document.write( "Question 889953: Please help me by simlifying the following logarithum function.\r
\n" ); document.write( "\n" ); document.write( "log(log(1-x^2)/log(log(cosx). In fact I need to simplify it to find the limit of the above function when xtenda to Zero.\r
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\n" ); document.write( "\n" ); document.write( "S B Roy \n" ); document.write( "

Algebra.Com's Answer #538563 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "The other tutor's answer is wrong.\r\n" );
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document.write( "You don't need to simplify it.\r\n" );
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document.write( "Use the theorem that if f is continuous in a neighborhood of a,\r\n" );
document.write( "and is not constant on any subinterval of that interval\r\n" );
document.write( "and lim(x/y) as x->a exists,\r\n" );
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document.write( "lim [f(x)/f(y)] = lim(x/y)\r\n" );
document.write( "x->a              x->a\r\n" );
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document.write( "then since cos(0) = 1,\r\n" );
document.write( "                                               _                 _\r\n" );
document.write( "lim  log[log(1-x^2)]      lim   1-x^2     lim |    1         x^2  |\r\n" );
document.write( "     ----------------- =       ------- =      | ------- - --------| = 1-0 = 1\r\n" );
document.write( "x->0  log[log(cos(x)]     x->0  cos(x)    x->0|_ cos(x)    cos(x)_|\r\n" );
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document.write( "Edwin

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