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# Annotation of /trunk/NationalProblemLibrary/OSU/accelerated_calculus_and_analytic_geometry_i/hmwk7/prob4.pg

 1 : jj 213 ##Ellis & Gulick section 6.6 2 : ##Authored by Zig Fiedorowicz 4/17/2000 3 : DOCUMENT(); 4 : 5 : loadMacros( 6 : "PG.pl", 7 : "PGbasicmacros.pl", 8 : "PGchoicemacros.pl", 9 : "PGanswermacros.pl", 10 : "PGauxiliaryFunctions.pl" 11 : ); 12 : 13 : $showPartialCorrectAnswers = 1; 14 : if (!($studentName =~ /PRACTICE/)) { 15 : $seed = random(1,4,1); 16 : if ($studentName =~ /VINCE VERSION1/) {$seed = 1;} 17 : if ($studentName =~ /VINCE VERSION2/) {$seed = 2;} 18 : if ($studentName =~ /VINCE VERSION3/) {$seed = 3;} 19 : if ($studentName =~ /VINCE VERSION4/) {$seed = 4;} 20 : SRAND($seed);} 21 : 22 : $aa = random(2,8,1); 23 :$bb = random(3,9,1); 24 : if ($aa==$bb){$aa++;} 25 :$b3 = $bb**3; 26 : 27 : TEXT(&beginproblem); 28 : BEGIN_TEXT 29 : Compute the following limits using l'H\^opital's rule if appropriate. 30 : Use INF to denote $$\infty$$ and MINF to denote $$-\infty$$. 31 :$PAR 32 : $$\lim_{x\to 0} \frac{x}{\int_x^{x^2}\sqrt[3]{b3-aa t^3}\,dt}$$ = \{ ans_rule()\} 33 : $PAR 34 : 35 : $$\lim_{x\to 0^+} \sin(x)\ln(x)$$ = \{ ans_rule()\} 36 :$PAR 37 : 38 : Note the first question has something to do with the Fundamental Theorem of 39 : Calculus, whereas the second is similar to problem 35 in Section 6.6 of the 40 : text. 41 : END_TEXT 42 : 43 : &ANS(std_num_str_cmp(-1/\$bb,['INF','MINF'])); 44 : &ANS(std_num_str_cmp(0,['INF','MINF'])); 45 : 46 : 47 : ENDDOCUMENT();