[rochester] / trunk / rochester_problib / setDerivatives1_5Tangents / ur_dr_1_5_3.pg Repository: Repository Listing bbplugincoursesdistsnplrochestersystemwww

# View of /trunk/rochester_problib/setDerivatives1_5Tangents/ur_dr_1_5_3.pg

Mon Jun 25 19:20:51 2001 UTC (11 years, 11 months ago) by sam
File size: 1166 byte(s)
added problem library as webwork/ww_prob_lib with revision tag prob-lib-2


    1 ##DESCRIPTION
2 ##  Find the equation of a tangent line at a point by finding its derivative
3 ##  at that point
4 ##ENDDESCRIPTION
5
6 ##KEYWORDS('tangent line', 'derivatives')
7
8 DOCUMENT();        # This should be the first executable line in the problem.
9
11 "PG.pl",
12 "PGbasicmacros.pl",
13 "PGchoicemacros.pl",
15 "PGauxiliaryFunctions.pl"
16 );
17
18 TEXT(&beginproblem);
19 $showPartialCorrectAnswers = 1; 20 21$a1 = random(1,8,1);
22
23 $x1=0; 24 while ($x1==0) {
25     $x1 = random(-5,5,1); 26 } 27$y1 = $a1/$x1;
28 $m1 = -$a1/$x1**2; 29 30 TEXT(EV2(<<EOT)); 31 If $$f(x) = \frac{a1}{x}$$, find $$f'( x1 )$$. 32 \{ ans_rule(20) \} 33$BR
34 EOT
35
36 $ans =$m1;
37 &ANS(std_num_cmp($ans)); 38 39 TEXT(EV2(<<EOT)); 40 Use this to find the equation of the tangent line to the hyperbola 41 $$y = \frac{a1}{x}$$ 42 at the point $$( x1 , {y1:%0.3f} )$$. 43 The equation of this tangent line can be written in the form $$y = mx+b$$ 44 where $$m$$ is:\{ans_rule(20) \} 45$BR
46 EOT
47 $ans =$m1;
48 &ANS(std_num_cmp($ans)); 49 50 TEXT(EV2(<<EOT)); 51 and where $$b$$ is: 52 \{ans_rule(20) \} 53$BR
54 EOT
55 $ans =$y1 -$m1*$x1;
56 &ANS(std_num_cmp(\$ans));
57
58 ENDDOCUMENT();        # This should be the last executable line in the problem.