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\providecommand{\tg}{\mbox{tg} \, }%
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\providecommand{\arctg}{\mbox{arctg} \, }\usepackage[brazil]{babel}
\usepackage{amssymb,graphicx}



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% !!! IMAGES START HERE !!!

{\newpage\clearpage
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$\displaystyle \int \frac{ \ln(x) dx}{\sqrt{x}} $%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline307}%
$\displaystyle \int \frac{3x^2+4x+2}{x(x^2+2x+1)} dx $%
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{\newpage\clearpage
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$f(x) = \mbox{sen} \, \left( \sqrt{x^2+3\pi^2} \right)$%
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{\newpage\clearpage
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$x=\pi$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline313}%
$\displaystyle \begin{array}{ll}
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline315}%
$\displaystyle \int \frac{ \ln(x) dx}{\sqrt{x}} =
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2 \sqrt{x} \ln(x) - 2 \int x^{-1/2} dx $%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
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$\displaystyle \int \frac{ \ln(x) dx}{\sqrt{x}} =
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2 \sqrt{x} \ln(x) - 4 \sqrt{x} + C $%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline319}%
$\displaystyle \frac{3x^2 + 4x + 2}{x(x^2+2x+1)} =
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline321}%
$\displaystyle \frac{3x^2 + 4x + 2}{x(x^2+2x+1)} =
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline323}%
$ \Rightarrow \displaystyle 3x^2 + 4x + 2 \equiv
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline325}%
$ \Rightarrow \displaystyle 3x^2 + 4x + 2 \equiv
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline327}%
$\displaystyle \left\{ \begin{array}{ccc}
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline329}%
$\displaystyle A =2 \Rightarrow B = 3-A = 3-2 = 1 $%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline331}%
$\displaystyle \rightarrow C = 4-2A-B= 4-4-1 = -1$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline333}%
$\displaystyle \frac{3x^2 + 4x + 2}{x(x^2+2x+1)} =
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\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline335}%
$\displaystyle \int \frac{3x^2 + 4x + 2}{x(x^2+2x+1)} dx =
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline337}%
$\displaystyle \int \frac{3x^2 + 4x + 2}{x(x^2+2x+1)} dx =
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\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline339}%
$\displaystyle \int \frac{3x^2 + 4x + 2}{x(x^2+2x+1)} dx =
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{\newpage\clearpage
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$C$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline343}%
$\displaystyle f'(x) = \cos \left( \sqrt{x^2+3\pi^2} \right) 
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\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline345}%
$\displaystyle f'(\pi) = \cos \left( \sqrt{(\pi)^2+3\pi^2} \right) 
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\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline347}%
$\displaystyle f'(\pi) = \cos \left( 2 \pi \right) 
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\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline349}%
$\displaystyle y - f(\pi) = f'(\pi)(x-\pi) $%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline351}%
$\Rightarrow y - \mbox{sen} \, \left( \sqrt{(\pi)^2 + 3 \pi^2} \right) =
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\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline353}%
$\Rightarrow y - \mbox{sen} \, \left( 2 \pi \right) =
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\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline355}%
$\displaystyle \Rightarrow y - 0 = \frac{1}{2} (x-\pi) $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline357}%
$12 m^2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline359}%
$4 m^2/h$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline361}%
$x$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline363}%
$h$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline365}%
$\displaystyle x^2 + 4 x h = 12 \Longrightarrow h = \frac{12 - x^2}{4x}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline367}%
$\displaystyle V = x^2 h \Longrightarrow V(x) = x^2 \cdot 
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\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline369}%
$(0,\sqrt{12})$%
\lthtmlinlinemathZ
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{\newpage\clearpage
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$12 - x^2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline373}%
$\displaystyle V'(x) = 3 - 3x^2/4 $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline375}%
$x^2/4 = 1 \Rightarrow x = 2$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline379}%
$V'(x)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline381}%
$\displaystyle V''(x) = - 3 x /2 < 0 $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline387}%
$V(x)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline389}%
$x = 2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline391}%
$h = 12/2^2 = 3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline393}%
$2 m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline395}%
$3 m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline397}%
$r$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline399}%
$V(r)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline401}%
$\displaystyle V(r) = \frac{4 \pi r^3}{3}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline403}%
$\displaystyle \frac{dV}{dt} = \frac{dV}{dr} \cdot \frac{dr}{dt}
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline405}%
$r = 1$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline407}%
$\displaystyle 4 = 4 \pi (1)^2 \ \frac{dr}{dt} \Longrightarrow
\frac{dr}{dt} = \frac{1}{\pi}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline409}%
$1/\pi \ m/h$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline411}%
$r = 1m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline413}%
$f(2) = 2 $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline415}%
$f(4)=3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline417}%
$\displaystyle
\lim_{x \rightarrow + \infty} f(x) = 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline419}%
$
\displaystyle \lim_{x \rightarrow -\infty} f(x) = +\infty$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline421}%
$f'(x) < 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline423}%
$x< 2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline425}%
$x > 4$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline427}%
$f''(x) > 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline431}%
$f(x) = x^2 e^{2x}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline433}%
$f$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline437}%
$y=1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline439}%
$(-\infty,2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline441}%
$(4,+\infty)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline443}%
$\displaystyle f'(x) = 2 x e^{2x} + x^2 (2) e^{2x} = 2 x(1+x)e^{2x}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline445}%
$e^{2x}$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline447}%
$y = x(1+x)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline449}%
$x=-1$%
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{\newpage\clearpage
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$x=0$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline453}%
$\displaystyle f'(x) < 0$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline455}%
$(-1,0) \Longrightarrow f(x) $%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline457}%
$[-1,0]$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline459}%
$\displaystyle f'(x) > 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline461}%
$(-\infty,-1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline463}%
$(0,+\infty) 
\Longrightarrow f(x) $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline465}%
$(-\infty,-1] \bigcup [0,+\infty) $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline471}%
$\displaystyle \lim_{x \rightarrow -\infty} f(x) = 
\lim_{x \rightarrow -\infty} x^2 e^{2x} \stackrel{\infty \cdot 0}{=} 
\lim_{x \rightarrow -\infty} \frac{x^2}{e^{-2x}} $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline473}%
$\displaystyle \lim_{x \rightarrow -\infty} f(x) = 
\lim_{x \rightarrow -\infty} \frac{2x}{-2e^{-2x}} \stackrel{LH}{=}
\lim_{x \rightarrow -\infty} \frac{2}{4e^{-2x}} = 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline475}%
$y=0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline477}%
$\displaystyle \lim_{x \rightarrow +\infty} f(x) = 
\lim_{x \rightarrow +\infty} x^2 e^{2x} \stackrel{\infty \cdot \infty}{=} 
+\infty$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline479}%
$x \rightarrow +\infty$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline481}%
$y = x^3 + 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline483}%
$y = 2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline485}%
$y$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline489}%
$\displaystyle V = \pi \int_0^1 (2^2 - (x^3 + 1)^2) dx =
4 \pi (1-0) - \pi \int_0^1(x^3 + 1)^2 dx $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline491}%
$\displaystyle V = 4 \pi  - \pi \int_0^1(x^6 + 2x^3+ 1) dx =
4 \pi - \pi \left[ \frac{x^7}{7} - \frac{2x^4}{4} + x 
\right]_0^1 = 4\pi - \pi \left( \frac{1}{7} - \frac{1}{2} + 1 \right) 
= 4 \pi - \frac{2 - 7 + 14}{14} \pi = \frac{(56-9)\pi}{14}=
\frac{47\pi}{14}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline493}%
$y^2 + 4 y - 10 x
+ 34 = 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline495}%
$\displaystyle y^2 + 4y + 4 = 10x - 34 + 4 \Longrightarrow
(y+2)^2 = 10(x-3)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline497}%
$(y-k)^2 = 4p(x-h)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline499}%
$\displaystyle k = -2, h = 3, 4p = 10 \Longrightarrow
p = 10/4 = 5/2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline501}%
$X$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline503}%
$V(3,-2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline505}%
$F(3+5/2,-2) = F(11/2,-2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline507}%
$x = 3-5/2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline509}%
$x = 1/2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}


\end{document}
