##DESCRIPTION
##   Interval of convergence for power series
##ENDDESCRIPTION

##KEYWORDS('Power Series')
## tsch tagged and PAID on 3-22-2004

## DBsubject('Calculus')
## DBchapter('Infinite Sequences and Series')
## DBsection('Power Series')
## Date('6/3/2002')
## Author('')
## Institution('')
## TitleText1('Calculus Early Transcendentals')
## EditionText1('4')
## AuthorText1('Stewart')
## Section1('11.8')
## Problem1('19')


DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl"
);

# No partial credit on this problem, so we say:
install_problem_grader(~~&std_problem_grader);


TEXT(&beginproblem);
$showPartialCorrectAnswers = 0;

$a = random(-10,-3,1);
$b = random(1,11,1);
$c = random(1,11,1);
$d = random(1,11,1);

TEXT(EV2(<<EOT));

Find  the interval of convergence for the given  power series.
\[  \sum_{n=1}^\infty \frac{(x - $b)^n }{n($a)^n} \]
The series is convergent 
$BR
from \( x \) = \{ ans_rule(5)\} to  \( x \) = \{ ans_rule(5)\}.

EOT

$ans1 =  $a + $b ;
$ans3 = $b  - $a ;

&ANS(std_num_cmp($ans1));
&ANS(std_num_cmp($ans3));

ENDDOCUMENT();        # This should be the last executable line in the problem.
________________________________________________________________________________

##DESCRIPTION
##   Interval of convergence for power series
##ENDDESCRIPTION

##KEYWORDS('Power Series')
## tsch tagged and PAID on 3-22-2004

## DBsubject('Calculus')
## DBchapter('Infinite Sequences and Series')
## DBsection('Power Series')
## Date('6/3/2002')
## Author('')
## Institution('')
## TitleText1('Calculus Early Transcendentals')
## EditionText1('4')
## AuthorText1('Stewart')
## Section1('11.8')
## Problem1('3')


DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl"
);

TEXT(&beginproblem);
$showPartialCorrectAnswers = 0;

$a = random(2,11,1);

$b = random(2,11,1);

$b1 = -1*$b;

TEXT(EV2(<<EOT));

Find  all the values of x such that the given series would converge.
 \[  \sum_{n=1}^\infty \frac{($b x)^n}{n^{$a}} \]
The series is convergent from \( x \) = \{ ans_rule(5)\}  to   \( x \) = \{ ans_rule(5)\}. 

EOT

## answer is [ \frac{-1}{$b} ,\frac{1}{$b} ]

$ans1 = 1/$b1 ;
$ans3 = 1/$b ;

&ANS(std_num_cmp($ans1));
&ANS(std_num_cmp($ans3));

ENDDOCUMENT();        # This should be the last executable line in the problem.
________________________________________________________________________________

##DESCRIPTION
##   Interval of convergence for power series
##ENDDESCRIPTION

##KEYWORDS('Power Series')
## tsch tagged and PAID on 3-22-2004

## DBsubject('Calculus')
## DBchapter('Infinite Sequences and Series')
## DBsection('Power Series')
## Date('6/3/2002')
## Author('')
## Institution('')
## TitleText1('Calculus Early Transcendentals')
## EditionText1('4')
## AuthorText1('Stewart')
## Section1('11.8')
## Problem1('20')


DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl"
);

TEXT(&beginproblem);
$showPartialCorrectAnswers = 0;

$a = random(2,11,1);

$b = random(2,11,1);

$a1 =2*($a);

TEXT(EV2(<<EOT));

Find  all the values of x such that the given series would converge.
\[  \sum_{n=1}^{\infty} \frac{(x - $a)^n}{$a^n} \]
The series is convergent from \( x \) = \{ ans_rule(5)\} to   \( x \) = \{ ans_rule(5)\}.  

EOT

## answer is  (0 ,$a1) 

$ans1 = 0 ;
$ans3 = $a1 ;

&ANS(std_num_cmp($ans1));
&ANS(std_num_cmp($ans3));

ENDDOCUMENT();        # This should be the last executable line in the problem.
________________________________________________________________________________

##DESCRIPTION
##   Interval of convergence for power series
##ENDDESCRIPTION

##KEYWORDS('Power Series')
## tsch tagged and PAID on 3-22-2004

## DBsubject('Calculus')
## DBchapter('Infinite Sequences and Series')
## DBsection('Power Series')
## Date('6/3/2002')
## Author('')
## Institution('')
## TitleText1('Calculus Early Transcendentals')
## EditionText1('4')
## AuthorText1('Stewart')
## Section1('11.8')
## Problem1('16')


DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl"
);

TEXT(&beginproblem);
$showPartialCorrectAnswers = 0;

$a = random(2,11,1);

$b = random(2,11,1);

$b1 = -1*$b;

TEXT(EV2(<<EOT));

Find  all the values of x such that the given series would converge.
$BR 
 \[  \sum_{n=1}^\infty \frac{(-1)^n x^n}{$b^n (n^2 + $a)} \]
$BR
The series is convergent from \(x = \) \{ ans_rule(5)\} to \(x = \) \{ ans_rule(5)\}.

EOT

## answer is [ \frac{-1}{$b} , \frac{1}{$b} ]

$ans1 = $b1 ;
$ans3 = $b ;

&ANS(std_num_cmp($ans1));
&ANS(std_num_cmp($ans3));

ENDDOCUMENT();        # This should be the last executable line in the problem.
________________________________________________________________________________

##DESCRIPTION
##   Interval of convergence for power series
##ENDDESCRIPTION

##KEYWORDS('Power Series')
## tsch tagged and PAID on 3-22-2004

## DBsubject('Calculus')
## DBchapter('Infinite Sequences and Series')
## DBsection('Power Series')
## Date('6/3/2002')
## Author('')
## Institution('')
## TitleText1('Calculus Early Transcendentals')
## EditionText1('4')
## AuthorText1('Stewart')
## Section1('11.8')
## Problem1('18')


DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl"
);

TEXT(&beginproblem);
$showPartialCorrectAnswers = 1;

$a = random(2,11,1);

$b = random(2,11,1);

$b1 = -1*$b;

TEXT(EV2(<<EOT));

Find  all the values of x such that the given series would converge.
 \[  \sum_{n=1}^\infty \frac{x^n}{($b)^n (\sqrt{n} +$a)} \]
The series is convergent from \(x =\) \{ ans_rule(5)\} to   \(x =\) \{ ans_rule(5)\}.

EOT

## answer is [ \frac{-1}{$b} ,\frac{1}{$b} ]

$ans1 = $b1 ;
$ans3 = $b ;

&ANS(std_num_cmp($ans1));
&ANS(std_num_cmp($ans3));

ENDDOCUMENT();        # This should be the last executable line in the problem.
________________________________________________________________________________

##DESCRIPTION
##   Interval of convergence for power series
##ENDDESCRIPTION

##KEYWORDS('Power Series')
## tsch tagged and PAID on 3-22-2004

## DBsubject('Calculus')
## DBchapter('Infinite Sequences and Series')
## DBsection('Power Series')
## Date('6/3/2002')
## Author('')
## Institution('')
## TitleText1('Calculus Early Transcendentals')
## EditionText1('4')
## AuthorText1('Stewart')
## Section1('11.8')
## Problem1('17')


DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl"
);

TEXT(&beginproblem);
$showPartialCorrectAnswers = 1;

$a = random(2,11,1);

$b = random(2,11,1);

$b1 = -1*$b;

TEXT(EV2(<<EOT));

Find  all the values of x such that the given series would converge.
 \[  \sum_{n=1}^\infty \frac{(-1)^n (x^n)(n+$a)}{($b)^n} \]
The series is convergent from \(x =\) \{ ans_rule(5)\} to   \(x =\) \{ ans_rule(5)\}. 

EOT

## answer is ( \frac{-1}{$b} ,\frac{1}{$b} ) 

$ans1 = $b1 ;
$ans3 = $b ;

&ANS(std_num_cmp($ans1));
&ANS(std_num_cmp($ans3));

ENDDOCUMENT();        # This should be the last executable line in the problem.
________________________________________________________________________________

##KEYWORDS('Power Series', 'Radius of Convergence', 'Interval of Convergence')
##DESCRIPTION
## Determine the radius of convergence
##ENDDESCRIPTION

## Shotwell cleaned

## DBsubject('Calculus')
## DBchapter('Infinite Sequences and Series')
## DBsection('Power Series')
## Date('6/3/2002')
## Author('')
## Institution('')
## TitleText1('Calculus Early Transcendentals')
## EditionText1('4')
## AuthorText1('Stewart')
## Section1('11.8')
## Problem1('23')

DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
"PGbasicmacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl"
);

TEXT(beginproblem());
$showPartialCorrectAnswers = 1;

$a = random(1,9,1);

BEGIN_TEXT
Find  all the values of x such that the given series would converge.
$BR 

 \[  \sum_{n=1}^\infty n!(x-$a)^n \]
$BR


The radius of convergence for this series is: \{ ans_rule(3)\} $BR

END_TEXT

ANS(num_cmp(0));

ENDDOCUMENT();        # This should be the last executable line in the problem.
________________________________________________________________________________

##KEYWORDS('Power Series', 'Radius of Convergence', 'Interval of Convergence')##DESCRIPTION
## Determine radius of convergence
##ENDDESCRIPTION

## Shotwell cleaned

## DBsubject('Calculus')
## DBchapter('Infinite Sequences and Series')
## DBsection('Power Series')
## Date('6/3/2002')
## Author('')
## Institution('')
## TitleText1('Calculus Early Transcendentals')
## EditionText1('4')
## AuthorText1('Stewart')
## Section1('11.8')
## Problem1('23 17 12 14')

DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl"
);

# No partial credit on this problem, so we say:
install_problem_grader(~~&std_problem_grader);


TEXT(beginproblem());
$showPartialCorrectAnswers = 0;

$a = random(2,11,1);
$b = random(2,11,1);
$a1 =2*($a);

$questStr1 = EV2( " \( \displaystyle \sum_{n=1}^\infty
	\frac{(x-$a)^n}{(n!)($a)^n} \) " );

$ansStr1 =EV2(  " \( ( -\infty , \infty ) \) " );

$questStr2 = EV2( " \( \displaystyle \sum_{n=1}^\infty
	\frac{(x - $a)^n}{$a ^n} \) " );

$ansStr2 =EV2(  " \( (0 ,$a1) \) " );

$questStr3 = EV2( " \( \displaystyle \sum_{n=1}^\infty
	\frac{n!( $b x-$a)^n}{$a^n} \) " );

$ansStr3 =EV2(  " \(  \lbrace $a/$b \rbrace \) " );

$questStr4 = EV2( " \( \displaystyle \sum_{n=1}^\infty
	\frac{($b x)^n}{n^{$a}} \) " );

$ansStr4 =EV2(   " \( [ \frac{-1}{$b} ,\frac{1}{$b} ] \) " );

@questions =( $questStr1,$questStr2,$questStr3,$questStr4);
@answers =( $ansStr1,$ansStr2,$ansStr3,$ansStr4);

# Now randomize the questions:
@slice = &NchooseK(4,4);
@shuffle = &shuffle(scalar(@slice));

BEGIN_TEXT
Match each of the power series with its interval of convergence. $BR

END_TEXT
TEXT(
&match_questions_list(@questions[@slice]),
&OL(@answers[@slice[@shuffle]])
);
ANS(str_cmp([@ALPHABET[&invert(@shuffle)]], filters=>["remove_whitespace","ignore_order","ignore_case"]));
     ##the correct answers are obtained by applying
     ##the inverse (adjoint) permutation to the captions.

ENDDOCUMENT();        # This should be the last executable line in the problem.
________________________________________________________________________________

#DESCRIPTION
#Representation of function as a power series
#ENDDESCRIPTION

#KEYWORDS('Power Series'  )
## tsch tagged and PAID on 3-22-2004

## DBsubject('Calculus')
## DBchapter('Infinite Sequences and Series')
## DBsection('Representations of Functions as Power Series')
## Date('6/3/2002')
## Author('')
## Institution('')
## TitleText1('Calculus Early Transcendentals')
## EditionText1('4')
## AuthorText1('Stewart')
## Section1('11.9')
## Problem1('20')


DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl"
);

TEXT(beginproblem());
$showPartialCorrectAnswers = 1;

$a = random(2,10,1);
$b = random(2,10,1);

BEGIN_TEXT

The function
	\( f(x) = $a x^2 \arctan(x^{$b}) \)
is represented as a power series $BR 
	\( \displaystyle f(x) = \sum_{n=0}^\infty c_n x^n .\) $BR
What is the lowest term with a nonzero coefficient. $BR
	\{ans_rule(20)\}  $BR
Find the radius of convergence \( R \) of the series. $BR 
	\( R = \)  \{ans_rule(20)\}  . $BR

END_TEXT

#@ans=();
$ans0 =  $b+2 ;
$ans1 =  1 ;

#ANS(num_cmp(relTol=>@ans));
#ANS(ordered_num_cmp_list(@ans) );
ANS(num_cmp($ans0));
ANS(num_cmp($ans1));

ENDDOCUMENT();        # This should be the last executable line in the problem.
________________________________________________________________________________

#DESCRIPTION
#Representation of function as a power series
#ENDDESCRIPTION

#KEYWORDS('Power Series'  )
## tsch tagged and PAID on 3-22-2004

## DBsubject('Calculus')
## DBchapter('Infinite Sequences and Series')
## DBsection('Representations of Functions as Power Series')
## Date('6/3/2002')
## Author('')
## Institution('')
## TitleText1('Calculus Early Transcendentals')
## EditionText1('4')
## AuthorText1('Stewart')
## Section1('11.9')
## Problem1('14')


DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl"
);

TEXT(beginproblem());
$showPartialCorrectAnswers = 1;

$a = random(1,10,1);

BEGIN_TEXT

The function 
	\( f(x) = $a x \ln(1 + 2x) \)
is represented as a power series $BR 
	\( \displaystyle f(x) = \sum_{n=0}^\infty c_n x^n .\) $BR
Find the FOLLOWING coefficients in the power series. $BR

\( c_0 = \) \{ans_rule(20)\}  $BR
\( c_1 = \) \{ans_rule(20)\}  $BR
\( c_2 = \) \{ans_rule(20)\}  $BR
\( c_3 = \) \{ans_rule(20)\}  $BR
\( c_4 = \) \{ans_rule(20)\}  $BR

Find the radius of convergence \( R \) of the series. $BR 
\( R = \)  \{ans_rule(20)\}  . $BR

END_TEXT

#@ans=();
$ans0 =  0;
$ans1 =  0;
$ans2 =  $a*2;
$ans3 =  $a*(-2);
$ans4 =  $a*8/3;
$ans5 =  1/2;

#ANS(num_cmp(relTol=>@ans));
#ANS(ordered_num_cmp_list(@ans) );
ANS(num_cmp($ans0));
ANS(num_cmp($ans1));
ANS(num_cmp($ans2));
ANS(num_cmp($ans3));
ANS(num_cmp($ans4));
ANS(num_cmp($ans5));

ENDDOCUMENT();        # This should be the last executable line in the problem.