Mathematica graphics

w6q1a

data file: w6q1a.mbb for labelling w6q1a.eps

%%AspectRatio: 1.6 :1.294
%%LDRU:{-5.24417, -171.787, 8.21328, 248.046}
LDRU:{-3.95, -148, 8.21328, 226}
StartData
,{-1.13851, 16.7698, amax}
,{4.94396, -92.2394, amin}
,{2.05478, 0.565704, bflat}
EndData

   X_Y-pic code:

\renewcommand{\xyWARMinclude}{\scaledfig{.85}}
\renewcommand{\objectstyle}{\scriptstyle}
%\let\small=\tiny
\ifx\undefined\pdftexversion
 \WARMprocessMMAR{w6q1a}{eps}{mbb}
\else
 \WARMprocessMMAR{w6q1a}{pdf}{mbb}
\fi
\begin{xy}
 \xyMarkedImport{}
% *\frm{-}\xyShowMarkPoints{*[red]@{x}}{-}
 \xyMarkedPos{amax}*+{}+UR
  ,\ar@{<-}+(.5,40)*+!D\txt\small{local\\maximum}
 \xyMarkedPos{amin}*+{}+UL
  ,\ar@{<-}+(-.5,50)*+!D\txt\small{local\\minimum}
 \xyMarkedPos{amin}*+{}+DL*!U!R(.5){x^3 - 6x^2 - 15x + 7},
 \xyMarkedPos{bflat}+(0,200)*!L(.2)!U{x^3 - 6x^2 + 12x - 9},
 \xyMarkedPos{bflat}*+{},\ar@{<-}+(1,80)
  ,*+!D\txt\small{flat point of\\inflection}
\end{xy}

See this in context.

w6q1b

data file: w6q1b.mbb for labelling w6q1b.eps

%%AspectRatio: 1.6 :0.66
%%LDRU:{-4.21727, -328.832, 3.19637, 371.677}
LDRU:{-3.56, -287, 3.16, 330}
StartData
,{-2.03436, -248.565, cmin1}
,{2.00195, -246.133, cmin2}
,{0.0249801, 9.26099, cflat}
EndData

   X_Y-pic code:

\renewcommand{\xyWARMinclude}{\scaledfig{.85}}
\renewcommand{\objectstyle}{\scriptstyle}
%\let\small=\tiny
\ifx\undefined\pdftexversion
 \WARMprocessMMAR{w6q1b}{eps}{mbb}
\else
 \WARMprocessMMAR{w6q1b}{pdf}{mbb}
\fi

\begin{xy}
 \xyMarkedImport{}
% *\frm{-}\xyShowMarkPoints{*[red]{\times}}{-}
 \xyMarkedPos{cflat}+(0,250)*{x^{10} - 5x^8 + 6},
 \xyMarkedPos{cflat}+{}+L(.5),\ar@{<-}+(0,100)
  *+!D\txt\small{very flat point\\of inflection}
 \xyMarkedPos{cmin1}*++{},\ar@{<-}+(2,20)
  *+\txt\small{local\\minima}="cmin"
 \xyMarkedPos{cmin2}*++{},\ar@{<-}"cmin"  
\end{xy}

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w6q2

data file: w6q2.mbb for labelling w6q2.eps

%%AspectRatio: 1.0
LDRU:{-5.09668, -22.6479, 6.23018, 31.4788}
StartData
,{-2.99029, -6.75055, f-3}
,{-2.03644, 18.0418, f-2}
,{-1.00312, 25.4227, fmax}
,{-0.0095315, 20.1236, f-0}
,{3.01097, -6.75055, fmin}
,{3.96481, 0.441109, f+3}
EndData

   X_Y-pic code:

\renewcommand{\xyWARMinclude}{\scaledfig{0.7}}
\ifx\undefined\pdftexversion
 \WARMprocessMMAR{w6q2}{eps}{mbb}
\else
 \WARMprocessMMAR{w6q2}{pdf}{mbb}
\fi
\begin{xy}
 \xyMarkedImport{}
% *\frm{-}\xyShowMarkPoints{*[red]{\times}}{-}
\end{xy}

See this in context.

Q1

data file: Q1.mbb for labelling Q1.eps

LDRU:{-3.89059, -43.2333, 4.21704, 43.0523}
StartData
,{1.5145, 5.44064, para}
,{2.03422, -9.67778, cub1}
,{-1.01481, 17.6091, cub2}
,{0.96013, 2.49071, neg1}
,{-1.04945, 2.49071, neg2}
EndData

   X_Y-pic code:

\ifx\pdfunknown\relax
 \WARMprocessMMA{Q1}{eps}{mbb}
\else
 \WARMprocessMMA{Q1}{pdf}{mbb}
\fi
\renewcommand{\xyWARMinclude}{\scaledfig{.7}}%
\begin{xy}
 \xyMarkedImport{}
% \xyShowMarkPoints{*[red]@{x}}{-}
 \xyMarkedPos{para}*+{}
   ,\ar@{<-}+(.7,25)*+!D\txt{base of parabola}
 \xyMarkedPos{cub1}*+++{},\ar@{<-}-(3.5,15)
  *+!U(.8)\txt{turning points\\of a cubic}="cub"
 \xyMarkedPos{cub2}*++{},\ar@{<-}"cub",
 \xyMarkedPos{neg1}*++{},\ar@{<-}+(.5,-25),
  *+!L(.6)\txt{local minima}="min"
 \xyMarkedPos{neg2}*+{},\ar@{<-}"min",
\end{xy}

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Q2

data file: Q2.mbb for labelling Q2.eps

%%AspectRatio: 1.19048
LDRU:{-4.20871, -5.00853, 4.20844, 5.04335}
StartData
,{-2.43485, 2.64342, hyp1}
,{2.85195, -2.9912, hyp2}
,{1.87807, -0.66083, circ}
,{1.66938, 3.86078, q1}
,{0.278116, 1.49563, q2}
,{-1.56531, 2.92167, q3}
,{2.15632, 2.22604, x1}
,{2.85195, -3.82596, x2}
,{-2.67832, 1.66954, x3}
,{-1.84356, -1.77384, x4}
EndData

   X_Y-pic code:

\ifx\pdfunknown\relax
 \WARMprocessMMAR{Q2}{eps}{mbb}
\else
 \WARMprocessMMAR{Q2}{pdf}{mbb}
\fi
\renewcommand{\xyWARMinclude}{\scaledfig{.7}}
\begin{xy}
 \xyMarkedImport{}
% \xyShowMarkPoints{*[red]@{x}}{-}
 \xyMarkedPos{hyp1}*++{},
  \ar@{<-}-(.8,3.8)*+!U!R(.2)\txt{hyperbola}="hyp"
 \xyMarkedPos{hyp2}*++{},\ar@{<-}"hyp"+DR+L(.2),
 \xyMarkedPos{circ}*!L\txt{circle},
 \xyMarkedPos{x1}*+{}
  ,\ar@{<-}+(1,-1)*+!U\txt{crossing\\lines}="xl",
 \xyMarkedPos{x2}*++{},\ar@{<-}"xl"+CD,
 \xyMarkedPos{q2},\ar@{<-}+(.5,3)*+!D(.8)
   \txt{three branches of\\an elliptic quartic}
    ="ell",
 \xyMarkedPos{q1}*++{},\ar@{<-}"ell",
 \xyMarkedPos{q3}*++{},\ar@{<-}"ell"
\end{xy}

See this in context.

QA1

data file: QA1.mbb for labelling QA1.eps

%%AspectRatio: .61803 
LDRU:{-2.42465, -3.80861, 6.6868, 3.25092}
StartData
,{2.29262, 2.27719, 3sinX}
,{1.54949, -0.927998, sin3X}
EndData

   X_Y-pic code:

\ifx\pdfunknown\relax
 \WARMprocessMMAR{QA1}{eps}{mbb}
\else
 \WARMprocessMMAR{QA1}{pdf}{mbb}
\fi
 \renewcommand{\xyWARMinclude}{\scaledfig{.7}}
\begin{xy}
 \xyMarkedImport{}
% \xyShowMarkPoints{*[red]@{x}}{-}
 \xyMarkedPos{3sinX},*+++!L{3\sin x}
 \xyMarkedPos{sin3X}*++{}
  ,\ar@{<-}+(.7,-1)*+!U!L(.4){\sin 3x}
\end{xy}

See this in context.

w8q3

data file: w8q3.mbb for labelling w8q3.eps

LDRU:{-2.20372,  -0.523331, 7.26973,  0.729998}
StartData
,{2.97862, 0.302727, anchor}
,{0.13989, 0.530605, tangent}
,{2.91261, -0.231362, serpent}
EndData

   X_Y-pic code:

\ifx\pdfunknown\relax
 \WARMprocessMMA{w8q3}{eps}{mbb}%
\else
 \WARMprocessMMA{w8q3}{pdf}{mbb}%
\fi
\renewcommand{\xyWARMinclude}[1]{\scaledfig{.7}{#1}}%
\begin{xy}
 \xyMarkedImport{}
% *\frm{-},\xyShowMarkPoints{*[red]@{x}}{-}
 \xyMarkedPos{anchor}*+!DL{(3,0.3)}
 \xyMarkedPos{tangent}*++!DL\txt\small{tangent line: $y=0.54-0.08x$}
 \xyMarkedPos{serpent}-(0,.05)*+!C[F-:red]\txt
  \large\bfseries{serpentine curve\\$y=x(1+x^2)^{-1}$}
\end{xy}

See this in context.

m130w10

data file: m130w10.mbb for labelling m130w10.eps

LDRU:{-3.33146, -2.06495, 5.36925, 2.06574}
StartData
,{1.6629, 0.18815, lmax1}
,{0.716603, -0.17485, lmin2}
,{0.00687766, 0.000391059, lmin3}
,{-2.01715, 0.55115, lmax3}
EndData

   X_Y-pic code:

\ifx\pdfunknown\relax
 \WARMprocessMMA{m130w10}{eps}{mbb}
\else
 \WARMprocessMMA{m130w10}{pdf}{mbb}
\fi
\renewcommand{\xyWARMinclude}{\scaledfig{.7}}
\begin{xy}
 \xyMarkedImport{}
 \xyMarkedPos{lmax1}*+{},\ar@{<-}+(.2,-1)*+!L(.65)!U\txt
 \small{maximum of $\displaystyle\frac{\log x}{x^2}$}
 ,\xyMarkedPos{lmin2},+(1.3,1.75)*+!L\txt{$x^2\log x$}
 ,\xyMarkedPos{lmax3}*++{}+U,*+!D\txt{$x^2e^x$}  
\end{xy}

See this in context.

ass1q1

data file: ass1q1.mbb for labelling ass1q1.eps

LDRU:{-1.87957, -3.12954, 2.6215, 5.12953}
StartData
,{-1.0129, 1.01438, A}
,{1.97849, 4.03599, B} 
,{0.496772, -1.97845, P}
EndData

   X_Y-pic code:

\ifx\pdfoutput\relax
\WARMprocessMMA{ass1q1}{eps}{mbb}%
\else
\WARMprocessMMA{ass1q1}{pdf}{mbb}%
\fi
\renewcommand{\xyWARMinclude}[1]
  {\scaledfig{.7}{#1}}%
\begin{xy}
 \xyMarkedImport{}
 \xyMarkedPos{A}*+!RU{A}
  ,+(0,2.8)*+!R(.5)[F-:red]\txt\large{$y=x^2$}
 \xyMarkedPos{B}*+!LU{B}
 \xyMarkedPos{P}*++!L{P}
\end{xy}

See this in context.

ass1q2

data file: ass1q2.mbb for labelling ass1q2.eps

LDRU:{-1.27685, -2.95236, 2.50319, 6.0}
StartData
,{-0.0124458, -0.0021488, station}
,{1.00171, 0.0487168, house} 
,{2.0027, 4.0671, train}
EndData

   X_Y-pic code:

\ifx\pdfoutput\relax
\WARMprocessMMA{ass1q2}{eps}{mbb}%
\else
\WARMprocessMMA{ass1q2}{pdf}{mbb}%
\fi
\renewcommand{\xyWARMinclude}[1]{\scaledfig{.7}{#1}}%
\begin{xy}
 \xyMarkedImport{}="a"
 \xyMarkedPos{train}*++!LU\txt\large\bfseries{train}
 \xyMarkedPos{house}*++!UL\txt\large\bfseries{house}
 \xyMarkedPos{station}*++!U[F-:red]\txt\large\bfseries{station}
 ,(2,0)*++!D\txt\large\bfseries{road}
 ,(-.5,1)*+!D\txt\large\bfseries{$y=x^2$}
\end{xy}

See this in context.

ass2q2

data file: ass2q2.mbb for labelling ass2q2.eps

LDRU:{-3.19622, -1.73032, 6.22917, 91.753}
StartData
,{-0.0324492, 27.3182, pool}
,{4.05408, 41.0502, lip} 
,{-2.0098, 41.0502, height}
EndData

   X_Y-pic code:

\ifx\pdfunknown\relax
 \WARMprocessMMA{ass2q2}{eps}{mbb}%
\else
 \WARMprocessMMA{ass2q2}{pdf}{mbb}%
\fi
\renewcommand{\xyWARMinclude}[1]{\scaledfig{.7}{#1}}%
\begin{xy}
 \xyMarkedImport{}
 \xyMarkedPos{pool}*\txt\bfseries{\textcolor{blue}{pool}}
 \xyMarkedPos{lip}*++!D!R(.5)\txt{water-level when full}
 \xyMarkedPos{height}+(0,40)*!L{y=6x^2 - x^3 + 8}
\end{xy}

See this in context.

ass2q5

data file: ass2q5.mbb for labelling ass2q5.eps

LDRU:{-11.9378, -1.23321, 9.98388, 1.08382}
StartData
,{-6.24286, 1.00346, peak-}
,{-0.00180389, 1.00346, peak0}
,{6.23925, 0.990064, peak+}
,{9.43779, -0.496581, neghalf}
EndData

   X_Y-pic code:

\ifx\pdfunknown\relax
 \WARMprocessMMA{ass2q5}{eps}{mbb}%
\else
 \WARMprocessMMA{ass2q5}{pdf}{mbb}%
\fi
\renewcommand{\xyWARMinclude}[1]{\scaledfig{.7}{#1}}%
\begin{xy}
 \xyMarkedImport{}
% *\frm{-},\xyShowMarkPoints{*[red]@{x}}{-}
 \xyMarkedPos{peak0}*+{},\ar@{<-}@[magenta]+(0,.5)
  *++!D(.5)[F-:magenta]\txt{local maxima of both $\cos x$ and $\cos 2x$}="max"
 ,\xyMarkedPos{peak-}*+{},\ar@{<-}@[magenta]"max"
 \xyMarkedPos{peak+}*+{},\ar@{<-}@[magenta]"max"
 \xyMarkedPos{neghalf}*++!L[F-:magenta]\txt{${-}\frac12$, six intersections}
\end{xy}

See this in context.

trajs

data file: trajs.mbb for labelling trajs.eps

%%AspectRatio: .48776
LDRU:{-0.0625471, -0.0485739, 1.06308, 0.499956}
StartData
,{0.157436, 0.0171355, traj1}
,{0.348851, 0.0657033, traj2}
,{0.460271, 0.145697, traj3}
,{0.877382, 0.111414, traj4}
,{0.631687, 0.302828, traj5}
,{0.420274, 0.408535, traj6}
,{0.194576, 0.459959, traj7}
EndData

   X_Y-pic code:

\renewcommand{\xyWARMinclude}{\scaledfig{.7}}
\ifx\pdfunknown\relax
 \WARMprocessMMAR{trajs}{eps}{mbb}
\else
 \WARMprocessMMAR{trajs}{pdf}{mbb}
\fi
\begin{xy}
 \xyMarkedImport{}
% *\frm{-}\xyShowMarkPoints{*[red]{\times}}{-}
 ,\xyMarkedPos{traj2}*-!DL{\theta=\frac{7\pi}{60}}
 ,\xyMarkedPos{traj3}*-!D{\theta=\frac{11\pi}{60}}
 ,\xyMarkedPos{traj4}*!DL{\theta=\frac{\pi}{4}}
 ,\xyMarkedPos{traj5}*!DL{\theta=\frac{19\pi}{60}}
 ,\xyMarkedPos{traj6}*!DL{\theta=\frac{23\pi}{60}}
 ,\xyMarkedPos{traj7}*!DL{\theta=\frac{9\pi}{20}}
 ,(1,0)*+++!UL{\frac{mV^2}{g}}
\end{xy}

See this in context.