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File:  [LON-CAPA] / loncom / homework / templates / HintMathResponse.problem
Revision 1.3: download - view: text, annotated - select for diffs
Mon May 21 22:11:07 2007 UTC (16 years, 11 months ago) by albertel
Branches: MAIN
CVS tags: version_2_9_X, version_2_9_1, version_2_9_0, version_2_8_X, version_2_8_99_1, version_2_8_99_0, version_2_8_2, version_2_8_1, version_2_8_0, version_2_7_X, version_2_7_99_1, version_2_7_99_0, version_2_7_1, version_2_7_0, version_2_6_X, version_2_6_99_1, version_2_6_99_0, version_2_6_3, version_2_6_2, version_2_6_1, version_2_6_0, version_2_5_X, version_2_5_99_1, version_2_5_99_0, version_2_5_2, version_2_5_1, version_2_5_0, version_2_4_X, version_2_4_99_0, version_2_4_2, version_2_4_1, version_2_4_0, bz5969, HEAD, GCI_2, GCI_1, BZ5971-printing-apage, BZ5434-fox
- add in &

<problem>
    <script type="loncapa/perl">
$a1 = &random(-6,6,4);
$a2 = &random(-6,6,4);
$n1 = &random(3,11,2);
$n2 = &random(2,10,2);
$function = "$a1*cos($n1*x)+$a2*sin($n2*x)";
$example=&xmlparse('An example would be <m eval="on">$(sin($n1\cdot x)+cos($n2\cdot x))/\sqrt{2}$</m>');
    </script>

    <startouttext />
Give an example of a function
<ol>
    <li>which is orthogonal to <algebra>$function</algebra> with respect to the
        scalar product
        <m>\[<g \mid h> = \frac{1}{\pi} \int_{-\pi}^{\pi}dx g(x) \cdot h(x)\]</m>
    </li>
    <li>whose norm is 1.</li>
</ol>
    <endouttext />

    <mathresponse answerdisplay="$example" cas="maxima" args="$function">

        <answer>
overlap:integrate((RESPONSE[1])*(LONCAPALIST[1]),x,-%pi,%pi)/%pi;
norm:integrate((RESPONSE[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi;
is(overlap=0 and norm=1);
        </answer>

        <textline readonly="no" size="50" />

        <hintgroup showoncorrect="no">

            <mathhint name="ortho" args="$function" cas="maxima">

                <answer>
overlap: integrate((LONCAPALIST[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi;
is(not overlap = 0);
                </answer>
            </mathhint>

            <mathhint name="norm" args="$function" cas="maxima">
                <answer>
norm: integrate((RESPONSE[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi;
is(not norm = 1);
                </answer>
            </mathhint>
           
            <hintpart on="norm">
                <startouttext />
The function you have provided does not have a norm of one.
                <endouttext />
            </hintpart>

            <hintpart on="ortho">
                <startouttext />
The function you have provided is not orthogonal.
                <endouttext />
            </hintpart>

        </hintgroup>
    </mathresponse>

    <postanswerdate>

        <startouttext />
<p>
    Note that with respect to the above norm, <m>$\cos(nx)$</m> is
    perpendicular to <m>$\sin(nx)$</m> and perpendicular to <m>$\cos(mx)$</m>
    for <m>$n\ne m$</m>.
</p>
        <endouttext />

    </postanswerdate>
</problem>
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