document.write( "Question 1117867: Without using l’Hopital’s Rule or Series find
\n" ); document.write( "Limit(((1+x)^(1/x)-e)/x) as x=0 \n" ); document.write( "
Algebra.Com's Answer #733170 by math_helper(2461)\"\" \"About 
You can put this solution on YOUR website!
Approaching 0 from the negative side:
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\n" ); document.write( "\n" ); document.write( "perl -e '$x=-.1; $e=2.718281828459; for($j=1; $j<6; $j++) { $a = ((1+$x)**(1/$x)-$e)/$x; print \"f($x) = $a\n\"; $x=$x/10;}'
\n" ); document.write( "f(-0.1) = -1.49690162333441
\n" ); document.write( "f(-0.01) = -1.37171979700281
\n" ); document.write( "f(-0.001) = -1.36038798385263
\n" ); document.write( "f(-0.0001) = -1.35926551149801
\n" ); document.write( "f(-1e-05) = -1.35915214047877
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\n" ); document.write( "\n" ); document.write( "And approaching 0 from the positive side:
\n" ); document.write( "perl -e '$x=.1; $e=2.718281828459; for($j=1; $j<6; $j++) { $a = ((1+$x)**(1/$x)-$e)/$x; print \"f($x) = $a\n\"; $x=$x/10;}'
\n" ); document.write( "f(0.1) = -1.24539368358998
\n" ); document.write( "f(0.01) = -1.34679990374718
\n" ); document.write( "f(0.001) = -1.35789622340665
\n" ); document.write( "f(0.0001) = -1.35901634074731
\n" ); document.write( "f(1e-05) = -1.35912667031945
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\n" ); document.write( "\n" ); document.write( "Which looks to be \"+highlight%28-e%2F2%29+\"\r
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