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Math Help - What is a lim?!?!?!?

  1. #1
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    What is a lim?!?!?!?

    Help i was reffering to ths tutorial and i dont understand what lim is... help!
    Computing Limits - HMC Calculus Tutorial
    Base on ur explanation what is a lim? and how is it defined... and how is it undefined?

    any help wud be appreciated... thanks!!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    Help i was reffering to ths tutorial and i dont understand what lim is... help!
    Computing Limits - HMC Calculus Tutorial
    Base on ur explanation what is a lim? and how is it defined... and how is it undefined?

    any help wud be appreciated... thanks!!
    Here I will talk about real valued function of a real variable only

    The limit of a function f(x) as its argument x approaches some value x0 is a
    real number, call it L that f(x) gets closer and closer to as x approaches x0.
    The value should not depend on how x approaches x0.

    When f is a well behaved continuous function in a region about x0 then
    the limit as x approaches x0 of f(x) is f(x), so in this case:

    lim(x->x0) f(x) = f(x0).

    Now there are many ways in which the function can be badly behaved
    near x0:

    1. f can be discontinuous at the point, an example is a jump discontinuity
    such as the following function has at x=0:

    f(x).= x+1, x<0
    ......= x, x>=0.

    Then as x approaches 0 from below (often written x->0-) f(x) approaches
    1, while if it approaches x0 from above (often written x->0+) f(x)
    approaches 0. As these are not equal we say that f(x) does not have
    a limit as x approaches 0.

    2. Another way that f can be discontinuous at a point is if it goes to
    infinity there. While we might write in this case:

    lim(x->x0) f(x) = infty,

    we would say that the limit does not exists (as infty is not normally
    considered a number).

    3. A third interesting case is exemplified by the "sinc" function which
    you will find used frequently in engineering applications, this is defined
    as:

    sinc(x) = sin(x)/x, x!=0,
    ..........= 1, x=0.

    The first line of the functions definition has to exclude the point x=0 as
    sin(x)/x is an indeterminate form when x=0 (we are not allowed to divide
    by 0). But for small x: sin(x)~=x, with the approximation becoming better and
    better as x becomes smaller and smaller. So we might expect:

    lim(x->0) sin(x)/x = 1.

    which indeed it does when one does the analysis of the problem rigorously.
    Because of this the sinc function is continuous at x=0.

    I hope that helps, I'm sure I have missed lots of interesting points that
    others will fill in.

    RonL
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  3. #3
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    PH posted a very good explanation here

    but you will have to wait for latex to get back online...
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