<html lang=en-x-mtfrom-zh><head><script>(function(){var b=window,f="chrome";(function(){function g(a){this.t={};this.tick=function(a,d,c){this.t[a]=[void 0!=c?c:(new Date).getTime(),d];if(void 0==c)try{b.console.timeStamp("CSI/"+a)}catch(e){}};this.tick("start",null,a)}var a;b.performance&&(a=b.performance.timing);var h=a?new g(a.responseStart):new g;b.jstiming={Timer:g,load:h};if(a){var d=a.navigationStart,e=a.responseStart;0<d&&e>=d&&(b.jstiming.srt=e-d)}if(a){var c=b.jstiming.load;0<d&&e>=d&&(c.tick("_wtsrt",void 0,d),c.tick("wtsrt_","_wtsrt",e),c.tick("tbsd_","wtsrt_"))}try{a= null,b[f]&&b[f].csi&&(a=Math.floor(b[f].csi().pageT),c&&0<d&&(c.tick("_tbnd",void 0,b[f].csi().startE),c.tick("tbnd_","_tbnd",d))),null==a&&b.gtbExternal&&(a=b.gtbExternal.pageT()),null==a&&b.external&&(a=b.external.pageT,c&&0<d&&(c.tick("_tbnd",void 0,b.external.startE),c.tick("tbnd_","_tbnd",d))),a&&(b.jstiming.pt=a)}catch(k){}})();})(); </script><script src="http://translate.googleusercontent.com/translate/releases/twsfe_w_20150330_RC03/r/js/translate_c.js"></script><script>_intlStrings._originalText = "-NeSe:";_intlStrings._interfaceDirection="ltr";_intlStrings._interfaceAlign="left";_intlStrings._langpair="zh-CN|en";_intlStrings._feedbackUrl="http://translate.google.com/translate_suggestion";_intlStrings._currentBy="S_MRvы/f1u%2$s(W %1$s[bv";_intlStrings._unknown="ZO Tы";_intlStrings._suggestTranslation="f}Yvы^" ;_intlStrings._submit="cO^";_intlStrings._suggestThanks="a"`:N Google ыcOы^0";_intlStrings._reverse=false;</script><style type="text/css">.google-src-text {display: none !important} .google-src-active-text {display: block!important;color:black!important; font-size:12px!important;font-family:arial,sans-serif!important}.google-src-active-text a {font-size:12px!important}.google-src-active-text a:link {color:#00c!important;text-decoration:underline!important}.google-src-active-text a:visited {color:purple!important;text-decoration:underline!important}.google-src-active-text a:active {color:red!important;text-decoration:underline!important}</style><meta http-equiv="X-Translated-By" content="Google"><link href=http://drhuang.com/chinese/science/mathematics/handbook/a263/a263.htm hreflang=zh-CN rel="alternate machine-translated-from"><base href=http://drhuang.com/chinese/science/mathematics/handbook/a263/a263.htm /><meta http-equiv=Content-Type content="text/html; charset=UTF-8"><link rel=Edit-Time-Data href=./3.files/editdata.mso><link rel=OLE-Object-Data href=./3.files/oledata.mso><title> 3 </title><style><!-- .Normal {text-align:justify; text-justify:inter-ideograph; font-size:12.0pt; font-family:"Times New Roman";} --> </style></head><body lang=ZH-CN class=Normal bgcolor=#ffffff><iframe src="http://translate.google.com.au/translate_un?depth=1&hl=zh-CN&rurl=translate.google.com.au&sl=zh-CN&tl=en&u=http://drhuang.com/chinese/science/mathematics/handbook/a263/a263.htm&lang=zh-CN&usg=ALkJrhg1Z5zVlNGHP62HicczxRlnYPM84g" width=0 height=0 frameborder=0 style="width:0px;height:0px;border:0px;display:none;"></iframe><p> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><span lang=EN-US>3.</span> <font face="[SO"><span style='font-family:wiSO_GB2312; "Times New Roman"'>SSfQpev[IN0Vb_Nyr_</span></font></span> <span lang=EN-US>3.</span> <font face="[SO"><span style='font-family:wiSO_GB2312; "Times New Roman"'>Definition of inverse hyperbolic functions, graphics and features</span></font></span> </p><p> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><span lang=EN-US style="font-family:wiSO_GB2312">[ <font face="[SO">SSfQpev[INSvQ[peh_</font> ]</span></span> <span lang=EN-US style="font-family:wiSO_GB2312"><font face="[SO">[Definition inverse hyperbolic function and its logarithmic expression]</font></span></span> </p><table border=0 cellspacing=0 cellpadding=0><tr><td width=138 valign=top class=Normal><pre align=center style=text-align:center> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><span style="font-family:wiSO_GB2312"><font face="[SO">Q</font></span></span> <span style="font-family:wiSO_GB2312"><font face="[SO">Letter</font></span></span> <span style="font-family:wiSO_GB2312"><font face="[SO"><span>&nbsp; </span></font></span> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><span style="font-family:wiSO_GB2312"><font face="[SO">pe</font></span></span> <span style="font-family:wiSO_GB2312"><font face="[SO">Number</font></span></span> </pre></td><td width=138 valign=top class=Normal><pre align=center style=text-align:center> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><span style="font-family:wiSO_GB2312"><font face="[SO"></font></span></span> <span style="font-family:wiSO_GB2312"><font face="[SO">Remember</font></span></span> <span style="font-family:wiSO_GB2312"><font face="[SO"><span>&nbsp; </span></font></span> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><span style="font-family:wiSO_GB2312"><font face="[SO">S</font></span></span> <span style="font-family:wiSO_GB2312"><font face="[SO">Number</font></span></span> </pre></td><td width=138 valign=top class=Normal><p align=center style=text-align:center> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><span style="font-family:wiSO_GB2312"><font face="[SO">[peh_</font></span></span> <span style="font-family:wiSO_GB2312"><font face="[SO">Logarithmic expression</font></span></span> <span style="font-family:wiSO_GB2312"><span lang=EN-US></span></span> </p></td></tr><tr><td width=138 valign=top class=Normal><p align=center style=text-align:center> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><span style="font-family:wiSO_GB2312"><font face="[SO">SSfck&_</font></span></span> <span style="font-family:wiSO_GB2312"><font face="[SO">Inverse hyperbolic sine</font></span></span> <span style="font-family:wiSO_GB2312"><span lang=EN-US></span></span> </p></td><td width=195 valign=top class=Normal><p> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><span style="font-family:wiSO_GB2312"><font face="[SO"></font></span> <span lang=EN-US><i>x</i> = sh <i>y</i> ,</span></span> <span style="font-family:wiSO_GB2312"><font face="[SO">If</font></span> <span lang=EN-US><i>x</i> = sh <i>y,</i></span></span> </p><p> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><span style='font-family:wiSO_GB2312;"Times New Roman"'><font face="[SO">R</font></span> <span lang=EN-US><i>y</i> = Ar sh <i>x</i></span></span> <span style='font-family:wiSO_GB2312;"Times New Roman"'><font face="[SO">Then</font></span> <span lang=EN-US><i>y</i> = Ar sh <i>x</i></span></span> </p></td><td width=312 valign=top class=Normal><p> <sub><span lang=EN-US style="font-family:wiSO_GB2312"><img width=100 height=28 src=./3.files/image002.gif v:shapes=_x0000_i1025></span></sub> </p></td></tr><tr><td width=138 valign=top class=Normal><p align=center style=text-align:center> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><span style="font-family:wiSO_GB2312"><font face="[SO">SSfYO&_</font></span></span> <span style="font-family:wiSO_GB2312"><font face="[SO">Inverse hyperbolic cosine</font></span></span> </p></td><td width=195 valign=top class=Normal><p><span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><font face="[SO"><span style="font-family:wiSO_GB2312"></span></font> <span lang=EN-US><i>x</i> =</span></span> <font face="[SO"><span style="font-family:wiSO_GB2312">If</span></font> <span lang=EN-US><i>x</i> =</span></span> <span lang=EN-US><i> </i></span> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><span lang=EN-US>ch <i>y</i> ,</span></span> <span lang=EN-US>ch <i>y,</i></span></span> </p><p> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><span style='font-family:wiSO_GB2312;"Times New Roman"'><font face="[SO">R</font></span> <span lang=EN-US><i>y</i> = Ar ch <i>x</i></span></span> <span style='font-family:wiSO_GB2312;"Times New Roman"'><font face="[SO">Then</font></span> <span lang=EN-US><i>y</i> = Ar ch <i>x</i></span></span> </p></td><td width=312 valign=top class=Normal><p> <sub><span lang=EN-US style="font-family:wiSO_GB2312"><img width=184 height=28 src=./3.files/image004.gif v:shapes=_x0000_i1026></span></sub> </p></td></tr><tr><td width=138 valign=top class=Normal><p align=center style=text-align:center> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><font face="[SO"><span style="font-family:wiSO_GB2312">SSfckR</span></font></span> <font face="[SO"><span style="font-family:wiSO_GB2312">Inverse hyperbolic tangent</span></font></span> <span style="font-family:wiSO_GB2312"><span lang=EN-US></span></span> </p></td><td width=195 valign=top class=Normal><p> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><font face="[SO"><span style="font-family:wiSO_GB2312"></span></font> <span lang=EN-US><i>x</i> = th <i>y</i> ,</span></span> <font face="[SO"><span style="font-family:wiSO_GB2312">If</span></font> <span lang=EN-US><i>x</i> = th <i>y,</i></span></span> </p><p> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><span style='font-family:wiSO_GB2312;"Times New Roman"'><font face="[SO">R</font></span> <span lang=EN-US><i>y</i> = Ar th <i>x</i></span></span> <span style='font-family:wiSO_GB2312;"Times New Roman"'><font face="[SO">Then</font></span> <span lang=EN-US><i>y</i> = Ar th <i>x</i></span></span> </p></td><td width=312 valign=top class=Normal><p> <sub><span lang=EN-US style="font-family:wiSO_GB2312"><img width=192 height=41 src=./3.files/image006.gif v:shapes=_x0000_i1027></span></sub> </p></td></tr><tr><td width=138 valign=top class=Normal><p align=center style=text-align:center> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><font face="[SO"><span style="font-family:wiSO_GB2312">SSfYOR</span></font></span> <font face="[SO"><span style="font-family:wiSO_GB2312">Inverse hyperbolic cotangent</span></font></span> <span style="font-family:wiSO_GB2312"><span lang=EN-US></span></span> </p></td><td width=195 valign=top class=Normal><p> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><font face="[SO"><span style="font-family:wiSO_GB2312"></span></font> <span lang=EN-US><i>x</i> = cth <i>y</i> ,</span></span> <font face="[SO"><span style="font-family:wiSO_GB2312">If</span></font> <span lang=EN-US><i>x</i> = cth <i>y,</i></span></span> </p><p> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><span style='font-family:wiSO_GB2312;"Times New Roman"'><font face="[SO">R</font></span> <span lang=EN-US><i>y</i> = Ar cth <i>x</i></span></span> <span style='font-family:wiSO_GB2312;"Times New Roman"'><font face="[SO">Then</font></span> <span lang=EN-US><i>y</i> = Ar cth <i>x</i></span></span> </p></td><td width=312 valign=top class=Normal><p> <sub><span lang=EN-US style="font-family:wiSO_GB2312"><img width=192 height=41 src=./3.files/image008.gif v:shapes=_x0000_i1031></span></sub> </p></td></tr><tr><td width=138 valign=top class=Normal><p align=center style=text-align:center> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><font face="[SO"><span style="font-family:wiSO_GB2312">SSfckrR</span></font></span> <font face="[SO"><span style="font-family:wiSO_GB2312">Inverse Hyperbolic Secant</span></font></span> <span style="font-family:wiSO_GB2312"><span lang=EN-US></span></span> </p></td><td width=195 valign=top class=Normal><p> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><font face="[SO"><span style="font-family:wiSO_GB2312"></span></font> <span lang=EN-US><i>x</i> = sech <i>y</i> ,</span></span> <font face="[SO"><span style="font-family:wiSO_GB2312">If</span></font> <span lang=EN-US><i>x</i> = sech <i>y,</i></span></span> </p><p><span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><font face="[SO"><span style='font-family:wiSO_GB2312;"Times New Roman"'>R</span></font> <span lang=EN-US><i>y</i> = Ar sech <i>x</i></span></span> <font face="[SO"><span style='font-family:wiSO_GB2312;"Times New Roman"'>Then</span></font> <span lang=EN-US><i>y</i> = Ar sech <i>x</i></span></span> </p></td><td width=312 valign=top class=Normal><p> <sub><span lang=EN-US style="font-family:wiSO_GB2312"><img width=200 height=52 src=./3.files/image010.gif v:shapes=_x0000_i1032></span></sub> </p></td></tr><tr><td width=138 valign=top class=Normal><p align=center style=text-align:center> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><span style="font-family:wiSO_GB2312"><font face="[SO">SSfYOrR</font></span></span> <span style="font-family:wiSO_GB2312"><font face="[SO">Inverse hyperbolic cosecant</font></span></span> <span style="font-family:wiSO_GB2312"><span lang=EN-US></span></span> </p></td><td width=195 valign=top class=Normal><p> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><span style="font-family:wiSO_GB2312"><font face="[SO"></font></span> <span lang=EN-US><i>x</i> = csch <i>x</i> ,</span></span> <span style="font-family:wiSO_GB2312"><font face="[SO">If</font></span> <span lang=EN-US><i>x</i> = csch <i>x,</i></span></span> </p><p> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><font face="[SO"><span style='font-family:wiSO_GB2312;"Times New Roman"'>R</span></font> <span lang=EN-US><i>y</i> = Ar csch <i>x</i></span></span> <font face="[SO"><span style='font-family:wiSO_GB2312;"Times New Roman"'>Then</span></font> <span lang=EN-US><i>y</i> = Ar csch <i>x</i></span></span> </p></td><td width=312 valign=top class=Normal><p> <sub><span lang=EN-US style="font-family:wiSO_GB2312"><img width=216 height=51 src=./3.files/image012.gif v:shapes=_x0000_i1033></span></sub> </p></td></tr></table><pre> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><span style="font-family:wiSO_GB2312">[ <font face="Verdana, Arial, Helvetica, sans-serif">SSfQpevVb_Nyr_</font> ]</span></span> <font face="Verdana, Arial, Helvetica, sans-serif"><span style="font-family:wiSO_GB2312">[Graphics and features inverse hyperbolic function]</span></font></span> </pre><pre><span>&nbsp;&nbsp; </span> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><span style="font-family:wiSO_GB2312"><font face="[SO">SSfck&_f~SSfYO&_f~</font></span></span> <span style="font-family:wiSO_GB2312"><font face="[SO">Inverse hyperbolic sine curve inverse hyperbolic cosine curve</font></span></span> </pre><pre><span>&nbsp;&nbsp; </span> <sub><img width=75 height=21 src=./3.files/image014.gif v:shapes=_x0000_i1034><img width=76 height=21 src=./3.files/image016.gif v:shapes=_x0000_i1035></sub> </pre><p><span>&nbsp;&nbsp; </span><img width=190 height=140 src=./3.files/image018.jpg v:shapes=_x0000_i1036><img width=178 height=141 src=./3.files/image020.jpg v:shapes=_x0000_i1037></p><pre> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><span style="font-family:wiSO_GB2312"><font face="[SO">f~sQNSp[y</font> . <font face="[SO"> f~sQN<i>x</i>t[y</font> .</span></span> <span style="font-family:wiSO_GB2312"><font face="[SO">Curve symmetric about the origin of the curve on the <i>x-axis</i> symmetry.</font></span></span> </pre><pre><span>&nbsp;&nbsp; </span> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><span style='font-family: wiSO_GB2312;"Times New Roman"'><font face="[SO">bp</font>  <font face="[SO"> Tf~[y-N_</font> </span></span> <span style='font-family: wiSO_GB2312;"Times New Roman"'><font face="[SO">Inflection (with the curve center of symmetry):</font></span></span> <span>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><span style='font-family:wiSO_GB2312;"Times New Roman"'><font face="[SO">vp</font> </span></span> <font face="[SO"><span style='font-family:wiSO_GB2312;"Times New Roman"'>Vertex:</span></font></span> <sub><span lang=EN-US><img width=44 height=21 src=./3.files/image022.gif v:shapes=_x0000_i1038 align=absmiddle></span></sub> </pre><pre><span>&nbsp;&nbsp; </span> <sub><img width=47 height=21 src=./3.files/image024.gif v:shapes=_x0000_i1039 align=absmiddle></sub> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><span style='font-family:wiSO_GB2312;"Times New Roman"'> <font face="[SO">勹pR~es:N</font></span> <span lang=EN-US>1</span></span> <font face="[SO"><span style='font-family:wiSO_GB2312;"Times New Roman"'>The slope of</span></font> <span lang=EN-US>a</span> <font face="[SO"><span style='font-family:wiSO_GB2312;"Times New Roman"'>tangent point</span></font></span> </pre><pre><span>&nbsp;&nbsp; </span> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><span style='font-family: wiSO_GB2312;"Times New Roman"'><font face="[SO">SSfckRf~</font></span></span> <span style='font-family: wiSO_GB2312;"Times New Roman"'><font face="[SO">Inverse hyperbolic tangent curve</font></span></span> <span>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><font face="[SO"><span style='font-family:wiSO_GB2312;"Times New Roman"'>SSfYORf~</span></font></span> <font face="[SO"><span style='font-family:wiSO_GB2312;"Times New Roman"'>Inverse hyperbolic cotangent curve</span></font></span> </pre><pre><span>&nbsp;&nbsp; </span> <sub><img width=75 height=21 src=./3.files/image026.gif v:shapes=_x0000_i1040><img width=81 height=21 src=./3.files/image028.gif v:shapes=_x0000_i1041></sub> </pre><p><span>&nbsp;&nbsp;&nbsp; </span><img width=139 height=171 src=./3.files/image030.jpg v:shapes=_x0000_i1042><img width=184 height=172 src=./3.files/image032.jpg v:shapes=_x0000_i1043></p><pre><span>&nbsp;&nbsp; </span> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><span style="font-family:wiSO_GB2312"><font face="[SO">f~sQNSp[y</font> . <font face="[SO">f~sQNSp[y</font> .</span></span> <font face="[SO"><span style="font-family:wiSO_GB2312">Curve symmetrical about the origin curve symmetrical about the origin.</span></font></span> </pre><pre><span>&nbsp;&nbsp; </span> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><span style="font-family:wiSO_GB2312"><font face="[SO">bp</font>  <font face="[SO"> Tf~[y-N_</font>  <font face="[SO"> Nޏ~p</font> </span></span> <font face="[SO"><span style="font-family:wiSO_GB2312">Inflection (curve with the center of symmetry): discontinuity:</span></font></span> <span style="font-family:wiSO_GB2312"><sub><img width=45 height=19 src=./3.files/image034.gif v:shapes=_x0000_i1044 align=absmiddle></sub></span> </pre><pre><span>&nbsp;&nbsp; </span> <sub><img width=47 height=21 src=./3.files/image036.gif v:shapes=_x0000_i1045 align=absmiddle></sub> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"> <span style="font-family:wiSO_GB2312"><font face="[SO">勹pR~es:N</font> 1 <font face="[SO">nя~</font> </span></span> <span style="font-family:wiSO_GB2312"><font face="[SO">The slope of</font> a <font face="[SO">tangent point asymptote:</font></span></span> <span style="font-family:wiSO_GB2312"><sub><img width=92 height=21 src=./3.files/image038.gif v:shapes=_x0000_i1046 align=absmiddle></sub></span> </pre><pre> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><font face="[SO"><span style="font-family:wiSO_GB2312"> SSfckrRf~SSfYOrRf~</span></font></span> <font face="[SO"><span style="font-family:wiSO_GB2312">Inverse hyperbolic secant hyperbolic cosecant curve curve</span></font></span> </pre><pre><span>&nbsp;&nbsp; </span> <sub><img width=89 height=21 src=./3.files/image040.gif v:shapes=_x0000_i1047><img width=89 height=21 src=./3.files/image042.gif v:shapes=_x0000_i1048></sub> </pre><p><span>&nbsp;&nbsp;&nbsp; </span><img width=172 height=222 src=./3.files/image044.jpg v:shapes=_x0000_i1049><img width=221 height=219 src=./3.files/image046.jpg v:shapes=_x0000_i1050></p><p> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><span style="font-family:wiSO_GB2312"><font face="[SO">f~sQN<i>x</i>t[y</font> . <font face="[SO">f~sQNSp[y</font> .</span></span> <font face="[SO"><span style="font-family:wiSO_GB2312">Curve on <i>the x-axis</i> symmetry. Curve symmetric about the origin.</span></font></span> </p><p><span>&nbsp;&nbsp;&nbsp; </span> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><span style='font-family:wiSO_GB2312;"Times New Roman"'><font face="[SO">vp</font> </span></span> <span style='font-family:wiSO_GB2312;"Times New Roman"'><font face="[SO">Vertex:</font></span></span> <sub><img width=44 height=21 src=./3.files/image047.gif v:shapes=_x0000_i1051 align=absmiddle></sub> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><span style='font-family:wiSO_GB2312;"Times New Roman"'><font face="[SO"> Nޏ~p</font> </span></span> <span style='font-family:wiSO_GB2312;"Times New Roman"'><font face="[SO">Discontinuous points:</font></span></span> <span lang=EN-US><sub><img width=37 height=19 src=./3.files/image049.gif v:shapes=_x0000_i1052 align=absmiddle></sub></span> </p><p><span>&nbsp;&nbsp;&nbsp; </span> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><span style='font-family:wiSO_GB2312;"Times New Roman"'><font face="[SO">bp</font> </span></span> <span style='font-family:wiSO_GB2312;"Times New Roman"'><font face="[SO">Inflection point:</font></span></span> <sub><img width=119 height=53 src=./3.files/image051.gif v:shapes=_x0000_i1053 align=absmiddle></sub> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><span style='font-family:wiSO_GB2312;"Times New Roman"'><font face="[SO">nя~</font> </span></span> <span style='font-family:wiSO_GB2312;"Times New Roman"'><font face="[SO">Asymptote:</font></span></span> <span lang=EN-US><sub><img width=84 height=21 src=./3.files/image053.gif v:shapes=_x0000_i1054 align=absmiddle></sub></span> </p><p><span>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span> <span class="notranslate" onmouseover="_tipon(this)" onmouseout="_tipoff()"><span class="google-src-text" style="direction: ltr; text-align: left"><span style='font-family:wiSO_GB2312; "Times New Roman"'><font face="[SO">T</font></span></span> <span style='font-family:wiSO_GB2312; "Times New Roman"'><font face="[SO">And</font></span></span> <span lang=EN-US><sub><img width=128 height=53 src=./3.files/image055.gif v:shapes=_x0000_i1055 align=absmiddle></sub></span> </p></body> <script>_addload(function(){_setupIW();_csi('zh-CN','en','http://drhuang.com/chinese/science/mathematics/handbook/a263/a263.htm');});</script></html>