qu.1.topic=Limits/Continuity/Difference Quotient@

qu.1.1.mode=Inline@
qu.1.1.name=Limit Using Conjugate@
qu.1.1.comment=<p>Remember, with a "0/0" limit, anything can happen!</p>@
qu.1.1.editing=useHTML@
qu.1.1.solution=@
qu.1.1.algorithm=$d=switch(rint(2),"(sqrt(11-2*x)-sqrt(5))/(x-3)","(sqrt(7)-sqrt(10-x))/(x-3)");
$disp=maple("printf(MathML[ExportPresentation]($d))");@
qu.1.1.uid=3e4763d2-a4ef-4c1d-9b2e-468f1a478613@
qu.1.1.weighting=1@
qu.1.1.numbering=alpha@
qu.1.1.part.1.name=sro_id_1@
qu.1.1.part.1.maple_answer=limit($d,x=3)@
qu.1.1.part.1.editing=useHTML@
qu.1.1.part.1.question=(Unset)@
qu.1.1.part.1.libname=@
qu.1.1.part.1.mode=Maple@
qu.1.1.part.1.allow2d=1@
qu.1.1.part.1.plot=@
qu.1.1.part.1.maple=is(($ANSWER)-($RESPONSE) = 0);@
qu.1.1.part.1.type=formula@
qu.1.1.question=<p>What is the following limit?</p><p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><munder><mo lspace='0.0em' rspace='0.1666667em' movablelimits='true'>lim</mo><mrow><mi>x</mi><mo lspace='0.2777778em' rspace='0.2777778em' stretchy='true'>&rightarrow;</mo><mn>3</mn></mrow></munder></mrow></mstyle></math> $disp</p><p>Note: For answers using <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msqrt><mrow><mi>x</mi></mrow></msqrt></mrow></mstyle></math> use sqrt(x).&nbsp; For example, if your answer was <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mfrac><mrow><mn>2</mn></mrow><mrow><msqrt><mrow><mn>3</mn></mrow></msqrt></mrow></mfrac></mrow></mstyle></math> you would enter 2/sqrt(3).</p><p>&nbsp;<span>&nbsp;</span><1><span>&nbsp;</span></p><p>&nbsp;</p><p>&nbsp;</p>@

qu.1.2.mode=Inline@
qu.1.2.name=Left Limit (Quadratic)@
qu.1.2.comment=<p>Here is what the step function looks like:</p>
<p>$n</p>@
qu.1.2.editing=useHTML@
qu.1.2.solution=@
qu.1.2.algorithm=$a=rint(2,4);
$m=maple("
randomize():
p := sort(randpoly(x, degree=2, coeffs=rand(1..4)), x, descending):
f:=limit(p,x=$a,right):
convert(f, string), MathML[ExportPresentation](p),convert(p,string)
");
$ANS=switch(0,$m);
$DISP=switch(1,$m);
$p=switch(2,$m);
$n=plotmaple("
p1 := plots[implicitplot]({seq(x=i, i=-5..8)}, x=-4..3, y=-3..8, colour=grey):
p2 := plots[implicitplot]({seq(y=i, i=-5..8)}, x=-4..3, y=-3..8, colour=grey):
p3 := plot($p,discont = [usefdiscont = [bins = 35]],x=-4..3,y=-3..8, thickness=2):
plots[display]({p1,p2,p3}), plotoptions='height=250, width=250'
");@
qu.1.2.uid=63637aa1-6a58-49f2-94c9-82984d62df95@
qu.1.2.weighting=1@
qu.1.2.numbering=alpha@
qu.1.2.part.1.name=sro_id_1@
qu.1.2.part.1.maple_answer=$ANS@
qu.1.2.part.1.editing=useHTML@
qu.1.2.part.1.question=(Unset)@
qu.1.2.part.1.libname=@
qu.1.2.part.1.mode=Maple@
qu.1.2.part.1.allow2d=1@
qu.1.2.part.1.plot=@
qu.1.2.part.1.maple=is(($ANSWER)-($RESPONSE) = 0);@
qu.1.2.part.1.type=formula@
qu.1.2.question=<p>What is the following limit?</p><p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><munder><mo lspace='0.0em' rspace='0.1666667em' movablelimits='true'>lim</mo><mrow><mi>x</mi><mo lspace='0.2777778em' rspace='0.2777778em' stretchy='true'>&rightarrow;</mo><msup><mi>$a</mi><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo></mrow></msup></mrow></munder></mrow></mstyle></math> $DISP</p><p>&nbsp;<span>&nbsp;</span><1><span>&nbsp;</span></p>@

qu.1.3.mode=Inline@
qu.1.3.name=0/0 Limit ii@
qu.1.3.comment=<p>Remember, with a "0/0" limit, anything can happen!</p>@
qu.1.3.editing=useHTML@
qu.1.3.solution=@
qu.1.3.algorithm=$d=switch(rint(4),"(x^2-x-12)/(x-4)","(x^2-2*x-8)/(-4+x)","(x^2-3*x-4)/(x-4)","(x^2-6*x+8)/(-4+x)");
$disp=maple("printf(MathML[ExportPresentation]($d))");@
qu.1.3.uid=3ba3631f-9625-47b5-8786-0f1d60f6c5d3@
qu.1.3.weighting=1@
qu.1.3.numbering=alpha@
qu.1.3.part.1.name=sro_id_1@
qu.1.3.part.1.maple_answer=limit($d,x=4)@
qu.1.3.part.1.editing=useHTML@
qu.1.3.part.1.question=(Unset)@
qu.1.3.part.1.libname=@
qu.1.3.part.1.mode=Maple@
qu.1.3.part.1.allow2d=1@
qu.1.3.part.1.plot=@
qu.1.3.part.1.maple=is(($ANSWER)-($RESPONSE) = 0);@
qu.1.3.part.1.type=formula@
qu.1.3.question=<p>What is the following limit?</p><p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><munder><mo lspace='0.0em' rspace='0.1666667em' movablelimits='true'>lim</mo><mrow><mi>x</mi><mo lspace='0.2777778em' rspace='0.2777778em' stretchy='true'>&rightarrow;</mo><mn>4</mn></mrow></munder></mrow></mstyle></math> $disp</p><p>&nbsp;<span>&nbsp;</span><1><span>&nbsp;</span></p><p>&nbsp;</p><p>&nbsp;</p>@

qu.1.4.mode=Inline@
qu.1.4.name=Left Limit (Step Function)@
qu.1.4.comment=<p>Here is what the step function looks like:</p>
<p>$n</p>@
qu.1.4.editing=useHTML@
qu.1.4.solution=@
qu.1.4.algorithm=$a=rint(2,7);


$n=plotmaple("
p1 := plots[implicitplot]({seq(x=i, i=-3..8)}, x=-1..8, y=-1..7, colour=grey):
p2 := plots[implicitplot]({seq(y=i, i=-3..8)}, x=-1..8, y=-1..7, colour=grey):
p3 := plot(floor(x),discont = [usefdiscont = [bins = 35]],x=-1..8,y=-1..7, thickness=2):
plots[display]({p1,p2,p3}), plotoptions='height=250, width=250'
");@
qu.1.4.uid=da548fb5-1de4-4193-bc03-237cfdbf94c3@
qu.1.4.weighting=1@
qu.1.4.numbering=alpha@
qu.1.4.part.1.name=sro_id_1@
qu.1.4.part.1.maple_answer=$a-1@
qu.1.4.part.1.editing=useHTML@
qu.1.4.part.1.question=(Unset)@
qu.1.4.part.1.libname=@
qu.1.4.part.1.mode=Maple@
qu.1.4.part.1.allow2d=1@
qu.1.4.part.1.plot=@
qu.1.4.part.1.maple=is(($ANSWER)-($RESPONSE) = 0);@
qu.1.4.part.1.type=formula@
qu.1.4.question=<p>What is the following limit?</p><p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><munder><mo lspace='0.0em' rspace='0.1666667em' movablelimits='true'>lim</mo><mrow><mi>x</mi><mo lspace='0.2777778em' rspace='0.2777778em' stretchy='true'>&rightarrow;</mo><msup><mi>$a</mi><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo></mrow></msup></mrow></munder><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow><mrow><mfenced open='&lobrk;' close='&robrk;' separators=','><mrow><mi>x</mi></mrow></mfenced></mrow></mstyle></math></p><p>&nbsp;<span>&nbsp;</span><1><span>&nbsp;</span></p>@

qu.1.5.mode=Inline@
qu.1.5.name=Right Limit (Step Function)@
qu.1.5.comment=<p>Here is what the function looks like:</p>
<p>$n</p>@
qu.1.5.editing=useHTML@
qu.1.5.solution=@
qu.1.5.algorithm=$a=rint(2,7);
$ANS=$a+3;
$n=plotmaple("
p1 := plots[implicitplot]({seq(x=i, i=-3..10)}, x=-3..10, y=-3..$ANS+2, colour=grey):
p2 := plots[implicitplot]({seq(y=i, i=-3..($ANS+2))}, x=-3..10, y=-3..$ANS+2, colour=grey):
p3 := plot(floor(x+3),discont = [usefdiscont = [bins = 35]],x=-3..10,y=-3..10, thickness=2):
plots[display]({p1,p2,p3}), plotoptions='height=250, width=250'
");@
qu.1.5.uid=ff410ab6-21f4-49cc-b760-29b6d6844c1e@
qu.1.5.weighting=1@
qu.1.5.numbering=alpha@
qu.1.5.part.1.name=sro_id_1@
qu.1.5.part.1.maple_answer=$ANS@
qu.1.5.part.1.editing=useHTML@
qu.1.5.part.1.question=(Unset)@
qu.1.5.part.1.libname=@
qu.1.5.part.1.mode=Maple@
qu.1.5.part.1.allow2d=1@
qu.1.5.part.1.plot=@
qu.1.5.part.1.maple=is(($ANSWER)-($RESPONSE) = 0);@
qu.1.5.part.1.type=formula@
qu.1.5.question=<p>What is the following limit?</p><p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><munder><mo lspace='0.0em' rspace='0.1666667em' movablelimits='true'>lim</mo><mrow><mi>x</mi><mo lspace='0.2777778em' rspace='0.2777778em' stretchy='true'>&rightarrow;</mo><msup><mi>$a</mi><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo></mrow></msup></mrow></munder><mo lspace='0.0em' rspace='0.0em'>&#32;</mo></mrow><mrow><mfenced open='&lobrk;' close='&robrk;' separators=','><mrow><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>3</mn></mrow></mfenced></mrow></mstyle></math></p><p><span>&nbsp;</span><1><span>&nbsp;</span></p>@

