Limits

Let f(x)=x+2

Assume we are playing a game or we keep putting a new wax in to see what comes out. If we let ‘x’ approach 3 then f(x) will approach 5.

The above is legitimate limit problem. However it is more typical to have a situation where if the dependent variable reaches the target then we will have a division by zero error.

Appendix A

Quantities, and the ratios of quantities, which in any finite time converge continually to equality, and before the end of that time approach nearer the one to the other than b any given difference, become ultimately equal.

If you deny it, suppose them to be ultimately unequal, and let D be the ultimate difference. Therefore they cannot approach near to equality than by that given by difference D, which is against the supposition.