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
Algebra ->
Inequalities
-> 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
Log On
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):
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.
