% This file is public domain % % These problems require arguments % % Arguments: #1->a_2, #2->a_1 and #3->a_0 % (Arguments must be integers) \newcount\ctr \newproblem[3][{1}{2}{3}]{diff:quad}{% \(f(x) = \ifnum#1=0 \else \ifnum#1=1\else#1\fi x^2 \fi \ifnum#2=0 \else \ifnum#2>0 \ifnum#1=0 \else + \fi \fi \ifnum#2=1\else#2\fi x \fi \ifnum#3=0 \else \ifnum#3>0 \ifnum#2=0 \ifnum#1=0 \else + \fi \else + \fi\fi #3 \fi\) }{% \(f'(x) = \ifnum#1=0 \else \ctr=2 \multiply\ctr by #1 \the\ctr x \fi \ifnum#2=0 \else \ifnum#2>0 \ifnum#1=0 \else + \fi \fi #2 \fi % print 0 if both #1 and #2 are 0 \ifnum#1=0 \ifnum#2=0 0 \fi\fi \) } \begin{defproblem}[1][{6}]{diff:sin} \begin{onlyproblem} \(f(x) = \sin(#1x)\) \end{onlyproblem} \begin{onlysolution} \(f'(x) = #1\cos(#1x)\) \end{onlysolution} \end{defproblem}