📄 第二节 用mathematica求极限和求微分.htm
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<P align=left class=MsoNormal style="line-height: 200%"><SPAN
lang=EN-US><b><font face="Times New Roman" size="4">(13)<SPAN style="mso-spacerun: yes">
</SPAN>In[13]:=Limit[Log[1
+ E^x]/x, x -> -Infinity]</font></b></SPAN></P>
<P align=left class=MsoNormal style="line-height: 200%"><SPAN
lang=EN-US><b><font face="Times New Roman" size="4"> Out[13]=0</font>
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<P align=left class=MsoNormal style="line-height: 200%"><SPAN
lang=EN-US><b><font face="Times New Roman" size="4">(14)<SPAN style="mso-spacerun: yes"> </SPAN>In[14]:=Limit[Log[1
+ E^x]/x, x -> Infinity]</font></b></SPAN></P>
<P align=left class=MsoNormal style="line-height: 200%"><SPAN
lang=EN-US><b><font face="Times New Roman" size="4"> Out[14]=1</font>
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<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">二、<a name="微分">微分</a></font></b></span></P>
<P align=left class=MsoNormal
style="text-indent: 20.9pt; line-height: 200%; margin-left: -2.95pt"><SPAN
style="mso-hansi-font-family: Times New Roman; mso-ascii-font-family: Times New Roman"><b><font face="宋体" size="4">微分学是微积分的重要组成部分，它主要包含导数与微分，其中导数反映出函数相对于自变量的变化快慢的程度，微分则指明当自变量有微小变化时，函数大体上变化多少。从实际中来又紧密联系现实世界的实际是微分的显著特点，对初学微分的同学，在学习方法上，要改变那种偏重解题技巧而忽视数学概念的思想方法的习惯，要知道微积分的精华，并不仅仅是解题的技巧，而是能更多的体会隐藏在各基本概念之后的数学思想，如果数学思想不明确，即使有一定的解题技巧，也不一定得到有价值的科学结论。</font></b></SPAN></P>
<P align=left class=MsoNormal
style="text-indent: 20.9pt; line-height: 200%; margin-left: -2.95pt"><SPAN
lang=EN-US><b><font face="宋体"><font size="4">Mathematica</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">关于导数和微分的命令如下：</SPAN></font></b></font></P>
<P align=left class=MsoNormal
style="text-indent: 20.9pt; line-height: 200%; margin-left: -2.95pt"><font color="#FF0000" face="宋体"><b><SPAN
style="mso-hansi-font-family: Times New Roman; mso-ascii-font-family: Times New Roman"><font size="4">导数命令格式： </font></SPAN></b></font></P>
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style="line-height: 200%; margin-left: 21pt"><b><font face="宋体" size="4"><span style="mso-font-kerning: 0pt" lang="EN-US">
D[f, x] f的导数或偏导数<!--[if gte vml 1]><V:SHAPE
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<O:P></O:P></span></font></b></P>
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style="line-height: 200%; margin-left: 21pt"><b><font face="宋体" size="4"><span style="mso-font-kerning: 0pt" lang="EN-US">
</span></font><span style="mso-font-kerning: 0pt" lang="EN-US"><font face="宋体" size="4">D[f,
<!--[if gte vml 1]><V:SHAPE
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v:shapes="_x0000_i1056" width="52" height="11">] f的高阶混合偏导数<!--[if gte vml 1]><V:SHAPE id=_x0000_i1057
style="HEIGHT: 33.75pt; WIDTH: 57.75pt" o:ole="" type="#_x0000_t75">
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<O:P></O:P></span></font></span></b></P>
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style="line-height: 200%; margin-left: 21pt"><b><font face="宋体" size="4"><span style="mso-font-kerning: 0pt" lang="EN-US">
</span></font><span style="mso-font-kerning: 0pt" lang="EN-US"><font face="宋体" size="4">D[f, {x, n}]
f对x求n阶导数或偏导数<O:P>
</O:P></font></span></b></P>
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style="line-height: 200%; margin-left: 21pt"><b><font face="宋体" size="4"><span style="mso-font-kerning: 0pt" lang="EN-US">
</span></font><span style="mso-font-kerning: 0pt" lang="EN-US"><font face="宋体" size="4">D[f, x，NonConstants->{<!--[if gte vml 1]><V:SHAPE id=_x0000_i1058
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}] <!--[if gte vml 1]><V:SHAPE id=_x0000_i1059
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,<br>
其中<!--[if gte vml 1]><V:SHAPE
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是关于x的函数以上函数当f为单变量函数时，指f对x的导数。</font></span></b></P>
<P align=left class=MsoNormal
style="line-height: 200%; margin-left: 21pt"><b><span style="mso-font-kerning: 0pt" lang="EN-US"><font face="宋体" size="4">以下为<font color="#FF0000">全微分</font>命令格式：<O:P>
</O:P></font></span></b></P>
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style="line-height: 200%; margin-left: 21pt"><b><font face="宋体" size="4"><span style="mso-font-kerning: 0pt" lang="EN-US">
</span></font><SPAN lang=EN-US
style="mso-font-kerning: 0pt"><font face="宋体" size="4">Dt[f]
f的微分或全微分df<O:P> </O:P></font></SPAN></b></P>
<P align=left class=MsoNormal
style="line-height: 200%; margin-left: 21pt"><b><font face="宋体" size="4"><span style="mso-font-kerning: 0pt" lang="EN-US">
</span></font><span style="mso-font-kerning: 0pt" lang="EN-US"><font face="宋体" size="4">Dt[f, x]
函数f对x的导数df/dx<O:P>
</O:P></font></span></b></P>
<P align=left class=MsoNormal
style="line-height: 200%; margin-left: 21pt"><b><font face="宋体" size="4"><span style="mso-font-kerning: 0pt" lang="EN-US">
</span></font><span style="mso-font-kerning: 0pt" lang="EN-US"><font face="宋体" size="4">Dt[f, {x, n}]
f对x求n阶导数<O:P>
</O:P></font></span></b></P>
<P align=left class=MsoNormal style="line-height: 200%; margin-left: 21pt"><b><font face="宋体" size="4"><span style="mso-font-kerning: 0pt" lang="EN-US">
</span></font></b><font face="宋体"><b><span style="mso-font-kerning: 0pt" lang="EN-US"><font size="4">Dt[f,
x，NonConstants->{<!--[if gte vml 1]><V:SHAPE id=_x0000_i1061
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}] <!--[if gte vml 1]><V:SHAPE id=_x0000_i1062
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,其中<!--[if gte vml 1]><V:SHAPE
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是常数<O:P>
</font></span></b><font size="4"><SPAN lang=EN-US
style="mso-hansi-font-family: Times New Roman; mso-font-kerning: 0pt"><b>
</O:P></b></SPAN></font></font></P>
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</span></font></b><SPAN
lang=EN-US style="mso-font-kerning: 0pt"><b><font face="宋体" size="4">y/:Dt[y,x]=0<SPAN
style="mso-spacerun: yes">
</SPAN>设置<SPAN style="mso-text-raise: -12.0pt"><!--[if gte vml 1]><V:SHAPE
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=0<O:P> </O:P></font></b></SPAN></P>
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