SOLUTION: 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 referen

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?
(sqrt(n*n + e*e) - n) < (n - sqrt(n*n - e*e))
I came across this inequality in the study of limits.
Answer by ikleyn(52798) (Show Source): You can put this solution on YOUR website!
.

Imagine the plot of the function y = .


The difference  is the same as the difference  and is the increment 
of the function y =  at the point x =  when you increase the argument "x" by the value of .


The difference  is the same as the difference  and is the increment 
of the same function y =  at the point x =  when you increase the argument "x" by the value of .


Then your statement follows the fact that the function y =  has lower grade at the point x =  than at the point x = .


Very visual proof.

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