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<p class="MsoNormal" style="MARGIN: 0cm 1.25pt 0pt 0cm; mso-para-margin-right: .12gd; tab-stops: 54.0pt 108.0pt 162.0pt 216.0pt 270.0pt 324.0pt 378.0pt;"><b><span style="COLOR: red; FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">二、可口可乐罐头为什么是这种样子</span></b><b><span lang="EN-US" style="COLOR: red; mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><font face="Times New Roman">?<p></p></font></span></b></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 10.55pt; LINE-HEIGHT: 15.75pt; mso-char-indent-count: 1.0; mso-layout-grid-align: none;"><b><span style="COLOR: blue; FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">在讲述最优化</span></b><b><span lang="EN-US" style="COLOR: blue; mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><font face="Times New Roman">(</font></span></b><b><span style="COLOR: blue; FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">导数的应用</span></b><b><span style="COLOR: blue; mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><font face="Times New Roman">
<span lang="EN-US">– </span></font></span></b><b><span style="COLOR: blue; FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">极值问题</span></b><b><span lang="EN-US" style="COLOR: blue; mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><font face="Times New Roman">)</font></span></b><b><span style="COLOR: blue; FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">的前一堂课结束前</span></b><b><span lang="EN-US" style="COLOR: blue; mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><font face="Times New Roman">5~10</font></span></b><b><span style="COLOR: blue; FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">分钟,先提出问题:可口可乐、雪碧、健力宝等销量极大的饮料罐</span></b><b><span lang="EN-US" style="COLOR: blue; mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><font face="Times New Roman">(</font></span></b><b><span style="COLOR: blue; FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">易拉罐</span></b><b><span lang="EN-US" style="COLOR: blue; mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><font face="Times New Roman">)</font></span></b><b><span style="COLOR: blue; FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">顶盖的直径和从顶盖到底部的高之比为多少</span></b><b><span lang="EN-US" style="COLOR: blue; mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><font face="Times New Roman">? </font></span></b><b><span style="COLOR: blue; FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">为什么</span></b><b><span lang="EN-US" style="COLOR: blue; mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><font face="Times New Roman">? </font></span></b><b><span style="COLOR: blue; FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">它们的形状为什么是这样的</span></b><b><span lang="EN-US" style="COLOR: blue; mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><font face="Times New Roman">? <p></p></font></span></b></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 10.55pt; LINE-HEIGHT: 15.75pt; mso-char-indent-count: 1.0; mso-layout-grid-align: none;"><b><span style="COLOR: blue; FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">也可以要求同学在下一堂课前做</span></b><b><span lang="EN-US" style="COLOR: blue; mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><font face="Times New Roman">(</font></span></b><b><span style="COLOR: blue; FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">或预习</span></b><b><span lang="EN-US" style="COLOR: blue; mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><font face="Times New Roman">)</font></span></b><b><span style="COLOR: blue; FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">传统的微积分教材中的一道例题,例如“面向二十一世纪课程教材”中由王绵森、马知恩主编的《工科数学分析基础》</span></b><b><span lang="EN-US" style="COLOR: blue; mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><font face="Times New Roman">(</font></span></b><b><span style="COLOR: blue; FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">上册</span></b><b><span lang="EN-US" style="COLOR: blue; mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><font face="Times New Roman">)</font></span></b><b><span style="COLOR: blue; FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">,高等教育出版社,</span></b><b><span lang="EN-US" style="COLOR: blue; mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><font face="Times New Roman">1998</font></span></b><b><span style="COLOR: blue; FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">,</span></b><b><span lang="EN-US" style="COLOR: blue; mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><font face="Times New Roman">pp. 154-155 </font></span></b><b><span style="COLOR: blue; FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">的例</span></b><b><span lang="EN-US" style="COLOR: blue; mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><font face="Times New Roman"> 6.7 </font></span></b><b><span style="COLOR: blue; FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">“用铁皮做成一个容积一定的圆柱形的无盖</span></b><b><span lang="EN-US" style="COLOR: blue; mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><font face="Times New Roman">(</font></span></b><b><span style="COLOR: blue; FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">或有盖</span></b><b><span lang="EN-US" style="COLOR: blue; mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><font face="Times New Roman">)</font></span></b><b><span style="COLOR: blue; FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">容器,问应当如何设计,才能使用料最省,这时圆柱的直径和高之比为多少</span></b><b><span lang="EN-US" style="COLOR: blue; mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><font face="Times New Roman">? </font></span></b><b><span style="COLOR: blue; FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">”</span></b><b><span lang="EN-US" style="COLOR: blue; mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><font face="Times New Roman">(</font></span></b><b><span style="COLOR: blue; FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">我们略有修改</span></b><b><span lang="EN-US" style="COLOR: blue; mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><font face="Times New Roman">)</font></span></b><b><span style="COLOR: blue; FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">或者《托马斯微积分第</span></b><b><span lang="EN-US" style="COLOR: blue; mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><font face="Times New Roman">10</font></span></b><b><span style="COLOR: blue; FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">版》,高等教育出版社,</span></b><b><span lang="EN-US" style="COLOR: blue; mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><font face="Times New Roman">2003</font></span></b><b><span style="COLOR: blue; FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">,例</span></b><b><span lang="EN-US" style="COLOR: blue; mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><font face="Times New Roman">2(pp.291-293). </font></span></b><b><span style="FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">实际上</span></b><b><span lang="EN-US" style="mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><font face="Times New Roman">, </font></span></b><b><span style="FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">用几何语言来表述就是</span></b><b><span lang="EN-US" style="mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><font face="Times New Roman">: </font></span></b><b><span style="COLOR: blue; FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">体积给定的圆柱体</span></b><b><span lang="EN-US" style="COLOR: blue; mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><font face="Times New Roman">, </font></span></b><b><span style="COLOR: blue; FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">其表面积最小的尺寸</span></b><b><span lang="EN-US" style="COLOR: blue; mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><font face="Times New Roman"> (</font></span></b><b><span style="COLOR: blue; FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">半径和高</span></b><b><span lang="EN-US" style="COLOR: blue; mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><font face="Times New Roman">)</font></span></b><b><span style="COLOR: blue; FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">为多少</span></b><font face="Times New Roman"><b><span lang="EN-US" style="COLOR: blue; mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;">?</span></b><b><span lang="EN-US" style="mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;">
<p></p></span></b></font></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 15.75pt; mso-layout-grid-align: none;"><b><span style="FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">表面积用</span></b><b><span style="mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><font face="Times New Roman">
<i><span lang="EN-US">S </span></i></font></span></b><b><span style="FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">表示</span></b><b><span lang="EN-US" style="mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><font face="Times New Roman">, </font></span></b><b><span style="FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">体积用</span></b><b><span style="mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><font face="Times New Roman">
<i><span lang="EN-US">V </span></i></font></span></b><b><span style="FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">表示</span></b><b><span lang="EN-US" style="mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><font face="Times New Roman">, </font></span></b><b><span style="FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">则有</span></b></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 15.75pt; mso-layout-grid-align: none;"><b><span style="FONT-FAMILY: 黑体; mso-bidi-font-size: 10.5pt; mso-ascii-font-family: "Times New Roman";">想继续知道的给我D题答案!</span></b><b><span lang="EN-US" style="mso-bidi-font-size: 10.5pt; mso-fareast-font-family: 黑体;"><p></p></span></b></p> |
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