📄 第二节 用mathematica求极限和求微分.htm
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-> 0]</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[3]=1</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">(4)<SPAN
style="mso-spacerun: yes"> </SPAN>In[4]:=Limit[(x^2 - 1)/(2x^2 - x - 1), x
-> 1]</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[4]=<SPAN
style="mso-text-raise: -12.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1048
style="HEIGHT: 30.75pt; WIDTH: 12pt" o:ole="" type="#_x0000_t75"> <V:IMAGEDATA
o:title=""
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image042.wmz"></V:SHAPE><![endif]--><IMG src="images/2.htm39.gif"
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</font>
</b>
</SPAN></P>
<P align=left class=MsoNormal style="line-height: 200%"><b><font face="Times New Roman"><SPAN lang=EN-US><font size="4">(5)<SPAN
style="mso-spacerun: yes"> </SPAN>In[5]:=Limit[(x^2 - 1)/(2x^2 - x -
1), x -> Infinity]<SPAN style="mso-spacerun: yes"> </SPAN></font></SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"></SPAN></font><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"><font size="4"><br>
（</font></SPAN><font size="4"><font face="Times New Roman"><SPAN
lang=EN-US>* Infinity</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"></SPAN></font><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">指正无穷大</SPAN><font face="Times New Roman"><SPAN
lang=EN-US>*</SPAN></font><SPAN
style="mso-hansi-font-family: Times New Roman; mso-ascii-font-family: Times New Roman">）</SPAN></font></b></P>
<P align=left class=MsoNormal style="line-height: 200%"><SPAN
lang=EN-US><b><font face="Times New Roman" size="4"> Out[5]=<SPAN
style="mso-text-raise: -12.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1049
style="HEIGHT: 30.75pt; WIDTH: 12pt" o:ole="" type="#_x0000_t75"> <V:IMAGEDATA
o:title=""
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image044.wmz"></V:SHAPE><![endif]--><IMG src="images/2.htm40.gif"
v:shapes="_x0000_i1049" width="16" height="41"></SPAN><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1049"
DrawAspect="Content" ObjectID="_1048959263">
</o:OLEObject>
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</font>
</b>
</SPAN></P>
<P align=left class=MsoNormal style="line-height: 200%"><b><font face="Times New Roman"><SPAN
lang=EN-US><font size="4">(6) In[6]:=Limit[(x^2 - 1)/(2x^2 - x - 1), x -> -Infinity]<SPAN
style="mso-spacerun: yes"> </SPAN></font></SPAN><SPAN
style="mso-hansi-font-family: Times New Roman; mso-ascii-font-family: Times New Roman"></SPAN></font><SPAN
style="mso-hansi-font-family: Times New Roman; mso-ascii-font-family: Times New Roman"><font size="4"><br>
（</font></SPAN><font size="4"><font face="Times New Roman"><SPAN
lang=EN-US>*- Infinity</SPAN><SPAN
style="mso-hansi-font-family: Times New Roman; mso-ascii-font-family: Times New Roman"></SPAN></font><SPAN
style="mso-hansi-font-family: Times New Roman; mso-ascii-font-family: Times New Roman">指负无穷大</SPAN><font face="Times New Roman"><SPAN
lang=EN-US>*</SPAN><SPAN
style="mso-hansi-font-family: Times New Roman; mso-ascii-font-family: Times New Roman"></SPAN></font><SPAN
style="mso-hansi-font-family: Times New Roman; mso-ascii-font-family: Times New Roman">）</SPAN></font></b></P>
<P align=left class=MsoNormal style="line-height: 200%"><SPAN
lang=EN-US><b><font face="Times New Roman" size="4"> Out[6]=
<SPAN style="mso-text-raise: -12.0pt"><!--[if gte vml 1]><V:SHAPE
id=_x0000_i1050 style="HEIGHT: 30.75pt; WIDTH: 12pt" o:ole=""
type="#_x0000_t75"><V:IMAGEDATA o:title=""
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image044.wmz"></V:SHAPE><![endif]--><IMG src="images/2.htm41.gif"
v:shapes="_x0000_i1050" width="16" height="41"></SPAN><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1050"
DrawAspect="Content" ObjectID="_1048959264">
</o:OLEObject>
</xml><![endif]-->
</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">(7)<SPAN
style="mso-spacerun: yes"> </SPAN>In[7]:=Limit[Tan[Pi/4 - x]^Cot[x], x
-> 0]</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[7]=
<SPAN style="mso-text-raise: -12.0pt"><!--[if gte vml 1]><V:SHAPE
id=_x0000_i1051 style="HEIGHT: 30.75pt; WIDTH: 17.25pt" o:ole=""
type="#_x0000_t75"><V:IMAGEDATA o:title=""
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image038.wmz"></V:SHAPE><![endif]--><IMG src="images/2.htm42.gif"
v:shapes="_x0000_i1051" width="23" height="41"></SPAN><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1051"
DrawAspect="Content" ObjectID="_1048959265">
</o:OLEObject>
</xml><![endif]-->
</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">(8)<SPAN
style="mso-spacerun: yes"> </SPAN>In[8]:=Limit[(Sin[1/x] + Cos[1/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[8]=e</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">(9) In[9]:=Limit[(Sin[1/x] + Cos[1/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[9]=e</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">(10)<SPAN
style="mso-spacerun: yes"> </SPAN>In[10]:=Limit[(Cos[x^(1/2)])^(1/x), x
-> 0]</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[10]=<SPAN
style="mso-text-raise: -14.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1052
style="HEIGHT: 33pt; WIDTH: 20.25pt" o:ole="" type="#_x0000_t75"> <V:IMAGEDATA
o:title=""
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image048.wmz"></V:SHAPE><![endif]--><IMG src="images/2.htm43.gif"
v:shapes="_x0000_i1052" width="27" height="44"></SPAN><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1052"
DrawAspect="Content" ObjectID="_1048959266">
</o:OLEObject>
</xml><![endif]-->
</font>
</b>
</SPAN></P>
<P align=left class=MsoNormal style="line-height: 200%"><b><font face="Times New Roman"><SPAN lang=EN-US><font size="4">(11)<SPAN
style="mso-spacerun: yes"> </SPAN>In[11]:=Limit[ArcTan[1/(1 - x)], x ->
1, Direction -> 1]<SPAN style="mso-spacerun: yes"> </SPAN></font></SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"></SPAN></font><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"><font size="4"><br>
（</font></SPAN><font size="4"><font face="Times New Roman"><SPAN
lang=EN-US>*</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"></SPAN></font><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">沿正向靠向于</SPAN><font face="Times New Roman"><SPAN
lang=EN-US>1</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"></SPAN></font><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">，即</SPAN><font face="Times New Roman"><SPAN
lang=EN-US>1</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"></SPAN></font><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">的左极限</SPAN><font face="Times New Roman"><SPAN
lang=EN-US>*</SPAN></font><SPAN
style="mso-hansi-font-family: Times New Roman; mso-ascii-font-family: Times New Roman">）</SPAN></font></b></P>
<P align=left class=MsoNormal style="line-height: 200%"><SPAN
lang=EN-US><b><font face="Times New Roman" size="4"> Out[11]=<SPAN
style="mso-text-raise: -12.0pt"><!--[if gte vml 1]><V:SHAPE id=_x0000_i1053
style="HEIGHT: 30.75pt; WIDTH: 12.75pt" o:ole="" type="#_x0000_t75">
<V:IMAGEDATA o:title=""
src="file:///C:/WINDOWS/TEMP/msoclip1/01/clip_image050.wmz"></V:SHAPE><![endif]--><IMG src="images/2.htm44.gif"
v:shapes="_x0000_i1053" width="17" height="41"></SPAN><!--[if gte mso 9]><xml>
<o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1053"
DrawAspect="Content" ObjectID="_1048959267">
</o:OLEObject>
</xml><![endif]-->
</font>
</b>
</SPAN></P>
<P align=left class=MsoNormal style="line-height: 200%"><b><font face="Times New Roman"><SPAN
lang=EN-US><font size="4">(12)<SPAN style="mso-spacerun: yes"> </SPAN>In[12]:=Limit[ArcTan[1/(1 - x)], x -> 1, Direction -> -1]<SPAN
style="mso-spacerun: yes"> </SPAN></font></SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"></SPAN></font><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"><font size="4"><br>
（</font></SPAN><font size="4"><font face="Times New Roman"><SPAN
lang=EN-US>*</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"></SPAN></font><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">沿负向靠向于</SPAN><font face="Times New Roman"><SPAN
lang=EN-US>1</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"></SPAN></font><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">，即</SPAN><font face="Times New Roman"><SPAN
lang=EN-US>1</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'"></SPAN></font><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'; mso-ascii-font-family: 'Times New Roman'">的右极限</SPAN><font face="Times New Roman"><SPAN
lang=EN-US>*</SPAN></font><SPAN
style="mso-hansi-font-family: Times New Roman; mso-ascii-font-family: Times New Roman">）</SPAN></font></b></P>
<P align=left class=MsoNormal style="line-height: 200%"><SPAN
lang=EN-US><b><font face="Times New Roman" size="4"> Out[12]=
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