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30 November 书店即景11月29号，星期四，阴有小阵雨。
午后，学校书店。
---你好，我想预订下学期微积分的课本，请问是在你这边填表么？
---课本现在不能单独预定。你要跟你们任课老师讲，让他来跟我们订购。
---可我就是啊~~~ >_< 28 November 极品~~某人前天发邮件说需要答疑，约到昨天早上11点。11点，未到；11点5分，未到；... ; 11点22分，响起敲门声。
----请进。
（推门，露头，一张大脸盯着我）
----请问xx在么？我找他来答疑。
。。。。。。 04 November 讲义我的讲义，生活不易。。~~~~~~~~~~~~~~
\begin{slide}[toc=,bm=]{Volumes by Cylindrical Shells} \begin{itemize} \item Find the volume of the solid obtained by rotating about the $y$-axis the region bounded by $y=2x^2-x^3$ and $y=0$. \vspace{-3mm} \begin{center}\psset{linewidth=0.6pt}\everypsbox{\scriptsize} \begin{pspicture*}(-0.5,-0.5)(5,3.4) \psset{unit=2} \pslabel\psaxes[ticksize=1.5pt,Dx=2,arrows=->](0,0)(-0.25,-0.25)(2.5,1.7) \uput[-135](2.5,0){$x$} \uput[-135](0,1.7){$y$} \uput[-135](0,0){$O$} \psplot[linecolor=red]{0}{2}{2 x 2 exp mul x 3 exp sub} \rput(1.9,1.3){\textcolor{red}{$y=2x^2-x^3$}} \pscustom[linestyle=none,fillstyle=solid,fillcolor=green!20!yellow]{% \psplot{0}{2}{2 x 2 exp mul x 3 exp sub} \psline(2,0)(0,0) } \psaxes(0,0)(-0.25,-0.25)(2.5,1.7) \psplot[linecolor=red]{0}{2}{2 x 2 exp mul x 3 exp sub} \parametricplot[linewidth=0.3pt,arrows=->]{30}{330} {t cos 0.2 mul t sin 0.07 mul 1.4 add} \psframe[linecolor=red,hatchcolor=green!90!black,hatchwidth=2pt,hatchsep=2pt,fillstyle=hlines] (1,0)(1.1,1) \pause \onslide*{4-}{% \psline[linewidth=0.3pt,linestyle=dashed,dash=2pt 2pt](0,1)(1,1) \pcline[linewidth=0.3pt,arrows=<->](0.7,0)(0.7,1) \Aput{$f(x)$} } \onslide*{5-}{% \psline[linewidth=0.3pt](1,-0.05)(1,-0.25) \psline[linewidth=0.3pt](1.1,-0.05)(1.1,-0.25) \psline[linewidth=0.3pt,arrows=->](0.8,-0.15)(1,-0.15) \psline[linewidth=0.3pt,arrows=->](1.3,-0.15)(1.1,-0.15) \rput(1.4,-0.15){$\Delta x$} } \end{pspicture*} \begin{pspicture*}(-1.8,-1.3)(2.4,2.7) \psset{unit=1.5} \parametricplotThreeD[linecolor=red](0,2) {0 t 2 t 2 exp mul t 3 exp sub} \pstThreeDLine[arrows=->](0,0,0)(0,2.2,0) \pstThreeDPut(0,2.1,0.3){$x$} \pstThreeDLine[arrows=->](0,0,0)(0,0,2) \pstThreeDPut(0.15,0,1.9){$y$} \pstThreeDPut(0,1.2,2.2){\textcolor{red}{$y=f(x)$}} \pstThreeDSquare[linecolor=red,hatchcolor=green!90!black,hatchwidth=2pt,hatchsep=2pt,fillstyle=hlines] (0,1,0)(0,0.1,0)(0,0,1) \pause \parametricplotThreeD[linestyle=none,fillstyle=gradient,gradangle=100, xPlotpoints=50,yPlotpoints=100](0,360)(0,1) {t cos 1.1 mul t sin 1.1 mul u} \pstThreeDSquare[linestyle=none,hatchcolor=green!90!black, hatchwidth=2pt,hatchsep=2pt,fillstyle=hlines] (0,1,0)(0,0.1,0)(0,0,1) \parametricplotThreeD[linestyle=none,fillstyle=solid,fillcolor=blue, xPlotpoints=50,yPlotpoints=100](0,360)(1,1.1) {t cos u mul t sin u mul 1} \pstThreeDSquare[linecolor=red,linestyle=dashed,dash=2pt 2pt,] (0,1,0)(0,0.1,0)(0,0,1) \parametricplotThreeD[linestyle=none,fillstyle=gradient,gradangle=-80,gradmidpoint=1, xPlotpoints=50,yPlotpoints=100](0,360)(0,1) {t cos u mul t sin u mul 1} \parametricplotThreeD[linecolor=red,linestyle=dashed,dash=2pt 2pt](0,1) {0 t 2 t 2 exp mul t 3 exp sub} \parametricplotThreeD[linecolor=red](1,2) {0 t 2 t 2 exp mul t 3 exp sub} \pstThreeDLine[linestyle=dashed,dash=2pt 2pt](0,0,0)(0,1.1,0) \pstThreeDLine[linestyle=dashed,dash=2pt 2pt](0,0,0)(0,0,0.44) \pstThreeDLine[arrows=->](0,0,0.44)(0,0,2) \end{pspicture*} \end{center} \vspace{-4mm}\pause[3] \begin{itemize} \item $\Delta V= \pause \underbrace{\pi[(x+\Delta x)^2-x^2]}_{\textrm{base area}} \cdot \underbrace{f(x)}_{\textrm{height}} \pause =\pi(2x+\Delta x)f(x)\cdot \Delta x$. \pause \item $\dfrac{dV}{dx} \pause = \lim\limits_{\Delta x\to 0} \dfrac{\Delta V}{\Delta x} \pause = \lim\limits_{\Delta x\to 0} \pi(2x+\Delta x)f(x) \pause = 2\pi x\,f(x)$. \end{itemize} \end{itemize} \end{slide} |
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