Limit of a Function

Discussion in 'Calculus' started by nycmathguy, Apr 2, 2022.

  1. nycmathguy

    nycmathguy

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    Calculus
    Section 1.5

    The late James Stewart said the following in the image below:

    "The following table gives values of f(x) for values of x close to 2 but not equal to 2."

    Ok. FOR VALUES OF X CLOSE TO 2 BUT NOT EQUAL TO 2 is like the Twilight Zone to me. What on earth does that mean?

    What does the table below even mean?



    Screenshot_20220402-122521_Samsung Notes.jpg
     
    nycmathguy, Apr 2, 2022
    #1
  2. nycmathguy

    MathLover1

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    VALUES OF X CLOSE TO 2 BUT NOT EQUAL TO 2 are values x= 1 and x<2

    or 1<= x<2

    that means values for x could be:
    x=1.0
    :
    x=1.01
    :
    x=1.1
    :
    x=1.2 and all between 1.2 and 1.3
    and so on up to x=1.999
     
    MathLover1, Apr 2, 2022
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  3. nycmathguy

    nycmathguy

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    This remains unclear to me. Sorry.
     
    nycmathguy, Apr 2, 2022
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  4. nycmathguy

    MathLover1

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    how unclear?
    There are infinity numbers between 1 and 2 like 1.01,1.001,1.0011 etc.
    But if you need an integer, there is no number between 1 and 2.

    so, in table above are used some of numbers between 1 and 2
     
    MathLover1, Apr 2, 2022
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  5. nycmathguy

    nycmathguy

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    Now it makes sense.

    Intuitive Definition of a Limit
     
    nycmathguy, Apr 3, 2022
    #5
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