Limit of a Function at a Point
The limit of the function, f(x), at point, x0, is essentially the value of y when x approaches x0.
Take for example, the function f(x) = x2 at the point x0 = 2.
When x becomes closer to 2 from the left and right side the value of the function will approach 4.
It is said that the limit of the function, f(x) , as x tends to x0, is L. If a real positive number is set, ε, greater than zero, there will be a positive number, δ, depending on ε , for all the values of x that differ from x0 that fulfill the condition |x - x0| < δ , and holds that |f(x) - L| <ε .