document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209884>Question 1209884</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the horizontal asymptote as x approaches positive infinity of the graph of<BR>\n" );
document.write( "y = \sqrt{4x^2 + 5x} - \sqrt{4x^2}?<BR>\n" );
document.write( "The horizontal asymptote is in the form y = mx + k.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850957 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850957\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "!!!! The equation of a horizontal asymptote is not in the form y = mx + k, unless you are letting m be 0.  The equation of a horizontal asymptote is of the form y = k.<br><BR>\n" );
document.write( "Ignoring that (or allowing the slope m to be 0)....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sqrt%284x%5E2%2B5x%29-sqrt%284x%5E2%29 ALIGN=MIDDLE  ALT=\"y=sqrt%284x%5E2%2B5x%29-sqrt%284x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Rationalize the numerator:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28sqrt%284x%5E2%2B5x%29-sqrt%284x%5E2%29%29%2A%28%28sqrt%284x%5E2%2B5x%29%2Bsqrt%284x%5E2%29%29%2F%28sqrt%284x%5E2%2B5x%29%2Bsqrt%284x%5E2%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28%284x%5E2%2B5x%29-%284x%5E2%29%29%2F%28sqrt%284x%5E2%2B5x%29%2Bsqrt%284x%5E2%29%29%29 ALIGN=MIDDLE  ALT=\"y=%28%284x%5E2%2B5x%29-%284x%5E2%29%29%2F%28sqrt%284x%5E2%2B5x%29%2Bsqrt%284x%5E2%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%285x%29%2F%28sqrt%284x%5E2%2B5x%29%2Bsqrt%284x%5E2%29%29%29 ALIGN=MIDDLE  ALT=\"y=%285x%29%2F%28sqrt%284x%5E2%2B5x%29%2Bsqrt%284x%5E2%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%285x%29%2F%282x%2Asqrt%281%2B5%2F4x%29%2B2x%29 ALIGN=MIDDLE  ALT=\"y=%285x%29%2F%282x%2Asqrt%281%2B5%2F4x%29%2B2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "As x goes to positive infinity, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F4x ALIGN=MIDDLE  ALT=\"5%2F4x\"   DISABLED_style= \"max-width:90%; height:auto;\" > goes to 0 so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281%2B5%2F4x%29 ALIGN=MIDDLE  ALT=\"sqrt%281%2B5%2F4x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > goes to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281%29 ALIGN=MIDDLE  ALT=\"sqrt%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1, and the expression approaches<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%285x%29%2F%282x%2B2x%29=%285x%29%2F%284x%29=5%2F4 ALIGN=MIDDLE  ALT=\"y=%285x%29%2F%282x%2B2x%29=%285x%29%2F%284x%29=5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5%2F4 ALIGN=MIDDLE  ALT=\"y=5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0x%2B5%2F4 ALIGN=MIDDLE  ALT=\"y=0x%2B5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >....)<br><BR>\n" );
document.write( "A graph....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-10%2C50%2C-1%2C2%2Csqrt%284x%5E2%2B5x%29-sqrt%284x%5E2%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-10%2C50%2C-1%2C2%2Csqrt%284x%5E2%2B5x%29-sqrt%284x%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );