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Math Help - Limit

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    Limit

    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.
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    Quote Originally Posted by wasee View Post
    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:
    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:
    derivative = \lim_{b \to a}\frac{f(b) - f(a)}{b - a}

    Typically this is given in the form of a function of x:
    f^{\prime}(x) = \lim_{a \to x}\frac{f(x) - f(a)}{x - a}

    -Dan
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