Fix bug 4690

OpenProblemLibrary/UBC/setTaylor/testingError.pg

@@ -3,6 +3,7 @@
 ## DBsection(Taylor series)
 ## Level(3)
 ## MO(1)
+## Static(1)
 ## This problem is a good template for questions with Taylor Polynomials
 
 DOCUMENT();      
@@ -24,7 +25,7 @@ Context("Numeric");
 #Number of decimals to use in the approximation
 $dec = 3;
 
-$smallDec = 10**{-$dec};
+$smallDec = 10**(-$dec)/2;
 Context()->flags->set(
   tolerance=>$smallDec,
   tolType=>"absolute"
@@ -43,23 +44,23 @@ $x = 10;
 $f[0] = Formula("(1+x)^(1/2)");
 
 # The zero degree approximation
-$tn[0] = $f[0]->eval(x=>"$a");
+$tn[0] = Real($f[0]->eval(x=>"$a"));
 
 # code to compute the nth degree approximation 
 $nfact = 1;
 for my $i (1..$n)
 {
-$f[$i] = $f[$i-1]->D;
-$fa = $f[$i]->eval(x=>"$a");
-$tn[$i] = $tn[$i-1]+$fa*($x-$a)**($i)/$nfact;
+$f[$i] = $f[$i-1]->D('x');
+$fa = $f[$i]->eval(x=>$a);
+$tn[$i] = Formula($tn[$i-1]+$fa*($x-$a)**($i)/$nfact);
 $nfact = $nfact*($i+1);
 }
 
-#decreasing the number of decimal places
-for my $i (1..$n)
-{
-$sTn[$i] = sprintf("%0.4f",$tn[$i]);
-}
+##decreasing the number of decimal places
+#for my $i (1..$n)
+#{
+#$sTn[$i] = sprintf("%0.4f",$tn[$i]);
+#}
 
 Context()->texStrings;
 BEGIN_TEXT
@@ -81,36 +82,44 @@ Context()->normalStrings;
 
 Context()->texStrings;
 BEGIN_TEXT
-$BR $BBOLD Use $dec decimal places in your answer $EBOLD
+$BR $BBOLD Your answer must be accurate to at least $dec decimal places.$EBOLD
 
 $PAR
 END_TEXT
 Context()->normalStrings;
 
-for $i (1..$n)
-{
-ANS(Compute("$sTn[$i]")->cmp() );
-}
+#for $i (1..$n)
+#{
+#ANS(Compute("$sTn[$i]")->cmp() );
+#}
+
+#for $i (1..$n) {
+#ANS(Compute($tn[$i]->eval(x=>$x))->cmp());
+#}
 
+ANS(Compute($tn[1])->cmp());
+ANS(Compute($tn[2])->cmp());
+ANS(Compute($tn[3])->cmp());
 
 
 # You will have to change most of the solution to fit the question
 Context()->texStrings;
 BEGIN_SOLUTION
 $PAR SOLUTION $PAR
-In general the \(n^{th}\) degree approximation of \(f($x)\) about \(x=$a\) is given by:
-$BR \(T_n = f($a) + f'($a)($x-a) + \ldots + \frac{f^n($x)}{n!}($x-$a)^n\)
+In general the \(n^{th}\) degree approximation of \(f(x)\) about \(x=$a\) is given by:
+$BR \(T_n = f($a) + f'($a)(x-$a) + \ldots + \frac{1}{n!}{f^{(n)}($a)}($x-$a)^n\)
 
 $PAR
-\(f'(x) = \frac{1}{x\sqrt{1+x}}\),
-$BR \(f''(x) = -\frac{1}{4(1+x)^{\frac{3}{2}}}\),
-$BR \(f'''(x) = \frac{3}{8(1+x)^{\frac{5}{2}}}\).
+Here,
+\(f'(x) = \frac{1}{2}(x+1)^{-1/2}\),
+$BR \(f''(x) = -\frac{1}{4}(x+1)^{-3/2}\),
+$BR \(f'''(x) = \frac{3}{8}(x+1)^{-5/2}\).
 
 $PAR
 Therefore,
-$BR \(T_1 = $sTn[1]\),
-$PAR \(T_2 = $sTn[2]\),
-$PAR \(T_3 = $sTn[3]\).
+$BR \(T_1($x) \approx $tn[1]\),
+$PAR \(T_2($x) \approx $tn[2]\),
+$PAR \(T_3($x) \approx $tn[3]\).
 
 END_SOLUTION
 Context()->normalStrings;