document.write( "Question 1208917: The function that can be redefined to be continuous at x= π /2 is ...
\n" ); document.write( "1) sqrt(x- π/2)
\n" ); document.write( "2) abs(sin(2x))/(2x- π)
\n" ); document.write( "3) cos(2x)/(x-π/2)
\n" ); document.write( "4) sqrt(cos(x) \n" ); document.write( "

Algebra.Com's Answer #847438 by mccravyedwin(421) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "In order that a real function undefined at x = π/2 can be redefined \r\n" );
document.write( "with a value f(π/2) and be continuous at x = π/2, it must:\r\n" );
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document.write( "A. be defined and continuous on both sides of π/2. That is, defined both\r\n" );
document.write( "on (π/2-a,π/2) and (π/2,π/2+b), for some nonnegative a and b, and\r\n" );
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document.write( "B. have the same limits on both sides of π/2.  That is\r\n" );
document.write( ", where both limits exist and are finite.\r\n" );
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document.write( "As it turns out none of the functions listed fit both requirements.\r\n" );
document.write( "None approach the same finite limit on both sides of π/2. \r\n" );
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document.write( "(1) is not defined left of π/2\r\n" );
document.write( "(2) and (3) have vertical asymptotes at π/2.\r\n" );
document.write( "(4) is not defined immediately to the right of π/2,\r\n" );
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document.write( "Now if you mis-typed the right parenthesis on\r\n" );
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document.write( "2) abs(sin(2x))/(2x- π)\r\n" );
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document.write( "and it should have been\r\n" );
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document.write( "2) abs(sin(2x)/(2x- π))\r\n" );
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document.write( "where both the numerator and denominator are included in the\r\n" );
document.write( "absolute value, then that would have satisfied both requirements.\r\n" );
document.write( "The limits on both sides of π/2 would be +1 and the function could\r\n" );
document.write( "be redefined with f(π/2)=1, and the function would be continuous at\r\n" );
document.write( "π/2.\r\n" );
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document.write( "If that is what you meant, or if you made some other typo, please \r\n" );
document.write( "re-post.\r\n" );
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document.write( "Edwin

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