.
Then f is continuous on [0, 
)
and differentiable on (0, ).
By the Mean Value theorem there exists a number c such that
Define the function f(x) = .
Then f is continuous on [0, )
and differentiable on (0, ).
By the Mean Value theorem there exists a number c such that
= f'(c) for
c between x and x + 1
But then
- = 1/2 *
1 / 
As x goes to infinity, so does c (it is always bigger than x). The left side of this equation goes to 0 as c goes to infinity. Therefore, the right side must also go to zero.
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