What is a limit?
In mathematics, the limit of a function is the value, towards which a function tends, as the independent variable of the given function gets closer and closer to some number. In other words, take our function to be equal to y = f(x), and x tends to x0. We say that the limit of f(x) as x tends to 0 (all possible notations will be given in a real session) is the value of f(x) towards which the function gets closer and closer, as x approaches the value of x0. Note that we don't care about the specific value of the function f(x0), as in the definition for limit, x never really becomes x0. A mathematical way to describe this would be the following: Let f be a defined function over the interval, which includes x = x0. Suppose then, that there exists an e (epsilon) > 0 with a respective dx, such that x0-dx < x0 < x0 + dx correlates with f(x0) - e < f(x0) < f(x0) + e. Then, for any e, there exists such f(x), that abs(f(x) - c) < e where "c" is a constant which is then called the limit of the function f(x) as x approaches x0. (Note that the real session would include graphs and examples to make it easier for the students!)
