limits-calculus

Do a search for "asymptotic limit" instead: if you only search for "limit" you're unlikely to find the mathematical meaning.

Here's an example of an asymptotic limit (blue line) you want to approximate by using small straight lines, or steps. As you make steps smaller and smaller (red function) the red line comes closer and closer to the blue line (its asymptotic limit) but never quite overlaps with it completely until and unless you use an infinite number of steps:


This is a specific function (for harmonic numbers) but if you search for asymptotic limit images you'll find lots more.

What are the lines and curves related with. What is the make of curve and other.

The BLUE curve is the LIMIT of the RED curve, as I said before.

The idea is to find the LIMIT of a function as you approach it by taking smaller and smaller steps. You better read this through carefully , especially the part about elementary functions - it's the paragraph that starts with:

http://en.wikipedia.org/wiki/Asymptote

Since I already explained twice in the simplest possible terms the relation of the blue and red lines in the graph I posted you should be able to understand it, and it's not possible to answer you in any more detail. If your problem is with English, look up all the terms in a dictionary.