document.write( "Question 1065200: I'm stuck trying to prove the following inequality for positive real numbers 'n', where 'e' is a sufficiently small positive real number. Do you have a clue, technique, or reference for me to try?
\n" ); document.write( "(sqrt(n*n + e*e) - n) < (n - sqrt(n*n - e*e))
\n" ); document.write( "I came across this inequality in the study of limits. \n" ); document.write( "

Algebra.Com's Answer #680375 by ikleyn(52802) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Imagine the plot of the function y = .\r\n" );
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document.write( "The difference  is the same as the difference  and is the increment \r\n" );
document.write( "of the function y =  at the point x =  when you increase the argument \"x\" by the value of .\r\n" );
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document.write( "The difference  is the same as the difference  and is the increment \r\n" );
document.write( "of the same function y =  at the point x =  when you increase the argument \"x\" by the value of .\r\n" );
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document.write( "Then your statement follows the fact that the function y =  has lower grade at the point x =  than at the point x = .\r\n" );
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document.write( "Very visual proof.\r\n" );
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