_A,_Problem_11|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 11&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">Find the derivative: <math style="vertical-align: -18px">g(x) = \frac{ln(x^3 + 7)}{(x^4 + 2x^2)}</math>&thinsp;. </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: <math style="vertical-align: -18px">g(x) = \frac{<ins class="diffchange diffchange-inline">\</ins>ln(x^3 + 7)}{(x^4 + 2x^2)}</math>&thinsp;. </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><span class="exam">''(Note: You do not need to simplify the derivative after finding it.)''</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">''(Note: You do not need to simplify the derivative after finding it.)''</div></td></tr> </table>

MathAdmin https://wiki.math.ucr.edu/index.php?title=022_Sample_Final_A&diff=880&oldid=prev MathAdmin: /*  Problem 8  */ 2015-06-05T05:20:06Z

<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 05:20, 5 June 2015</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l27" >Line 27:</td> <td colspan="2" class="diff-lineno">Line 27:</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_Sample_Final_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_Sample_Final_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>Find ther <del class="diffchange diffchange-inline">marginial </del>productivity of labor and marginal productivity of capital for the following Cobb-Douglas production function: </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>Find ther <ins class="diffchange diffchange-inline">marginal </ins>productivity of labor and marginal productivity of capital for the following Cobb-Douglas production function: </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>::<math>f(k, l) = 200k^{\,0.6}l^{\,0.4}.</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>::<math>f(k, l) = 200k^{\,0.6}l^{\,0.4}.</math></div></td></tr> </table>

MathAdmin https://wiki.math.ucr.edu/index.php?title=022_Sample_Final_A&diff=869&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=..." 2015-06-04T23:11:55Z

<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_Sample Final A,_Problem_1|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 1&nbsp;</span></span>]] ==<br /> <span class="exam">Find all first and second partial derivatives of the following function, and demostrate that the mixed second partials are equal for the function <math> f(x, y) = \frac{2xy}{x-y}.</math><br /> <br /> == [[022_Sample Final A,_Problem_2|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 2&nbsp;</span>]] ==<br /> <span class="exam"> A dairy farmer plans to enclose a rectangular pasture adjacent to a river. To provide enough grass for his cows, the fenced pasture must contain 200 square meters of grass. If no fencing is required along the river, what dimensions will use the smallest amount of fencing?<br /> <br /> == [[022_Sample Final A,_Problem_3|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 3&nbsp;</span>]] ==<br /> <span class="exam"> Find the antiderivative: <math>\int \frac{6}{x^2 - x - 12}\,dx.</math><br /> <br /> == [[022_Sample Final A,_Problem_4|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 4&nbsp;</span>]] ==<br /> <span class="exam"> Use implicit differentiation to find&thinsp; <math>\frac{dy}{dx}: \quad x+y = x^3y^3</math>.<br /> <br /> == [[022_Sample Final A,_Problem_5|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 5&nbsp;</span>]] ==<br /> <span class="exam"> Find producer and consumer surpluses if the supply curve is given by <math style="vertical-align: -4px"> p = 18 + 3x^2</math>, and the demand curve is given by <math style="vertical-align: -4px">p = 150 - 4x</math>.<br /> <br /> == [[022_Sample_Final_A,_Problem_6|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 6&nbsp;</span>]] ==<br /> <span class="exam"> Sketch the curve, including all relative exterma and points of inflection: <math style="vertical-align: -4px">y = 3x^4 - 4x^3</math>.<br /> <br /> == [[022_Sample_Final_A,_Problem_7|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 7&nbsp;</span>]] ==<br /> <span class="exam">Find the present value of the income stream <math style="vertical-align: -2px">Y = 20 + 30x</math> from now until 5 years from now, given an interest rate <math style="vertical-align: -1px">r = 10%.</math><br /> <br><br /> ''(Note: Once you plug in the limits of integration, you are finished; you do not need to simplify our answer beyond that step.)''<br /> <br /> == [[022_Sample_Final_A,_Problem_8|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 8&nbsp;</span>]] ==<br /> <span class="exam"><br /> Find ther marginial productivity of labor and marginal productivity of capital for the following Cobb-Douglas production function: <br /> <br /> ::<math>f(k, l) = 200k^{\,0.6}l^{\,0.4}.</math><br /> <br /> <span class="exam">''(Note: You must simplify so your solution does not contain negative exponents.)''<br /> <br /> == [[022_Sample_Final_A,_Problem_9|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 9&nbsp;</span>]] ==<br /> <span class="exam"> Given demand <math style="vertical-align: -3.25px">p = 116 - 3x</math>, and cost&thinsp; <math style="vertical-align: -2.1px">C = x^2 + 20x + 64</math>, find:<br /> <br /> ::<span class="exam">a) Marginal revenue when ''x'' = 7 units.<br /> ::<span class="exam">b) The quantity (''x''-value) that produces minimum average cost.<br /> ::<span class="exam">c) Maximum profit (find both the ''x''-value <u>'''and'''</u> the profit itself).<br /> <br /> == [[022_Sample_Final_A,_Problem_10|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 10&nbsp;</span>]] ==<br /> <span class="exam">Set up the formula to find the amount of money one would have at the end of 8 years if she invests $2100 in an account paying 6% annual interest, compounded quarterly.<br /> <br /> == [[022_Sample_Final_A,_Problem_11|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 11&nbsp;</span>]] ==<br /> <span class="exam">Find the derivative: <math style="vertical-align: -18px">g(x) = \frac{ln(x^3 + 7)}{(x^4 + 2x^2)}</math>&thinsp;. <br /> <br /> <span class="exam">''(Note: You do not need to simplify the derivative after finding it.)''<br /> <br /> == [[022_Sample_Final_A,_Problem_12|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 12&nbsp;</span>]] ==<br /> <span class="exam"> Find the antiderivative: <math>\int x^2e^{3x^3}dx.</math><br /> <br /> == [[022_Sample_Final_A,_Problem_13|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 13&nbsp;</span>]] ==<br /> <span class="exam">Use differentials to find <math style="vertical-align: -4px">dy</math> given <math style="vertical-align: -4px">y = x^2 - 6x, ~ x = 4, ~dx = -0.5.</math><br /> <br /> == [[022_Sample_Final_A,_Problem_14|<span class="biglink"><span style="font-size:80%">&nbsp;Problem 14&nbsp;</span>]] ==<br /> <span class="exam"> Find the following limit: <math style="vertical-align: -15px">\qquad \lim_{x \rightarrow \,-3}\frac{x^2 + 7x + 12}{x^2 - 2x - 14}</math>.</div>

MathAdmin