document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197595>Question 1197595</A>: <I><SPAN STYLE=\"word-break: break-all;\"> without L'Hospitals rule prove that :<BR>\n" );
document.write( "limt(x^(1/x)) = 1 when (x → ∞) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #830954 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52778)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=830954\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "(1)  &nbsp;&nbsp;I am glad to see that after my notice you posted a fixed version.\r<BR>\n" );
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document.write( "     &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;This time, it is in correct mathematical form, so I will help you.\r<BR>\n" );
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document.write( "(2)  &nbsp;&nbsp;If you take logarithm of both sides of your equation, &nbsp;you will see that your statement is equivalent to this one\r<BR>\n" );
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document.write( "     &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;lim <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28x%29%2Fx ALIGN=MIDDLE  ALT=\"ln%28x%29%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0  &nbsp;&nbsp;as x --> infinity.\r<BR>\n" );
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document.write( "(3)  &nbsp;&nbsp;This last statement is proven under this link\r<BR>\n" );
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document.write( "     &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;https://www.youtube.com/watch?v=QCAax866If4        \r<BR>\n" );
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document.write( "     &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(youtube video-lesson) &nbsp;without using the &nbsp;L'Hospital rule.\r<BR>\n" );
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document.write( "Have fun &nbsp;(&nbsp;!&nbsp;)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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