document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=908637>Question 908637</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Evaluate the following limits by using the L'Hopital's Theorem\r<BR>\n" );
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document.write( "a. lim as x approaches to positive infinity (2^x)/(e^(x^2)) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #551212 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=551212\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) f(x) = 2^x and g(x) = e^(x^2)<BR>\n" );
document.write( "f'(x) = 2^x * log(2)<BR>\n" );
document.write( "g'(x) = 2e^(x^2)x<BR>\n" );
document.write( "then lim as x approaches infinity is 2^x * log(2) / (2e^(x^2)x = L<BR>\n" );
document.write( "we see that lim as x approaches infinity of g(x) is +infinity which satisfies L'Hopital's Theorem criteria and<BR>\n" );
document.write( "lim as x approaches infinity is 2^x * log(2) / (2e^(x^2)x = 1<BR>\n" );
document.write( "b) lim as x approaches to 0 (sinx)^lncosx is 1<BR>\n" );
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