## DESCRIPTION ## Differential calculus: answer is a number or formula with units ## ENDDESCRIPTION ## KEYWORDS('differential calculus', 'units') ## DBsubject('WeBWorK') ## DBchapter('WeBWorK Tutorial') ## DBsection('Fort Lewis Tutorial 2011') ## Date('01/30/2011') ## Author('Paul Pearson') ## Institution('Fort Lewis College') ## TitleText1('') ## EditionText1('') ## AuthorText1('') ## Section1('') ## Problem1('') ############################## # Initialization DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", "parserNumberWithUnits.pl", "parserFormulaWithUnits.pl", ); TEXT(beginproblem()); ############################# # Setup Context("Numeric")->variables->are(t=>"Real"); $h = Formula("-16 t^2 + 16");$v = $h->D('t');$v1 = $v->eval(t=>1);$a = $v->D('t');$answer[0] = FormulaWithUnits("$v","ft/s");$answer[1] = NumberWithUnits("$v1","ft/s");$answer[2] = FormulaWithUnits("$a","ft/s^2"); ############################# # Main text Context()->texStrings; BEGIN_TEXT Suppose the height of a falling object, in feet above the ground, is given by $$h(t) = h$$ for $$t \geq 0$$, where time is measured in seconds.$BR $BR (a) What is the velocity of the object? Include units in your answer.$BR \{ ans_rule(20) \} \{ helpLink("units") \} $BR$BR (b) What is the velocity of the object when it hits the ground? Include units in your answer. $BR \{ ans_rule(20) \} \{ helpLink("units") \}$BR $BR (c) What is the acceleration of the object? Include units in your answer.$BR \{ ans_rule(20) \} \{ helpLink("units") \} END_TEXT Context()->normalStrings; ############################ # Answers $showPartialCorrectAnswers = 1; foreach my$i (0..2) { ANS( $answer[$i]->cmp() ); } ############################ # Solution Context()->texStrings; BEGIN_SOLUTION ${PAR}SOLUTION:${PAR} Solution explanation goes here. END_SOLUTION Context()->normalStrings; COMMENT("MathObject version."); ENDDOCUMENT(); ########################### # Initialization DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", "parserDifferenceQuotient.pl", ); TEXT(beginproblem()); ########################### # Setup Context("Numeric"); $limit = DifferenceQuotient("2*x+h","h");$fp = Compute("2 x"); ########################### # Main text Context()->texStrings; BEGIN_TEXT Simplify and then evaluate the limit. $BR$BR $$\displaystyle \frac{d}{dx} \big( x^2 \big) = \lim_{h \to 0} \frac{(x+h)^2-x^2}{h} = \lim_{h \to 0} \big($$ \{ ans_rule(15) \} $$\big) =$$ \{ ans_rule(15) \} END_TEXT Context()->normalStrings; ############################ # Answer evaluation $showPartialCorrectAnswers = 1; ANS($limit->cmp() ); ANS( $fp->cmp() ); ############################ # Solution Context()->texStrings; BEGIN_SOLUTION${PAR}SOLUTION:\${PAR} Solution explanation goes here. END_SOLUTION Context()->normalStrings; COMMENT('MathObject version.'); ENDDOCUMENT();