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| 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(); |
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