document.write( "Question 179643: Explain a process for finding a limit
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\n" ); document.write( "Write a concise description of the meaning of lim f(x)=10 as x approaches to 3
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\n" ); document.write( "Examine the continuity of g(x) = x+3 and the point x=2.
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Algebra.Com's Answer #134592 by Edwin McCravy(20055) $\"\"$ $\"About$

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Explain a process for finding a limit
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document.write( "means, colloqually, for any required degree of tolerance\r\n" );
document.write( ", (a positive number usually thought of as very small)\r\n" );
document.write( "there exists another positive number  (also usually thought \r\n" );
document.write( "of as very small) such that whenever x is less than  units \r\n" );
document.write( "away from ,  will always be less than  units away from .\r\n" );
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document.write( "To write it concisely,\r\n" );
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document.write( "For any , there exists a \r\n" );
document.write( "  such that  whenever .\r\n" );
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\n" ); document.write( "Examine the continuity of g(x) = x+3 and the point x=2.
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document.write( " will be continuous at  if  and\r\n" );
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document.write( "Suppose we have any required tolerance, . Then\r\n" );
document.write( "we need to find a  such that if ,\r\n" );
document.write( "then .\r\n" );
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document.write( " if and only if\r\n" );
document.write( " if and only if\r\n" );
document.write( " if and only if\r\n" );
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document.write( "So we simply take any  such that \r\n" );
document.write( " and then turn the above \r\n" );
document.write( "backwards and we have:\r\n" );
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document.write( " =>  =>\r\n" );
document.write( " => \r\n" );
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document.write( "Edwin

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