I need a little help on the notion of limit.Can somebody show mw what it is and how it is used in derivatives? I shall be thankful.
In basic terms, a limit is what a function tends toward as the argument of the function approaches a point, not necessarily in the domain of the function.
The derivative is derived from a "secant function" which takes the slope between two points on the function:
$\displaystyle slope = \frac{f(b) - f(a)}{b - a}$
The derivative is the limit of this function as the two points become very close, or ideally meet:
$\displaystyle derivative = \lim_{b \to a}\frac{f(b) - f(a)}{b - a}$
Typically this is given in the form of a function of x:
$\displaystyle f^{\prime}(x) = \lim_{a \to x}\frac{f(x) - f(a)}{x - a}$
-Dan