document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=637331>Question 637331</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The calculation of lim   5x + 5h + 1 - (5x + 1)/h<BR>\n" );
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document.write( "h -> 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #401599 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3759)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=401599\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm going to assume that your problem is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim%28h-%3E0%2C+%28%285x%2B5h%2B1%29-%285x%2B1%29%29%2Fh%29 ALIGN=MIDDLE  ALT=\"lim%28h-%3E0%2C+%28%285x%2B5h%2B1%29-%285x%2B1%29%29%2Fh%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(Please use parentheses to make your expressions clearer.)<br><BR>\n" );
document.write( "Let's simplify the fraction. In the numerator, the 5x's and the 1's cancel out:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim%28h-%3E0%2C+%285h%29%2Fh%29 ALIGN=MIDDLE  ALT=\"lim%28h-%3E0%2C+%285h%29%2Fh%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Next we could cancel the h's, <i>but only if h is not zero!</i> An important thing to understand about this limit is that we are interested in what happens when h gets infinitely close to zero <i>but not actually zero.</i> Since h is never actually zero, it is OK to cancel the h's:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim%28h-%3E0%2C+5%29 ALIGN=MIDDLE  ALT=\"lim%28h-%3E0%2C+5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And since the limit of a constant is that constant, this simplifies to just<BR>\n" );
document.write( "5<br><BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim%28h-%3E0%2C+%28%285x%2B5h%2B1%29-%285x%2B1%29%29%2Fh%29+=+5 ALIGN=MIDDLE  ALT=\"lim%28h-%3E0%2C+%28%285x%2B5h%2B1%29-%285x%2B1%29%29%2Fh%29+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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