Intensidad de variación relativa

<body topmargin=0 leftmargin=0 marginheight=0 marginwidth=0> <table cellpadding=0 cellspacing=0 border=0><tr> <td valign="top" colspan=3 height=24 BGCOLOR="#006666" TEXT="#080000"> <div> <B>C á l c u l o   2 1</B><FONT SIZE="4" COLOR="#FFCC66" FACE="Bell MT" ><B> </B></FONT><FONT SIZE="4" COLOR="#FFFFCC" FACE="Bell MT" >   </FONT><B>  </B>|   <A HREF="index.htm" TARGET="_top" TITLE="Cálculo 21"><U>Home</U></A>  |  <A HREF="id98.htm" TARGET="_top" TITLE="Contenido"><U>Contenido</U></A>  |  <A HREF="id307.htm" TARGET="_top" TITLE="Introducción al cálculo diferencial"><U>Cálculo diferencial</U></A>  |</div> <bR> <div> </div> </td> </tr><tr> <td valign="top" rowspan="2" width=160 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> <B> <script async src="//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:inline-block;width:160px;height:600px" data-ad-client="ca-pub-1578463498418701" data-ad-slot="3073775660"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script>  </B></div> </td> <td valign="top" height=432 colspan=2 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> Intensidad de variación relativa</div> <bR> <div>  <script async src="//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:block" data-ad-client="ca-pub-1578463498418701" data-ad-slot="3926688482" data-ad-format="auto" data-full-width-responsive="true"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script>  </div> <bR> <div> <TABLE BORDER="1" CELLPADDING="1" CELLSPACING="1" WIDTH="612" BORDERCOLORLIGHT="#006600" BORDERCOLORDARK="#009900" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP COLSPAN=3 BGCOLOR=#FFFFCC HEIGHT= 191 WIDTH="600"><div>  <A NAME="ejercicios_resueltos"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" ><B>Ejercicios resueltos</B></FONT></div> <div> <FONT SIZE="3" COLOR="#0000FF" FACE="Times New Roman" ><B>          </B></FONT><FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" ><B>E</B></FONT>n los ejercicios <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" >1</FONT> a <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" >3</FONT>, una partícula se desplaza a lo largo de una recta horizontal de acuerdo con la ecuación indicada donde <I>s</I> centímetros representa la distancia de la partícula desde un punto O a los <I>t</I> segundos. Determine la velocidad instantánea <I>v</I>(<I>t</I>) cm/s a los <I>t</I> segundos; y luego calcule <I>v</I>(<I>t</I><FONT SIZE="1" COLOR="#000000" FACE="Times New Roman" >1</FONT>) para el valor particular de <I>t</I><FONT SIZE="1" COLOR="#000000" FACE="Times New Roman" >1</FONT> indicado. </div> <div>            <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" ><B>E</B></FONT>n los ejercicios <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" >4</FONT> y <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" >5</FONT>, una partícula se desplaza a lo largo de una recta horizontal de acuerdo con la ecuación indicada, donde <I>s</I> centímetros es la distancia dirigida de la partícula desde un punto O a los <I>t</I> segundos. El sentido positivo es a la derecha. Determine los intervalos de tiempo cuando la partícula se desplaza a la derecha y cuando lo hace a la izquierda. También determine cuándo la partícula cambia de sentido. Muestre el comportamiento de la partícula con una figura.</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 48 ><NOBR><div> <A HREF="#1" TITLE="Intensidad de variación relativa"><U><IMG SRC="1e9c89190.gif" border=0 width="137" height="25" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> <tD VALIGN=TOP WIDTH="198"><div> <A HREF="#2" TITLE="Intensidad de variación relativa"><U><IMG SRC="1e9d7c290.gif" border=0 width="124" height="41" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> <tD VALIGN=TOP WIDTH="198"><div> <A HREF="#3" TITLE="Intensidad de variación relativa"><U><IMG SRC="1e9e83290.gif" border=0 width="131" height="41" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 48 ><NOBR><div> <A HREF="#4" TITLE="Intensidad de variación relativa"><U><IMG SRC="1e9f94150.gif" border=0 width="148" height="21" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </NOBR></tD> <tD VALIGN=TOP WIDTH="198"><div> <A HREF="#5" TITLE="Intensidad de variación relativa"><U><IMG SRC="1ea057290.gif" border=0 width="87" height="41" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> <tD VALIGN=TOP WIDTH="198"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="48" ALIGN="bottom" WIDTH="198" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP COLSPAN=3 HEIGHT= 108 ><NOBR><div> <A HREF="#6" TITLE="Intensidad de variación relativa"><U><B><IMG SRC="1ea1ec650.gif" border=0 width="492" height="101" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></U></A></div> </NOBR></tD> </tR> </TABLE></div> <bR> <div> <B>S o l u c i o n e s</B><FONT SIZE="3" COLOR="#FF0000" FACE="Times New Roman" ><B> </B></FONT></div> <bR> <div>  <A NAME="1"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><FONT SIZE="3" COLOR="#0099FF" FACE="Times New Roman" ><IMG SRC="1ea289190.gif" border=0 width="137" height="25" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT></div> <div> <IMG SRC="1ea3f08d0.gif" border=0 width="240" height="141" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="2"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><FONT SIZE="3" COLOR="#0099FF" FACE="Times New Roman" ><IMG SRC="1ea47c290.gif" border=0 width="124" height="41" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT></div> <div> <IMG SRC="1ea5dfe00.gif" border=0 width="223" height="224" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="3"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><FONT SIZE="3" COLOR="#0099FF" FACE="Times New Roman" ><IMG SRC="1ea683290.gif" border=0 width="131" height="41" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT></div> <div> <IMG SRC="1ea77efb0.gif" border=0 width="382" height="251" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="4"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><FONT SIZE="3" COLOR="#0099FF" FACE="Times New Roman" ><IMG SRC="1ea894150.gif" border=0 width="148" height="21" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT></div> <div> <IMG SRC="1ea9695b0.gif" border=0 width="617" height="347" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <TABLE BORDER="0" CELLPADDING="2" CELLSPACING="1" WIDTH="750" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 270 ><NOBR><div> <TABLE BORDER="1" CELLPADDING="1" CELLSPACING="1" WIDTH="102" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 20 WIDTH="28"><div> <I><B>t</B></I></div> </tD> <tD VALIGN=TOP WIDTH="28"><div> <I><B>s</B></I></div> </tD> <tD VALIGN=TOP WIDTH="28"><div> <I><B>v</B></I></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="28"><div> -5</div> </tD> <tD VALIGN=TOP WIDTH="28"><div> -1</div> </tD> <tD VALIGN=TOP WIDTH="28"><div> 36</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="28"><div> -4</div> </tD> <tD VALIGN=TOP WIDTH="28"><div> 24</div> </tD> <tD VALIGN=TOP WIDTH="28"><div> 15</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="28"><div> -3</div> </tD> <tD VALIGN=TOP WIDTH="28"><div> 31</div> </tD> <tD VALIGN=TOP WIDTH="28"><div> 0</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="28"><div> -2</div> </tD> <tD VALIGN=TOP WIDTH="28"><div> 26</div> </tD> <tD VALIGN=TOP WIDTH="28"><div> -9</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="28"><div> -1</div> </tD> <tD VALIGN=TOP WIDTH="28"><div> 15</div> </tD> <tD VALIGN=TOP WIDTH="28"><div> -12</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="28"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="28"><div> 4</div> </tD> <tD VALIGN=TOP WIDTH="28"><div> -9</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="28"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="28"><div> -1</div> </tD> <tD VALIGN=TOP WIDTH="28"><div> 0</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="28"><div> 2</div> </tD> <tD VALIGN=TOP WIDTH="28"><div> 6</div> </tD> <tD VALIGN=TOP WIDTH="28"><div> 15</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="28"><div> 3</div> </tD> <tD VALIGN=TOP WIDTH="28"><div> 31</div> </tD> <tD VALIGN=TOP WIDTH="28"><div> 36</div> </tD> </tR> </TABLE></div> <bR> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> <IMG SRC="1eaa58f50.gif" border=0 width="600" height="245" ALT="Imagen de mapa de bits" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> </tR> </TABLE></div> <div>  <A NAME="5"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><FONT SIZE="3" COLOR="#0099FF" FACE="Times New Roman" ><IMG SRC="1eab57290.gif" border=0 width="87" height="41" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT></div> <div> <IMG SRC="1eac668c0.gif" border=0 width="614" height="396" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <TABLE BORDER="0" CELLPADDING="2" CELLSPACING="1" WIDTH="750" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 252 ><NOBR><div> <TABLE BORDER="1" CELLPADDING="1" CELLSPACING="1" WIDTH="135" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 20 WIDTH="28"><div> <I><B>t</B></I></div> </tD> <tD VALIGN=TOP WIDTH="40"><div> <I><B>s</B></I></div> </tD> <tD VALIGN=TOP WIDTH="49"><div> <I><B>v</B></I></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="28"><div> -9</div> </tD> <tD VALIGN=TOP WIDTH="40"><div> -0.1</div> </tD> <tD VALIGN=TOP WIDTH="49"><div> -0.009</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="28"><div> -3</div> </tD> <tD VALIGN=TOP WIDTH="40"><div> -0.17</div> </tD> <tD VALIGN=TOP WIDTH="49"><div> 0</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="28"><div> -1</div> </tD> <tD VALIGN=TOP WIDTH="40"><div> -0.1</div> </tD> <tD VALIGN=TOP WIDTH="49"><div> 0.08</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="28"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="40"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="49"><div> 0.1</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="28"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="40"><div> 0.1</div> </tD> <tD VALIGN=TOP WIDTH="49"><div> 0.08</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="28"><div> 3</div> </tD> <tD VALIGN=TOP WIDTH="40"><div> 0.17</div> </tD> <tD VALIGN=TOP WIDTH="49"><div> 0</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="28"><div> 9</div> </tD> <tD VALIGN=TOP WIDTH="40"><div> 0.1</div> </tD> <tD VALIGN=TOP WIDTH="49"><div> -0.009</div> </tD> </tR> </TABLE></div> <bR> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> <IMG SRC="1ead58f50.gif" border=0 width="600" height="245" ALT="Imagen de mapa de bits" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </NOBR></tD> </tR> </TABLE></div> <bR> <div>  <A NAME="6"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" ><B>6.</B></FONT>  <U>Solución</U>:</div> <div> <IMG SRC="1eae0c130.gif" border=0 width="12" height="19" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><IMG SRC="1eafe1210.gif" border=0 width="737" height="289" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <bR> <bR> </td> </tr><tr> <td valign="top" colspan=2 height=24 BGCOLOR="#006666" TEXT="#080000"> <div> <B> <form 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