##DESCRIPTION ##KEYWORDS('derivatives', 'trigonometric functions', 'product rule') ## differentiation of x^n*sin(x) ##ENDDESCRIPTION DOCUMENT(); # This should be the first executable line in the problem. loadMacros( "PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl" ); TEXT(&beginproblem); $showPartialCorrectAnswers = 1;$an = random(2,5,1); $as = random(-1,1,2);$a = $an *$as; $n = random(2,8,1);$funct1 = "$a*x^($n-1)*($n*sin(x)+ x*cos(x))"; TEXT(EV2(<[-.99/$n, .99/$n] )); ENDDOCUMENT(); # This should be the last executable line in the problem. ________________________________________________________________________________ ##DESCRIPTION ##KEYWORDS('derivatives', 'logarithmic functions') ## differentiation of log function a sqrt(x)*ln(x) ##ENDDESCRIPTION DOCUMENT(); # This should be the first executable line in the problem. loadMacros( "PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl" ); TEXT(&beginproblem);$showPartialCorrectAnswers = 1; $an = random(2,5,1);$as = random(-1,1,2); $a =$an * $as;$n = random(2,8,1); $funct1 = "$a*$n*x^($n-1)*(sec($a x^$n)^2)"; TEXT(EV2(<[sqrt($an),2*sqrt($an)])); ENDDOCUMENT(); # This should be the last executable line in the problem. ________________________________________________________________________________ ##DESCRIPTION ##KEYWORDS('derivatives', 'logarithmic functions','exponential functions','product rule') ## differentiation of log function a exp(x^n)*ln(nx) ##ENDDESCRIPTION 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(2,5,1); $n = random(2,8,1);$funct1 = "e^{x^$a} *(1/x)+ln($n x) e^{x^{$a}} *$a*x^{$a-1}"; TEXT(EV2(<$q1) { $ans = "INF"; &ANS(num_cmp($ans,strings=>["INF","-INF"])); } elsif ( $p1 ==$q1 ) { $ans =$c1/$k1; &ANS(num_cmp($c1/$k1)); } else {$ans = 0; &ANS(strict_num_cmp(0,0)); } ENDDOCUMENT(); ________________________________________________________________________________ ##DESCRIPTION ## limits ##ENDDESCRIPTION ##KEYWORDS ('limit', 'la Hospital') DOCUMENT(); loadMacros( "PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl" ); TEXT(&beginproblem); $showPartialCorrectAnswers = 1;$problem = random(1, 2, 1); $k1 = random(2, 12, 1);$p1 = random(3, 6, 1); $q1 = random(3, 6, 1); if ($problem ==1) { TEXT(EV3(<<'EOT')); Evaluate $\lim_{x \rightarrow \infty} \frac{e^{p1 x}}{k1 x^q1}.$ $PAR If the limit is $$\infty$$, enter 'INF', and if the limit is $$-\infty$$, then enter '-INF'.$PAR Limit = \{ ans_rule(20) \} $BR EOT$ans = "INF"; &ANS(num_cmp($ans,strings=>["INF","-INF"])); } else { TEXT(EV3(<<'EOT')); Evaluate $\lim_{x \rightarrow \infty} \frac{k1 x^q1.}{e^{p1 x}}$$PAR If the limit is $$\infty$$, enter 'INF', and if the limit is $$-\infty$$, then enter '-INF'. $PAR Limit = \{ ans_rule(20) \}$BR EOT $ans = 0; &ANS(strict_num_cmp(0,0)); } ENDDOCUMENT(); ________________________________________________________________________________ ##DESCRIPTION ## limits ##ENDDESCRIPTION ##KEYWORDS ('limit', 'la Hospital') DOCUMENT(); loadMacros( "PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl" ); TEXT(&beginproblem);$showPartialCorrectAnswers = 1; $problem = random(1, 2, 1);$k1 = random(2, 12, 1); $p1 = random(3, 6, 1);$q1 = random(3, 6, 1); if ($problem ==1) { TEXT(EV3(<<'EOT')); Evaluate $\lim_{x \rightarrow \infty} \frac{k1 sqrt(x)}{ln(p1 x)}.$$PAR If the limit is $$\infty$$, enter 'INF', and if the limit is $$-\infty$$, then enter '-INF'. $PAR Limit = \{ ans_rule(20) \}$BR EOT $ans = "INF"; &ANS(num_cmp($ans,strings=>["INF","-INF"])); } else { TEXT(EV3(<<'EOT')); Evaluate $\lim_{x \rightarrow \infty} \frac{ln(p1 x)}{k1 sqrt(x)}.$ $PAR If the limit is $$\infty$$, enter 'INF', and if the limit is $$-\infty$$, then enter '-INF'.$PAR Limit = \{ ans_rule(20) \} $BR EOT$ans = 0; &ANS(strict_num_cmp(0,0)); } ENDDOCUMENT();