document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=987649>Question 987649</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose the side length of a cube is x = 11 cm. If x changes by an amount &#948;x = 0.01 cm, what is the corresponding approximate change in the volume of the cube &#948;V?\r<BR>\n" );
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document.write( "THANK YOU :-)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #608377 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=608377\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "\"...changes by an amount...\" is non-specific.  Did the measure of the edge of the cube get larger or smaller?  Either one is a change, and the amount specified is a positive number does not alter the ambiguity.  \"approximate\" without a specification of required precision is non-specific.  \"A little bit bigger (or smaller)\" is an unassailably correct answer to this question as posed.\r<BR>\n" );
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document.write( "Be that as it may, the volume of a cube with edges that measure <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> units has a volume of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x^3\"> cubic units.  If the measure of the edge is increased by some value <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large h\">, then the new volume is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x\ +\ h)^3\ =\ x^3\ +\ 3x^2h\ +\ 3xh^2\ +\ h^3\">, and the difference between the original volume and the new volume is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \Delta{V}\ =\ 3x^2h\ +\ 3xh^2\ +\ h^3\">.  Similarly, if the edge is decreased some value <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large h\">, then the new volume is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x\ -\ h)^3\ =\ x^3\ -\ 3x^2h\ +\ 3xh^2\ -\ h^3\">, and the difference between the original volume and the new volume is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \Delta{V}\ =\ -3x^2h\ +\ 3xh^2\ -\ h^3\">.\r<BR>\n" );
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document.write( "Once you decide whether you are getting larger or smaller, you can plug your values of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ 11\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large h\ =\ 0.01\"> into the appropriate expression for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \Delta{V}\">, do the arithmetic, and round to whatever precision you need or desire.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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