document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1001509>Question 1001509</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please tell me if my process is right or wrong.\r<BR>\n" );
document.write( "\n" );
document.write( "lim x->-&#8734; &#8730;(6x^6-1)/(5x^3+1)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for this since it's infinity then -1 and +1 can be disregarded. And therefore I am left with:\r<BR>\n" );
document.write( "\n" );
document.write( "lim x->-&#8734; &#8730;(6x^6)/(5x^3)\r<BR>\n" );
document.write( "\n" );
document.write( "The part I don't remember is an algebra rule, when we sqrt the 6x^6 do we break them up or take them together? I think we take them as separate terms 6 and x^6 if so then it's:\r<BR>\n" );
document.write( "\n" );
document.write( "lim x->-&#8734; (&#8730;(6)&#8730;(x^6))/(5x^3)\r<BR>\n" );
document.write( "\n" );
document.write( "then nothing happens to the &#8730;(6), however, another rule I forget is when you squareroot something this is the same as (x^6)^(1/2) right? so then it becomes x^3 however, why does this become an absolute number like so |x^3| I don't remember this rule at all. When you squareroot something whatever it is that becomes absolute?\r<BR>\n" );
document.write( "\n" );
document.write( "Then the problem becomes:\r<BR>\n" );
document.write( "\n" );
document.write( "lim x->-&#8734; &#8730;(6)*|x^3| / (5x^3)<BR>\n" );
document.write( "then<BR>\n" );
document.write( "lim x->-&#8734; &#8730;(6)*|-&#8734;^3| / (5(-&#8734;)^3)\r<BR>\n" );
document.write( "\n" );
document.write( "since its abs value w/e the value is it will be positive. therefore:<BR>\n" );
document.write( "lim x->-&#8734; &#8730;(6)(&#8734;)^3/(5(-&#8734;)^3)\r<BR>\n" );
document.write( "\n" );
document.write( "so the &#8734;'s cancel to be -1 and the &#8730;(6)/5 remain constant.\r<BR>\n" );
document.write( "\n" );
document.write( "lim x->-&#8734; - &#8730;(6)/5\r<BR>\n" );
document.write( "\n" );
document.write( "Please explain out the algebra confusion\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #618680 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=618680\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The output of the numerator is always positive.<BR>\n" );
document.write( "The domain is limited because of the square root.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E6-1%3E=0 ALIGN=MIDDLE  ALT=\"6x%5E6-1%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E6%3E=1%2F6 ALIGN=MIDDLE  ALT=\"x%5E6%3E=1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=1%2F6%5E%281%2F6%29 ALIGN=MIDDLE  ALT=\"x%3E=1%2F6%5E%281%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=-1%2F6%5E%281%2F6%29 ALIGN=MIDDLE  ALT=\"x%3C=-1%2F6%5E%281%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So when, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=1%2F6%5E%281%2F6%29 ALIGN=MIDDLE  ALT=\"x%3E=1%2F6%5E%281%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the denominator is positive, so when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > heads towards <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the function value heads to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%286%29%2F5 ALIGN=MIDDLE  ALT=\"sqrt%286%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and when,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=-1%2F6%5E%281%2F6%29 ALIGN=MIDDLE  ALT=\"x%3C=-1%2F6%5E%281%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the denominator is negative, so when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > heads towards <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity ALIGN=MIDDLE  ALT=\"-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the function values heafs to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%286%29%2F5 ALIGN=MIDDLE  ALT=\"-sqrt%286%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );