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Difference between the value of function at A and the limit

  1. Jul 15, 2010 #1
    what is the difference between the value of function at A and the limit of function at A.
    to find the limit of function by direct substitution we just put the value A in function which gives the limit.but i think it should give the value of function at that point .how it become limit?
     
  2. jcsd
  3. Jul 15, 2010 #2

    radou

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    Re: limit

    A function may not be defined at some point c, but the limit, as x --> c, may exist. A function whose limit, as x --> c through the domain, exists and equals f(c) is continuous at the point c.
     
  4. Jul 15, 2010 #3

    HallsofIvy

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    Re: limit

    That only works if the function is continuous. In fact it is the definition of continuous:
    A function is said to be "continuous at a" if and only if [itex]\lim_{x\to a} f(x)= f(a)[/itex]".

    Otherwise, there is no relationship at all between f(a) and [itex]\lim_{x\to a} f(x)[/itex].


    For example, "f(x)= 3x for x any number except 1 and f(1)= 5" is a perfectly valid function. It's value at x= 1 is 5 but the limit as x goes to 1 is 3.
     
    Last edited: Jul 17, 2010
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