This is a standard calculus question. If you search out L'Hopital's Rule you will find that there are only Calculus examples present. If you use calculus, the answer comes to 1/8. The only way I can think of doing this without the use of Calculus is to let x = something very small -- say x = 0.0001 That approaches 0, but it is not quite = to 0.
So let's try it.
16 + 0.00001 = 16.00001
sqrt(16.0001) = 4.00000125
Now subtract 4
4.00000125 - 4
0.00000125
Now divide by 0.00001
0.12499998
which is close to 0.125.
If someone else can give you an answer that is "purer" than this one, take it.
