display fixes and clarifying directions

Author: brittnilorton

Contrib/CCCS/CalculusOne/02.1/CCD_CCCS_Openstax_Calc1_C1-2016-002_02_1_7_9.pg

@@ -36,7 +36,7 @@ install_weighted_grader();
 
 TEXT(beginproblem());
 $showPartialCorrectAnswers = 1;
-$refreshCaschedImages = 0;
+$refreshCaschedImages = 1;
 
 ###########################
 
@@ -191,7 +191,7 @@ add_functions($gr3, "$f_temp for x in <-8,8>" .
 add_functions($gr3, "$tanline_temp for x in <-8,8>" .
   " using color:black and weight:2");
 
-$b=random(-5, 5,1);
+do{$b=random(-5, 5,1);}until($d!=$b);
 
 $f_temp = Formula("sqrt(x)+$b")->reduce();
 

Contrib/CCCS/CalculusOne/03.9/CCD_CCCS_Openstax_Calc1_C1-2016-002_3_9_332.pg

@@ -33,7 +33,6 @@ $showPartialCorrectAnswers = 1;
 #  Setup
 
 Context("Numeric");
-Context()->variables->add(u => 'Real');
 
 $a=non_zero_random(-10,0,1);
 $b=non_zero_random(-10,10,1);
@@ -42,15 +41,14 @@ $d=random(2,10,1);
 
 $f=Formula("e^($a x)/x")->reduce;
 
-
-$ans=Formula("($a e^($a x) x-e^($a x))/(x^2)");
+$ans=Formula("($a e^($a x) x-e^($a x))/(x^2)")->reduce;
 
 ###########################
 #  Main text
-## I hope you get [`[$ans1]`], [`[$ans2]`], and [`[$ans3]`].
+
 BEGIN_PGML
 
-Find `f^\prime(x)` for [`f(x)=[$f]`].
+Find `f^\prime(x)` for [``f(x)=[$f]``].
 
 `f^\prime(x)=`[_______________________________]{$ans} [@ AnswerFormatHelp("formulas") @]*
 

Contrib/CCCS/CalculusOne/03.9/CCD_CCCS_Openstax_Calc1_C1-2016-002_3_9_333.pg

@@ -38,17 +38,17 @@ Context()->variables->add(u => 'Real');
 $a=non_zero_random(-10,10,1);
 
 
-$f=Formula("e^(x^$a ln(x))")->reduce;
+$f=Formula("x^$a ln(x)");
 
 
 $ans=Formula("e^(x^$a ln(x))($a x^($a-1)ln(x)+x^($a-1))")->with(limits=>[1,2]);
 
 ###########################
 #  Main text
-## I hope you get [`[$ans1]`], [`[$ans2]`], and [`[$ans3]`].
+
 BEGIN_PGML
 
-Find `f^\prime(x)` for [`f(x)=[$f]`].
+Find `f^\prime(x)` for [`` f(x)=e^{([$f])}``].
 
 `f^\prime(x)=`[_______________________________]{$ans} [@ AnswerFormatHelp("formulas") @]*
 

Contrib/CCCS/CalculusOne/03.9/CCD_CCCS_Openstax_Calc1_C1-2016-002_3_9_345.pg

@@ -41,24 +41,22 @@ $c=non_zero_random(2,10,1);
 $d=random(2,10,1);
 $e=random(2,10,1);
 
-
-#$f=Formula("($c^(x^$d-$e))");
 $f=Formula("($c^x)");
 $g=Formula("$a^x");
 
-
-
-#$ans3=Formula("($a^x*ln($a)*ln($f)/$lnb+$a^x*$d*x^($d-1))(ln($c)/ln($b))")->reduce;
 $ans3=Formula("$a^x*ln($a)*x*ln($c)/ln($b)+$a^x*ln($c)/ln($b)");
 ###########################
 #  Main text
-## I hope you get [`[$ans1]`], [`[$ans2]`], and [`[$ans3]`].
+
 BEGIN_PGML
 
-Find `f^\prime(x)` for [`f(x)=[$g] \cdot \log_{[$b]}([$f])`].
+Find `f^\prime(x)` for [``f(x)=[$g] \cdot \log_{[$b]}([$f])``].
 
 `f^\prime(x)=`[_______________________________]{$ans3} [@ AnswerFormatHelp("formulas") @]*
 
+Note: In WeBWorK, to enter [`\log_b(x)`] you'll need to use the change of base formula of [`` \log_b(x) = \frac{\ln(x)}{\ln(b)}``].
+
+So, if you want to enter [``\log_{[$b]}([$c])``] then you'll need to instead enter [``\frac{\ln([$c])}{\ln([$b])}``]
 
 
 END_PGML

Contrib/CCCS/CalculusOne/04.10/CCD_CCCS_Openstax_Calc1_C1-2016-002_4_10_471.pg

@@ -1,11 +1,11 @@
 ## DESCRIPTION
-## Calculus One, find the limit of a function at infinity using l'Hopital's Rule.
+## Calculus One
 ## ENDDESCRIPTION
 
 
 ## DBsubject(Calculus - single variable)
 ## DBchapter(Integrals)
-## DBsection(Antiderivatives (without trigonometric functions))
+## DBsection(Antiderivatives (with trigonometric functions))
 ## Date(06/05/2018)
 ## Institution(Community College of Denver, Colorado Community College System)
 ## Author(Percy Makita)

Contrib/CCCS/CalculusOne/04.10/CCD_CCCS_Openstax_Calc1_C1-2016-002_4_10_482.pg

@@ -34,10 +34,10 @@ $showPartialCorrectAnswers = 1;
 
 ###########################
 #  Setup
-$k=random(.5,5.5,.5);
+
 $a=non_zero_random(-10,10,2);
-$f=Formula("$a*sin($k*x)cos($k*x)")->reduce;
-$F=FormulaUpToConstant("{$a }/{2*$k}sin^2($k*x)+C")->reduce;
+$f=Formula("$a*sin(1/2 x)cos(1/2 x)")->reduce;
+$F=FormulaUpToConstant("{$a }sin^2(1/2 x)+C")->reduce;
 $ans=$F;
 
 ###########################
@@ -56,7 +56,10 @@ Find the family of antiderivatives of the function
 END_PGML
 ############################
 BEGIN_PGML_HINT
-.
+
+This can be done by first simplifying the funciton using a trig identity, or this can be done by using a u-substitution. 
+
+
 
 Rewriting the function using the trig identity [`2\sin(x)\cos(x) = \sin(2x)`] might make this easier.
 
@@ -66,6 +69,8 @@ Then, the following formulas will be helpful.
 
 [`` \int \cos(ax)dx = \frac{1}{a} \sin(ax)+C``]
 
+
+
 END_PGML_HINT
 ############################
 #  Solution

Contrib/CCCS/CalculusOne/04.10/CCD_CCCS_Openstax_Calc1_C1-2016-002_4_10_488.pg

@@ -34,11 +34,11 @@ $showPartialCorrectAnswers = 1;
 
 ###########################
 #  Setup
-$k=random(1,10);
-$a=random(-5,5);
+
+$a=non_zero_random(-5,5);
 $b=random(-5,5);
-$f=Formula("$a*sec($k*x)[sec($k*x)-$b*tan($k*x)]")->reduce;
-$F=FormulaUpToConstant("{$a }/{$k }[tan($k*x)-$b*sec($k*x)]+C")->reduce;
+$f=Formula("$a*sec(x)[sec(x)-$b*tan(x)]")->reduce;
+$F=FormulaUpToConstant("{$a }[tan(x)-$b*sec(x)]+C")->reduce;
 $ans=$F;
 
 ###########################

Contrib/CCCS/CalculusOne/04.10/CCD_CCCS_Openstax_Calc1_C1-2016-002_4_10_489.pg

@@ -35,11 +35,10 @@ $showPartialCorrectAnswers = 1;
 ###########################
 #  Setup
 $k=non_zero_random(-5,5,.5);
-$p=random(1,5);
 $a=non_zero_random(-5,5,.5);
 $b=non_zero_random(-5,5,.5);
-$f=Formula("$a*e^{$k*x}-$b*sin($p*x)")->reduce;
-$F=FormulaUpToConstant("{$a/$k}*e^{$k*x}+{$b/$p}*cos($p*x)+C")->reduce;
+$f=Formula("$a*e^{$k*x}-$b*sin(x)")->reduce;
+$F=FormulaUpToConstant("{$a/$k}*e^{$k*x}+{$b}*cos(x)+C")->reduce;
 $ans=$F;
 
 ###########################

Contrib/CCCS/CalculusOne/04.10/CCD_CCCS_Openstax_Calc1_C1-2016-002_4_10_507.pg

@@ -34,14 +34,16 @@ $showPartialCorrectAnswers = 1;
 
 ###########################
 #  Setup
+
+Context()->noreduce('(-x)-y','(-x)+y');
 $k=non_zero_random(-3,3);
 $a=random(-10,10);
 $b=random(-10,10);
 $bk=$b+$k;
 $c=random(-10,10);
-$f3=Formula("$k^3*cos($k*x)")->reduce;
-$ans1=Formula("-sin($k*x)+.5*$a*x^(2)+($b+$k)*x+$c")->reduce;
-$ans2=Formula("-sin($k*x)+.5*$b*x^(2)+($c+$k)*x+$a")->reduce;;
+$f3=Formula("($k)*cos(x)")->reduce;
+$ans1=Formula("-$k*sin(x)+.5*$a*x**2+($b+$k)*x+$c")->reduce;
+$ans2=Formula("-$k*sin(x)+.5*$b*x**2+($c+$k)*x+$a")->reduce;;
 
 ###########################
 #  Main text

Contrib/CCCS/CalculusOne/05.1/CCD_CCCS_Openstax_Calc1_C1-2016-002_5_1_42.pg

@@ -47,9 +47,9 @@ if($n==3){$ans=44;}
 else{$ans=48;}
 
 
-$gr = init_graph(-1,-1,16,16,
+$gr = init_graph(-1,-1,14,9,
 axes=>[0,0],
-grid=>[17,17],
+grid=>[15,10],
 size=>[600,600]
 );
 
@@ -61,12 +61,22 @@ add_functions($gr, "$f2 for x in <5,7>" .
 
 add_functions($gr, "$f3 for x in <7,12>" . 
   " using color:blue and weight:3");
+$gr->new_color("lightgreen",187,255,153); 
+
+$gr->moveTo(0,0);
+$gr->lineTo(0,1.1,"black",2);  
+$gr->moveTo(12,0);
+$gr->lineTo(12,1.1,"black",2);  
+$gr->moveTo(0,0);
+$gr->lineTo(12,0,"black",2);  
+$gr->fillRegion([5,0.5,"lightgreen"]);
+
 ###########################
 #  Main text
 
 BEGIN_PGML
 
-Estimate the areas under the curve by computing the left Riemann sum [`L_{[$n]}`].
+Estimate the area below the shown curve on the interval [`[0,12]`] (the shaded region) by computing the left Riemann sum [`L_{[$n]}`].
 
 >>[@ image(insertGraph($gr), width=>400, height=>400), @]*<<