📄 第二节 用mathematica求极限和求微分.htm
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<P align=center class=MsoNormal
style="text-align: center; text-indent: 17.95pt; line-height: 200%"><b><SPAN
style="mso-hansi-font-family: Times New Roman; mso-ascii-font-family: Times New Roman"><font face="宋体" color="#FF0000" size="5">第二节</font></SPAN>
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<SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">用</SPAN><SPAN
lang=EN-US>Mathematica</SPAN><SPAN
style="mso-hansi-font-family: Times New Roman; mso-ascii-font-family: Times New Roman">求极限和求微分</SPAN></font></b></P>
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style="mso-hansi-font-family: Times New Roman; mso-ascii-font-family: Times New Roman"><font face="宋体" size="4">
极限是微积分的重要基础，微分是微积分的重要组成部分。本节分为两部分，我们将分别讨论</font></SPAN><font face="宋体" size="4"><SPAN
lang=EN-US>Mathematica4.0</SPAN><SPAN
style="mso-hansi-font-family: Times New Roman; mso-ascii-font-family: Times New Roman">处理极限和微分的方法。</SPAN></font></b></P>
<P class=MsoNormal style="line-height: 200%"><SPAN
style="mso-hansi-font-family: Times New Roman; mso-ascii-font-family: Times New Roman"><b><font face="宋体" size="5" color="#FF0000">一、<a name="极限">极限</a></font></b></SPAN></P>
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style="mso-hansi-font-family: Times New Roman; mso-ascii-font-family: Times New Roman"><b><font face="宋体" size="4">
为了掌握变量的变化规律，往往需要从它的变化过程中来判断它的变化趋势，于是极限方法就逐渐形成了。在高等数学中有很多重要的概念和方法都和极限有关，微积分学中处理变量的基本方法就是极限，这种方法是建立在无限观念的基础上的，因而它与处理常量的基本方法有着本质的区别。它已成为高等数学中的一种基本方法。研究极限将为学习好微积分打好基础。</font></b></SPAN></P>
<P class=MsoNormal style="text-indent: 17.95pt; line-height: 200%"><SPAN
lang=EN-US><b><font face="宋体"><font size="4">Mathematica4.0</font></font></b></SPAN><font face="宋体"><b><font size="4"><SPAN
style="mso-hansi-font-family: Times New Roman; mso-ascii-font-family: Times New Roman">提供的用于求解极限的函数如下：</SPAN></font></b></font></P>
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lang=EN-US><b><font face="宋体"><font size="4">Limit[expr,x-><SPAN style="mso-text-raise: -6.0pt"><!--[if gte vml 1]><V:SHAPETYPE id=_x0000_t75
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style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">可以为</SPAN><SPAN
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时expr的极限</SPAN></font></b></P>
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lang=EN-US><b><font face="宋体"><font size="4">Limit[expr,x-><SPAN style="mso-text-raise: -6.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1032
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时expr的极限</SPAN><SPAN lang=EN-US style="mso-spacerun: yes"> </SPAN></font></b></font></P>
<P align=left class=MsoNormal style="line-height: 200%"><b><SPAN
style="mso-hansi-font-family: Times New Roman; mso-ascii-font-family: Times New Roman"><font face="宋体" size="4">例</font></SPAN><font face="宋体" size="4"><SPAN
lang=EN-US>1</SPAN><SPAN
style="mso-hansi-font-family: Times New Roman; mso-ascii-font-family: Times New Roman">求下列极限：</SPAN></font></b></P>
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style="mso-hansi-font-family: Times New Roman; mso-ascii-font-family: Times New Roman"><font face="宋体" size="4">（</font></SPAN><font face="宋体" size="4"><SPAN
lang=EN-US>1</SPAN><SPAN
style="mso-hansi-font-family: Times New Roman; mso-ascii-font-family: Times New Roman">）</SPAN><SPAN
lang=EN-US><SPAN style="mso-text-raise: -10.0pt"><!--[if gte vml 1]><V:SHAPE
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