How do you determine the limit algebraically?

0.125

Step-by-step explanation:

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.

4444444444444 i think