4-2 Calculus Practice

source/sec-4-2-Riemann.xml

@@ -3,28 +3,25 @@
 
 <section xmlns:xi="http://www.w3.org/2001/XInclude" xml:id="sec-4-2-Riemann">
   <title>Riemann sums</title>
-  <!-- <objectives>
+  <objectives>
     <ul>
       <li>
         <p>
-          How can we use a Riemann sum to estimate the area between a given curve and the horizontal axis over a particular interval?
+          Become familiar with <em>sigma notation</em> for adding a list of terms sharing a common pattern.
         </p>
       </li>
-
       <li>
         <p>
-          What are the differences among left, right,
-          middle, and random Riemann sums?
+          Formalize the rectangle approximations of area between a given curve and the horizontal axis over a particular interval using <em>Riemann sums</em>.
         </p>
       </li>
-
       <li>
         <p>
-          How can we write Riemann sums in an abbreviated form?
+          Calculate left, right, and middle Riemann sums, in expanded form and in sigma notation.
         </p>
       </li>
     </ul>
-  </objectives> -->
+  </objectives>
   <subsection xml:id="subsec-Riemann-foundations">
     <title>Foundations</title>
     <p>
@@ -34,10 +31,67 @@
 
   <exercises xml:id="cp-Riemann">
     <title>Calculus Practice</title>
-    <introduction>
-      <p>
-        Coming soon.
-      </p>
-    </introduction>
+
+    <exercise label="sigma-notation-meaning"><title>The meaning of sigma notation</title>
+      <webwork source="Contrib/CCCS/CalculusOne/05.1/CCD_CCCS_Openstax_Calc1_C1-2016-002_5_1_34.pg" />
+    </exercise>
+
+    <exercise label="sigma-notation-calculation1"><title>Calculating a sum given in sigma notation</title>
+      <webwork source="Contrib/Valdosta/APEX_Calculus/5.3/APEX_5.3_5-6.pg" />
+    </exercise>
+
+    <exercise label="sigma-notation-calculation2"><title>Calculating more sums given in sigma notation</title>
+      <webwork source="Contrib/Valdosta/APEX_Calculus/5.3/APEX_5.3_8-10.pg" />
+    </exercise>
+
+    <exercise label="sigma-notation-writingsum1"><title>Writing an expanded sum using sigma notation</title>
+      <webwork source="Contrib/Valdosta/APEX_Calculus/5.3/APEX_5.3_12.pg" />
+    </exercise>
+
+    <exercise label="sigma-notation-writingsum2"><title>Writing an expanded sum using sigma notation</title>
+      <webwork source="Contrib/Valdosta/APEX_Calculus/5.3/APEX_5.3_14.pg" />
+    </exercise>
+
+    <!-- <exercise label="riemannsums-area-meaning1"><title>Connecting left, right, or middle Riemann sums with area</title>
+      <webwork source="Contrib/Valdosta/APEX_Calculus/5.3/APEX_5.3_27.pg" />
+    </exercise> -->
+    <!-- too similar to one in AC already -->
+
+    <exercise label="riemannsums-area-meaning1"><title>Connecting left, right, or middle Riemann sums with area</title>
+      <webwork source="Contrib/Valdosta/APEX_Calculus/5.3/APEX_5.3_30.pg" />
+    </exercise>
+
+    <exercise label="riemannsums-area-meaning2"><title>Connecting left, right, or middle Riemann sums with area</title>
+      <webwork source="Library/Valdosta/APEX_Calculus/5.3/APEX_5.3_29.pg" />
+    </exercise>
+
+    <exercise label="riemannsums-area-velocity"><title>Calculating Riemann sums and interpreting</title>
+      <webwork source="Library/Rochester/setIntegrals0Theory/S05.01.AreaDistance.PTP03.pg" />
+    </exercise>
+
+    <exercise label="riemannsums-area1"><title>Calculating Riemann sums</title>
+      <webwork source="Library/Rochester/setIntegrals0Theory/ur_in_0_1_mo.pg" />
+    </exercise>
+
+    <exercise label="riemannsums-area2"><title>Calculating Riemann sums</title>
+      <webwork source="Contrib/CCCS/CalculusOne/05.1/CCD_CCCS_Openstax_Calc1_C1-2016-002_5_1_17.pg" />
+    </exercise>
+
+    <exercise label="riemannsums-calculating1"><title>Calculating Riemann sums</title>
+      <webwork source="Library/UCSB/Stewart5_6_1/Stewart5_6_1_39.pg" />
+    </exercise>
+
+    <exercise label="riemannsums-calculating2"><title>Calculating Riemann sums</title>
+      <!-- <webwork source="Library/UVA-Stew5e/setUVA-Stew5e-C05S01-AreaDistance/5-1-03.pg" /> -->
+       <webwork><xi:include parse="text" href="../webworkfiles/riemannsumscalculation.pg"/></webwork>
+    </exercise>
+
+    <exercise label="riemannsums-general-limit1"><title>Calculating a Riemann sum for arbitrary <m>n</m></title>
+      <webwork source="Library/UCSB/Stewart5_5_1/Stewart5_5_1_22.pg" />
+    </exercise>
+
+    <exercise label="riemannsums-general-limit2"><title>Calculating a Riemann sum for arbitrary <m>n</m></title>
+      <webwork source="Contrib/Hope/Calc1/05-02-Riemann-sums/Riemann-sums-03.pg" />
+    </exercise>
   </exercises>
 </section>

webworkfiles/riemannsumscalculation.pg

@@ -0,0 +1,82 @@
+## DESCRIPTION
+##  Calculus: Areas and Distances
+## ENDDESCRIPTION
+
+## Tagged by XW
+
+
+## DBsubject(Calculus - single variable)
+## DBchapter(Integrals)
+## DBsection(Riemann sums)
+## Date(5/30/2005)
+## Institution(UVA)
+## Author(Jeff Holt)
+## MLT(AI-A-approx)
+## Level(3)
+## TitleText1('Calculus: Early Transcendentals')
+## AuthorText1('Stewart')
+## EditionText1('5')
+## Section1('5.1')
+## Problem1('3')
+## TitleText2('Calculus: Early Transcendentals')
+## AuthorText2('Stewart')
+## EditionText2('6')
+## Section2('5.1')
+## Problem2('')
+## KEYWORDS('calculus', 'areas', 'distances')
+
+
+DOCUMENT();
+
+loadMacros(
+  "PGstandard.pl",
+  "PGchoicemacros.pl",
+  "PGcourse.pl"
+);
+
+TEXT(beginproblem());
+$showPartialCorrectAnswers = 1;
+
+$a = random(3,7,1);
+$r = random(4,6,1);
+$rend = 1 + $r;
+
+$rans = 0;
+$xi = 2;
+while ($xi <= $rend) {
+    $rans += $a/$xi;
+    $xi++;
+}
+
+$lans = 0;
+$xi = 1;
+while ($xi < $rend) {
+    $lans += $a/$xi;
+    $xi++;
+}
+
+BEGIN_TEXT
+
+(A) Estimate the area under the graph of
+$BR
+\[
+f(x) = \frac{$a}{x}
+\]
+from \(x = 1\) to \(x = $rend\) using $r approximating rectangles and right
+endpoints.
+$BR
+$BR
+Estimate =  \{ans_rule(20) \}
+$BR
+$BR
+(B) Repeat part (A) using left endpoints.
+$BR
+$BR
+Estimate =  \{ans_rule(20) \}
+$BR
+END_TEXT
+
+@ans = ( num_cmp($rans), num_cmp($lans) );
+ANS(@ans);
+
+ENDDOCUMENT();