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Finding the limits of this expression

  1. Dec 31, 2012 #1
    1. The problem statement, all variables and given/known data

    I did two attempts. I find attempt no. 1 slightly fishy and attempt 2 more rigorous. Can anyone tell me what's wrong with attempt no. 1?



    3. The attempt at a solution

    Attempt no. 1:
    v6nqcy.png

    Attempt no. 2:
    357keme.png
     
  2. jcsd
  3. Dec 31, 2012 #2

    lurflurf

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    Homework Helper

    They are both basically right. In one though
    (F(x)-F(2))'=F'(x)-0=f(x)
    F(2)' is not equal to F'(2)

    This can be seen as the derivative of the anti-derivative of sin(x)/x

    or the average of sin(x)/x over x near 2

    in either case we get

    sin(2)/2
     
  4. Jan 1, 2013 #3
    An example of F'(2) would be say...the first f' term in the taylor's expansion. F(2)' would be say, differentiating the constant term in taylor's expansion.

    I see what you mean..thanks!
     
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