document.write( "Question 1200072: Evaluate the limit (as x approaches to 0+) x^4sin(1/x) \n" ); document.write( "

Algebra.Com's Answer #834090 by ikleyn(52798) $\"\"$ $\"About$

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document.write( "The given function is limited from the top by the function   = \r\n" );
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document.write( "and is limited from the bottom by the function   = \r\n" );
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document.write( "     <=  <= .\r\n" );
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document.write( "Both functions    and    have the limit 0 (zero) as x approaches to 0+.\r\n" );
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document.write( "Therefore, the given function    has the limit 0 (zero)  as x approaches to 0+.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, with complete explanations.\r
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\n" ); document.write( "\n" ); document.write( "The referenced theorem of Calculus has a joking folklore name \"two policemen theorem\".\r
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\n" ); document.write( "\n" ); document.write( "It says \"if two police officers are bringing an intoxicated prisoner between them to a cell, the prisoner must also end up in the cell\".\r
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\n" ); document.write( "\n" ); document.write( "In our problem, two limiting functions do represent two police officers,
\n" ); document.write( "while the given function does represent an intoxicated prisoner.\r
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\n" ); document.write( "\n" ); document.write( "See this link \r
\n" ); document.write( "\n" ); document.write( "https://en.wikipedia.org/wiki/Squeeze_theorem\r
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\n" ); document.write( "\n" ); document.write( "together with the accompanying figures.\r
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\n" ); document.write( "\n" ); document.write( "One of these figures is close visual presentation to your function and my limiters.\r
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