Removable Discontinuity...1

Discussion in 'Calculus' started by nycmathguy, May 16, 2022.

  1. nycmathguy

    nycmathguy

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    Calculus
    Section 2.5

    Before answering 25, explain in layman terms the idea of removable discontinuity. I need 25 (a & b).

    Thank you.

    Screenshot_20220516-084019_Samsung Notes.jpg
     
    nycmathguy, May 16, 2022
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  2. nycmathguy

    MathLover1

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    Removable Discontinuity: A removable discontinuity is a point on the graph that is undefined or does not fit the rest of the graph. There is a gap at that location when you are looking at the graph. When graphed, a removable discontinuity is marked by an open circle on the graph at the point where the graph is undefined or is a different value like this. In other words, a removable discontinuity is a point at which a graph is not connected but can be made connected by filling in a single point.

    25.
    f(x)=(x-3)/(x^2-9).........note: you can factor denominator

    f(x)=(x-3)/((x-3)(x+3)).........now you can cancel (x-3).........since (x-3) is zero that we have removed, at x=3 functions will be continuous, but f is undefined

    simplyfy

    f(x)=1/(x+3)

    [​IMG]
     
    MathLover1, May 16, 2022
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  3. nycmathguy

    nycmathguy

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    Let me see.

    After factoring the denominator of the original function, the result is 1/(x + 3). We have removed the discontinuity at x = 3 because (x - 3) was canceled. In other words, we filled in the hole making the function continuous at x = 3. Yes? Still, I don't understand why the function is undefined. Are you saying the original function is undefined?
     
    nycmathguy, May 17, 2022
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  4. nycmathguy

    MathLover1

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    yes, we filled in the hole making the function continuous at x = 3
    the function is undefined because that (x-3) exists in given function f(x)=(x-3)/(x^2-9).

    here is another example:

     
    MathLover1, May 17, 2022
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  5. nycmathguy

    nycmathguy

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    Thank you for the clip.
     
    nycmathguy, May 17, 2022
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